ALEKS - Manual for Educators K12 - August 2008

Teacher’s Manual

for K-12 Education

Harold D. Baker, Ph.D.

ALEKS Corporation

ii

ALEKS Teacher’s Manual for K-12 Education, Version 3.8.Copyright © 2008 ALEKS Corporation.Revised July 24, 2008.Prepared by Harold D. Baker, Ph.D.

ALEKS®

is a registered trademark of ALEKS Corporation.

Contents

Preface xv

1 Introduction 1

1.1 What is ALEKS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The ALEKS Teacher’s Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Quick Start 3

2.1 Obtaining a Class Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Registering Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Setup Guide for Teachers 5

3.1 Teacher Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.4 Teacher Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.5 Lab Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.6 Student Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.7 Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.8 Teacher Authorization of Student Registration . . . . . . . . . . . . . . . . . . . . . 9

3.9 Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.10 First Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.11 Report Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.12 Beginning the Learning Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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iv CONTENTS

4 Assessment Mode 15

4.1 Assessments in ALEKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Rules for Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Scheduling of Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.4 Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.5 Answer Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.6 Manipulators for Mathematical Expressions . . . . . . . . . . . . . . . . . . . . . . . 19

4.7 Mathematical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.8 Types of Mathematical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.9 Advanced Mathematical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.10 The Answer Editor for the Number Line . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.11 The Answer Editor for Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.12 The Answer Editor for Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.13 Assessment Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.13.1 Standard Report Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.13.2 Interpreting the Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.14 Multiple Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.15 Ready to Learn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.16 Progress Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Learning Mode 33

5.1 The ALEKS Learning Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.1 Exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.2 English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.4 Print . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.5 Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.6 Dictionary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.7 Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.8 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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5.2.9 Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.2.10 Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.2.11 Message . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.2.12 Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2.13 MyPie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 The Learning Mode Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3.1 Item Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3.2 Explanation Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.3.3 Practice Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.3.4 Wrong Answer Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.3.5 Dictionary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Feedback in Learning Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.6 Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.7 Ask a Friend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6 Teacher Module: Basic Interface 45

6.1 How do I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.2 Class Admin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.1 Create a new course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.2 View all your courses and course codes . . . . . . . . . . . . . . . . . . . . . . 49

6.2.3 Customize a course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.4 Password issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.5 Account preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.6 Student Account preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.7 Move a student from one class to another . . . . . . . . . . . . . . . . . . . . 50

6.2.8 Unenroll a student from a class . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.2.9 Delete a class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.3 School Admin (Administrator) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.3.1 Create a new teacher account . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.3.2 Password issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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6.3.3 Teacher account preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.3.4 Move a class from one teacher to another . . . . . . . . . . . . . . . . . . . . 52

6.3.5 Delete an Teacher Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.4 Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.4.1 Class Progress options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.4.2 Download Excel spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.4.3 Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.4.4 Statistical information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.4.5 State standards report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.4.6 Individual learning progress since latest assessment . . . . . . . . . . . . . . . 57

6.4.7 Individual detailed progress history . . . . . . . . . . . . . . . . . . . . . . . . 58

6.4.8 Individual overall progress in assessment . . . . . . . . . . . . . . . . . . . . . 59

6.4.9 Scheduled assessment report . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.4.10 Average report (pie chart) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.4.11 Display options for Average Report . . . . . . . . . . . . . . . . . . . . . . . . 61

6.4.12 Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.4.13 Ready to learn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.4.14 What students can do . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.4.15 Quiz results for all the students . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.4.16 State standards report for a single student . . . . . . . . . . . . . . . . . . . . 64

6.4.17 Progress report for a single student in this class . . . . . . . . . . . . . . . . . 65

6.4.18 Report for a single student in this class (pie chart) . . . . . . . . . . . . . . . 66

6.4.19 Complete list of topics mastered . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.4.20 Quiz results for a particular student . . . . . . . . . . . . . . . . . . . . . . . 67

6.5 Taking Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.5.1 Schedule a new assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.5.2 Detailed scheduling options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.5.3 Grading with Scheduled Assessments . . . . . . . . . . . . . . . . . . . . . . . 69

6.5.4 Cancel an assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.5.5 Change the name, date, grading scale of an assessment . . . . . . . . . . . . . 70

6.5.6 Create a quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

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6.5.7 Tips for making quizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.5.8 Grading with quizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5.9 Availability of quizzes to students. . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5.10 Edit a quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5.11 Delete a quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5.12 Authorize a student account . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.5.13 View/Create Worksheets for a single student . . . . . . . . . . . . . . . . . . 72

6.6 Advanced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.6.1 Show me a tutorial for the “Advanced” Teacher Module. . . . . . . . . . . . . 72

6.6.2 Enter the “Advanced” Teacher Module now. . . . . . . . . . . . . . . . . . . 73

7 Advanced Teacher Module: Results & Progress 75

7.1 The ALEKS Advanced Teacher Module . . . . . . . . . . . . . . . . . . . . . . . . . 75

7.2 Teacher Tutorial (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . 75

7.3 Access to the Advanced Teacher Module . . . . . . . . . . . . . . . . . . . . . . . . . 77

7.4 Online Help in the Advanced Teacher Module . . . . . . . . . . . . . . . . . . . . . . 78

7.5 View Student Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.6 View Student Assessment Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.7 View Class Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.8 View Class Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.9 Schedule Student Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7.10 Schedule Class Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.11 Create, Edit, View Quizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

7.12 Send Message . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.13 Check Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.14 Check Server Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.15 Create Teacher Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.16 Edit Teacher Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.17 Create Class Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.18 Edit Class Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.19 Textbook Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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7.20 Enroll and Unenroll Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.21 Edit Student Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.22 Authorize Student Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.23 Intermediate Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.24 Content Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.25 Assign Learning Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8 Advanced Teacher Module: Standards & Programs 111

8.1 Items, Programs, and Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2 Navigation and Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

8.3 Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.4 Program Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.4.1 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.4.2 Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.4.3 Using the Program Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

9 QuickTables 119

9.1 Setting Up QuickTables for your Class . . . . . . . . . . . . . . . . . . . . . . . . . . 119

9.2 How Your Students Use QuickTables . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

9.3 Reporting your Students’ Progress in QuickTables . . . . . . . . . . . . . . . . . . . 124

9.4 Additional Features in QuickTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

10 Teaching with ALEKS 127

10.1 The ALEKS Educational Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

10.2 The Teacher and ALEKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

10.3 Planning the ALEKS Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

10.4 Preparing Your Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

10.5 Focused Instruction with ALEKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

10.6 Models of Classroom Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

10.7 Monitoring Student Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

10.8 Monitoring the Progress of a Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

10.9 Monitoring Individual Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

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10.10Moving a Student to a New Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

10.11Ordering Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

10.12Independent Study and Distance Learning . . . . . . . . . . . . . . . . . . . . . . . . 136

10.13The ALEKS Knowledge Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

10.14Modification of Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

10.15Learning Rates in ALEKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

11 Knowledge Spaces and the Theory Behind ALEKS 141

11.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

11.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

11.2.1 Domain, Items, and Instances . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

11.2.2 Knowledge States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

11.2.3 Knowledge Structures and Knowledge Spaces . . . . . . . . . . . . . . . . . . 143

11.2.4 Inner and Outer Fringes of a Knowledge State . . . . . . . . . . . . . . . . . 144

11.2.5 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

11.3 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

12 Frequently Asked Questions 153

12.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

12.2 Technical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

12.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

12.4 Assessments & Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

12.5 Learning Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

12.6 Educational Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

13 Support 163

A ALEKS Student User’s Guide 165

A.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

A.2 System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

A.3 Registration and Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

A.4 Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

x CONTENTS

A.5 Assessments and Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.5.1 Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.5.3 Learning Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

A.5.4 Progress in the Learning Mode . . . . . . . . . . . . . . . . . . . . . . . . . . 170

A.5.5 Additional Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

A.6 Logging on to Your Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

A.7 Installation on Additional Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

A.8 Guidelines for Effective Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

A.9 QuickTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

A.10 Frequently Asked Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

A.11 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

B Programs in ALEKS 183

B.1 Mathematics - LV3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

B.2 Mathematics - LV4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

B.3 Mathematics - LV5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

B.4 Mathematics - LV6 / Essential Mathematics . . . . . . . . . . . . . . . . . . . . . . . 197

B.5 Middle School Math 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

B.6 Middle School Math 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

B.7 Middle School Math 3 / Foundations of High School Math . . . . . . . . . . . . . . . 218

B.8 Middle School Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

B.9 Pre-Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

B.10 Algebra 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

B.11 High School Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

B.12 Algebra 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

B.13 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

B.14 PreCalculus without Trigonometry / College Algebra . . . . . . . . . . . . . . . . . . 260

B.15 PreCalculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

B.16 AP Statistics (Quantitative) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

List of Figures


3.2 The ALEKS Website . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Registration (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11



4.1 The Answer Editor for Mathematical Expressions (Assessment) . . . . . . . . . . . . 18

4.2 Mathematical Expressions Produced by the Answer Editor . . . . . . . . . . . . . . 19

4.3 Using Special Keys in the Answer Editor . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4 The Answer Editor for the Number Line . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.5 The Answer Editor for Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.6 The Answer Editor for Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.7 Assessment Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1 The Options Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2 The Help Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 Item Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.4 Explanation Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.5 Practice Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.6 Wrong Answer Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.7 Dictionary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.8 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.9 Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

xi

xii LIST OF FIGURES

6.1 Teacher Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.2 How do I Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.3 Class Admin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.4 School Admin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.5 Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.6 State standards report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.7 Individual learning progress since latest assessment . . . . . . . . . . . . . . . . . . . 57

6.8 Individual detailed progress history . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.9 Individual overall progress in assessment . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.10 Scheduled Assessment Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.11 Average report (pie chart) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.12 Quiz results for all the students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.13 State standards report for a single student . . . . . . . . . . . . . . . . . . . . . . . . 64

6.14 Progress report for a single student in this class . . . . . . . . . . . . . . . . . . . . . 65

6.15 Report for a single student in this class . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.16 Taking Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.17 Schedule a new assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.18 Grading with Scheduled Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.19 Advanced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.1 Tutorial for the Advanced Teacher Module . . . . . . . . . . . . . . . . . . . . . . . . 76

7.2 The Results and Progress Directory (Advanced Teacher Module) . . . . . . . . . . . 77

7.3 Student Progress (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . 79

7.4 Student Report (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . . 81

7.5 Class Progress (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . . 82

7.6 Class Report (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . . . 86

7.7 Student Assessment (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . 88

7.8 Class Assessment (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . 89

7.9 Grading with Scheduled Assessment (Advanced Teacher Module) . . . . . . . . . . . 90

7.10 Creating a Quiz (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . 92

7.11 Send Message (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . . 95

LIST OF FIGURES xiii

7.12 Server Statistics (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . 96

7.13 Teacher Account (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . 97

7.14 Class Account (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . . 99

7.15 Textbook Integration (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . 101

7.16 Student Account (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . 104

7.17 Intermediate Objectives List (Advanced Teacher Module) . . . . . . . . . . . . . . . 105

7.18 Intermediate Objectives (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . 106

7.19 Content Editor (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . . . . 108

7.20 Assign Learning Rates (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . 109

8.1 The Standards & Programs Directory (Advanced Teacher Module) . . . . . . . . . . 112

8.2 The Program Editor (Advanced Teacher Module) . . . . . . . . . . . . . . . . . . . . 115

9.1 QuickTables Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

9.2 QuickTables Learning Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

9.3 QuickTables Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

9.4 QuickTables Advanced Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9.5 QuickTables Worksheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

11.1 Domain of Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

11.2 Knowledge State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

11.3 Learning Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

11.4 Outer Fringe of a Knowledge State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

11.5 Inner Fringe of a Knowledge State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146


A.1 The ALEKS Website . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

A.2 Class Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

A.3 The Answer Editor (Tutorial) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.4 Assessment Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

A.5 ALEKS QuickTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

A.6 QuickTables Learning Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

xiv LIST OF FIGURES

Preface

Congratulations on your interest in ALEKS! This is an online educational system likenone you have encountered before, a system that uses computer technology to promotemath learning that is pedagogically sound and cutting edge.

The features of ALEKS make it a self-contained tool, opening new horizons for educa-tors and learners alike in any educational context. The ALEKS Class ManagementSystem enables teachers and administrators to oversee and monitor their students’progress, communicate with them, track usage levels, and focus instruction. By itsunprecedented use of Artificial Intelligence, ALEKS determines quickly and preciselywhat your students know and what they need to learn, guiding them down individual-ized learning paths to mastery. Assessment and practice problems are algorithmicallygenerated, so the students cannot predict them. The programs used in ALEKS arecustomizable, letting you conveniently add or subtract topics. Since ALEKS is accessedover the World Wide Web using standard browsers, no complicated technical prepa-ration is needed—and your students can work at any time, from home or from theclassroom!

It’s a personal tutor for each of your students, at a fraction of what such servicesnormally cost.

The benefits of using ALEKS are striking. Students work in a dynamic, interactivelearning environment on precisely those materials that they are individually ready tolearn, building momentum toward mastery. It is the personalized, “just-in-time” learn-ing system.

ALEKS may be used in a variety of classroom situations—whether in a traditionalclassroom or in a self-directed or distance-learning environment.

This Teacher’s Manual is intended to provide complete information on the functioningof ALEKS. A description of its contents can be found in Chapter 1.

xv

xvi PREFACE

Chapter 1

Introduction

1.1 What is ALEKS?

ALEKS is an online system for the assessment and individualized teaching of math-ematics. It is accessed over the World Wide Web on any suitable computer and isdesigned to allow the monitoring and management of entire classes and schools. Thecore of the system is an efficient, adaptive assessment engine that determines quicklyand precisely what an individual student knows. Based on that assessment data, thesystem is able to offer material that the student is best able to learn at a given time.The ALEKS Learning Mode includes explanations and algorithmically generated prac-tice problems, ongoing assessment of student knowledge, an online math dictionary, andfacilities for review and collaborative help. It can be used on an independent basis oras a supplement to classroom instruction.

The ALEKS system is the product of years of cutting-edge research into the math-ematical modeling of human knowledge (See Chapter 11). The creators of ALEKS arecognitive scientists, software engineers, and university professors. In designing ALEKS,their goal was to achieve the utmost simplicity of use without compromising the depth,rigor, or richness of mathematics instruction at its inspirational best. ALEKS is a toolto empower both teachers and learners of math: it opens doors and windows into theassessment and representation of knowledge, and it breaks down barriers to success byrecognizing the vast diversity of paths that lead to mastery. The ALEKS system canmake a radical difference in how math learning is experienced.

1.2 The ALEKS Teacher’s Manual

The purpose of the ALEKS Teacher’s Manual is to give teachers using ALEKSinformation on the operation of the system that is as complete as possible. The systemis not complex. ALEKS can be and often is used with no documentation whatsoever.

1

2 CHAPTER 1. INTRODUCTION

At the same time, we wish to offer teachers a clear idea of everything ALEKS does, howit works, and where to find answers to their students’ questions.

ALEKS is designed to be used without help from the Teacher’s Guide. Feelfree to use the system now. If questions arise, or if you want to learnmore about ALEKS, this Teacher’s Guide is intended as a convenient andcomprehensive reference.

NOTE. For a brief, comprehensive overview of ALEKS, please turn directly to the“Frequently Asked Questions” in Chapter 12.� The first chapters are those most likely to be turned to by teachers using ALEKS

for the first time. Chapter 2, “Quick Start,” contains a concise checklist for be-ginning to use ALEKS. Chapter 3, “Setup Guide for Teachers,” provides all ofthe information necessary for preparing to use ALEKS with one or more classes.This ranges from technical requirements and installation through the students’ firstALEKS session (which typically involves registration, tutorial, initial assessment,and entry into the Learning Mode). (Much of the information is the same as thatin Appendix A.)� Chapters 4 through 8 contain descriptions of the principal parts of the ALEKSsystem: Assessment Mode, Learning Mode, and Teacher Module. The TeacherModule is discussed in three chapters. Chapter 6 presents the Teacher Modulegenerally and is followed by treatments of the more specialized capacities of theAdvanced Teacher Module. Chapter 7 covers Results & Progress, the facilityfor monitoring student use of ALEKS and managing accounts. Chapter 8 coversStandards & Class Program, the facility for reviewing and modifying the curricularinformation used by ALEKS for a particular school or class.� Chapters 11 through 13 provide additional information that may be necessary orof interest to teachers using ALEKS. Chapter 11, “Knowledge Spaces and theTheory Behind ALEKS,” explains the history of Knowledge Space theory and itsfundamental concepts, along with the evolution of ALEKS itself. Also includedis a Bibliography for those seeking to understand the theory behind ALEKS ingreater depth. Chapter 12 provides answers to frequently asked questions aboutALEKS. Chapter 13 gives the information necessary for obtaining technical andother support.� Appendix A contains the complete text of the ALEKS Student User Guide. Ap-pendix B contains content summaries for ALEKS course products.

Chapter 2

Quick Start

The purpose of this chapter is to provide a summary of the steps involved in starting aclass with ALEKS.

2.1 Obtaining a Class Code

In order to use ALEKS with your class, you will need to have at least one Class Code.You give this code to the students in your class; they will use this Class Code to register.The Class Code is all your students need to register with ALEKS. When they register,they will receive a Login Name and Password; after this they will no longer need theClass Code. Students should not use the Class Code to register a second time, as doingso will create a new account in their name, unconnected with the first.

You can have as many classes and sections as you need or want in ALEKS. For each classor section, there is one unique Class Code. Students who register using this code willbe enrolled in the corresponding class. Students who accidentally enroll in the wrongclass can easily be moved to the right one at any time, without any unwanted effect ontheir work or records (moving a student to a class using a new domain in ALEKS maytrigger a new assessment). To obtain the Class Code for any class, log on toyour teacher account, click on “Class Admin,” and then on “View all yourclasses and class codes” (See Sec. 6.2.2). Or, in the Advanced Teacher Module,simply select the name of the class and click “Edit.” The Code will appear in the upperright-hand part of the screen (See Sec. 7.18).

You will normally be provided with a teacher Login Name and Password by ALEKSCorporation; a colleague at your school with Administrator privileges in ALEKS canalso create an teacher account for you. Once you are logged on to ALEKS as a teacher,you can create one or more classes through “Create a new class” (under “Class Admin”).

3

4 CHAPTER 2. QUICK START

2.2 Registering Students

Students should use the following steps to register.

1. Go to the ALEKS website.

http://www.aleks.com

2. Click on the link for “SIGN UP NOW” to the upper left (This is the only timethey will click on that button.)

3. On the page that follows, enter the Class Code in the spaces to the left of thewindow. Do not use the button on the right-hand side.

4. Enter other information as prompted (students in high school are asked for theirfull names, those below high school only for their first name and last initial).

5. Record their Login Name and Password, provided by the system. (Students canchange their Password now or later if they wish.)

6. Wait for the teacher to authorize their registration. They can log off at this pointand log back in later, using the Login Name and Password provided. As soon asthe teacher authorizes their registration it will be complete.

7. Begin using ALEKS by taking the Student Tutorial and an initial Assessment.

Students will subsequently use their Login Name and Password to enter their accounts.NOTE. For a complete description of how teachers authorize the registration of theirstudents, see Sec. 3.8.

Chapter 3

Setup Guide for Teachers

3.1 Teacher Preparation

As an instructor using ALEKS with your classes, it is important that you clearly un-derstand the system’s functioning and its underlying ideas. Take the time to studyall materials provided to you, including this Teacher’s Guide, and try out the systemthoroughly. The school administrator for ALEKS can contact ALEKS Corporation forconsultation at any time, preferably well in advance of the first session (See Chapter 13.).

3.2 System Requirements

The following table presents the system requirements for ALEKS in summary form.

PC Macintosh

Operating System Windows MacOS 10.2+(10.3+ for Quick-Tables)

Processor 166+ MHz AnyRAM Memory 32+ MB 32+ MBBrowser Explorer 6.0+, Firefox 1.0+, Netscape 7.1+,

Mozilla 1.6+OS 10.3+: Sa-fari, Firefox 1.0+;OS 10.2: Ex-plorer 5.2

Screen Resolution 800x600 (1024x768 for Chemistry) 800x600 (1024x768for Chemistry)

Modem Speed 28+ kbps 28+ kbps

Figure 3.1: System Requirements

Your browser should be configured with Java enabled. Both Netscape and Internet

5

6 CHAPTER 3. SETUP GUIDE FOR TEACHERS

Figure 3.2: The ALEKS Website

Explorer usually ship with Java. You can also install Sun Microsystems’ Java® VM,version 1.4.1+, which can be obtained from Sun.

Note that any of the kinds of direct connection (cable, ISDN, DSL) that are typicalin computer labs are adequate for use with ALEKS. If your computer lab has securitysafeguards in place, you will need the cooperation of your LAN administrator, systemadministrator, or lab technician to install the ALEKS plugin.

3.3 Installation

Installation of the ALEKS plugin takes place from the ALEKS website (Fig. 3.2):


NOTE. You must use this URL to access ALEKS. Although there are other ALEKSwebsites that you may find using an Internet search engine, only this one contains yourregistration data as a licensed ALEKS teacher. It is advisable to mark this website inyour browser with a “Bookmark” or “Favorite” or by creating a shortcut of some kind.

Close all applications other than your web browser before beginning installation.

3.4. TEACHER MODULE 7

Installation of the ALEKS plugin is automatic. If you attempt to use the systemdirectly by clicking on “Be our Guest” or on “Register with ALEKS,” the system willautomatically check to see whether your computer has the most recent plugin currentlyinstalled. If it does not, the system will download the plugin and ask for your permissionto install. (This is not a high-risk operation for your computer. The ALEKS pluginis a small library of Java classes which are used by your browser when you are loggedon to ALEKS. They are inactive at other times and do not do anything except providefunctionality for ALEKS. They can easily be removed from the computer with no othereffect except that ALEKS ceases to be available on that computer. ALEKS CorporationCustomer Support will be happy to answer any questions about the plugin.) When yougrant permission, it will install. Following installation you must close and reopen yourbrowser application. Installation is automatic for registered users as well.

If you need to download and install the plugin and this does not occur automatically,click on “Download the ALEKS plugin.”

There is also a “streaming” plugin which can be used in situations where it is notpossible to download to the local computer. Go to the following website:

http://www.aleks.com/plugin

Log on as usual. It will take one or more minutes for the plugin to load into memory.Once this is done, you will be able to use ALEKS in the usual way.

3.4 Teacher Module

The teacher enters the ALEKS Teacher Module by logging on to ALEKS with theirTeacher Login Name and Password. The Teacher Module is an extremely importantcomponent of the ALEKS system, permitting teachers to monitor and manage theirALEKS classes. The Teacher Module is designed for the utmost ease of use; it guidesusers through the steps needed to accomplish tasks in such a way that no separatetraining is needed and mistakes or confusion are unlikely. See Chapter 6 for a completedescription of the Teacher Module.

After the teacher is familiar with the features of the Teacher Module, he or she maywish to try the Advanced Teacher Module, which is somewhat more complex than thestandard interface but offers greater efficiency in some operations. Some teachers findthe Advanced Teacher Module more convenient to use once they are used to it. There isa Tutorial in ALEKS explaining the use and features of the Advanced Teacher Module(See below).


3.5 Lab Check

To ensure the best possible experience of ALEKS for your students, we recommendthat you check the computer lab in which ALEKS will be used in advance of the firstsession. This means installing and testing the plugin on some or (preferably) all of thecomputers in the lab. If security measures are in effect, you will need the cooperationof the lab administrator to install the plugin. To install and test, simply log on toALEKS through ”Be Our Guest” on each computer or use your teacher login to enteryour account. Installation will occur automatically. Following installation, restart thebrowsers and attempt login again. This time you should access ALEKS.

If the ALEKS plugin is not preinstalled and tested in this way, it will be installed whenyour students first access the system. This will take away a certain amount of time fromtheir use of the system. Also, if there is some problem in the lab that makes installationdifficult, it is far better to catch and resolve it before the students arrive.

3.6 Student Orientation

It is strongly recommended that the first ALEKS session be conducted under super-vision, perhaps with another teacher on hand to help your students get started. Youmay also choose to schedule supervised assessments at regular intervals and at the endof the course. It is not generally necessary to schedule a separate orientation meetingbefore the students actually begin using the system, although in some cases there maybe reasons for doing so. It is also advisable to emphasize the few requirements forassessments in ALEKS: paper and pencil are needed, as well as simple calculators. Cal-culators without graphic or symbolic functions are permitted for Algebra only. (A basiccalculator is part of ALEKS.) Remind your students that help is not allowed duringthe assessment because if the student being assessed does not do their own work, theassessment results may not be accurate, and this will hinder that student’s progress inthe Learning Mode.

If at all possible, the students’ first session with ALEKS should be long enough for themto complete their assessments and begin work in the Learning Mode. One hour may beconsidered a reasonable period of time. If the students cannot finish their assessmentsduring this time, ALEKS will automatically keep their place, and they will resume nexttime where they had left off. No work will be lost.

3.7 Registration

Students register with ALEKS by going to the ALEKS website and clicking on “SIGNUP NOW.” This will be expedited if the browsers used by the students have ”Book-marks” or ”Favorites” pointing to the website (See Sec. 3.3).

3.8. TEACHER AUTHORIZATION OF STUDENT REGISTRATION 9

NOTE. In order to register, all students must have the Class Code for the class thatyou are teaching. The Class Code is sent to the teacher by ALEKS Corporation orobtained by the teacher when creating the class (See Sec. 6.2.1). You are responsiblefor giving this code to the students at the time of the first session.

To obtain the Class Code for any class, log on to your teacher account, clickon “Class Admin,” and then on “View all your classes and class codes” (SeeSec. 6.2.2). Or, in the Advanced Teacher Module, simply select the name of the classand click “Edit.” The Code will appear in the upper right-hand part of the screen (SeeSec. 7.18).

The student registration process is described in detail in the Student User Guide (SeeAppendix A). There are complete online instructions for every step of this simpleprocedure. Among other information, some students may be able to supply their emailaddress (so they can be helped more promptly in case of difficulties) and their StudentID number (if you wish to have this in the system). Special care should be taken inentering the latter, as the system cannot detect mistyping. Both email and Student IDare optional information.

Near the conclusion of Registration students receive a Login Name and Password. Theseshould be noted carefully, as they will be essential for all further work with ALEKS. Youmay wish to advise the students to change their Passwords at the earliest opportunity.They should use a Password they will remember easily but that will be hard for othersto guess. Login Name and Password can be typed with upper- or lower-case letters.Neither may contain spaces or punctuation.

At the end of Registration, students are asked to wait for their teacher’s authorization.For a complete description of how teachers authorize the registration of their students,see Sec. 3.8. The students can log off at this point and log back in later, using the LoginName and Password provided. As soon as the teacher authorizes their registration itwill be complete.

3.8 Teacher Authorization of Student Registration

The following is a more detailed description of the student registration process, high-lighting the actions by which you authorize students’ registration.

A student wishing to register with ALEKS begins on the ALEKS home page by clickingon the link marked “SIGN UP NOW,” located to the upper left of the home page(Fig. 3.2).

Next the student is asked to enter the Class Code which has been provided by theteacher (Fig. 3.3). Since each Class Code is assigned to a class defined by grade level,the Class Code entered by the student tells ALEKS the grade level at which the studentis seeking to register. The spaces for this code are in the left-hand part of the window.The steps by which the student completes registration follow two paths, one for studentsbelow High School, and another for students in High School.


Figure 3.3: Registration

Following entry of the Class Code, the student is given information on the class selectedand on the process of beginning to use ALEKS.

Subsequently, if the student is in 8th grade or below, ALEKS asks for the student’sfirst name and last initial (Fig. 3.4). ALEKS does not ask for the student’s full lastname so that there is no personally identifying information in the system for students in8th grade or below. The student is then provided with a Login Name consisting of thestudent’s first name, last initial, and possibly a number. If the student is beyond the8th grade, ALEKS asks for full first and last names, and then provides a Login Nameconsisting of the student’s first initial, last name, and possibly a number (Fig. 3.4). Thestudent is also provided with a password, which can be changed at this time or later,as the student desires.

Students above the 8th grade have the opportunity to enter an email address and aStudent id number. No students are required to provide this information; students inthe 8th grade and below are never asked for it or given any way to provide it.

At this point the student is told that authorization is needed from the teacher beforeregistration can be completed (Fig. 3.5). Until the teacher logs onto ALEKS and pro-vides authorization, the student will not be able to get further than this page. Once

3.8. TEACHER AUTHORIZATION OF STUDENT REGISTRATION 11

Figure 3.4: Registration (continued)


authorization is provided, the student will be able to click “Next” and begin usingALEKS. If the teacher cannot authorize immediately, the student is able to log off atthis point and log back on at a later time using the Login Name and Password provided;if the teacher has authorized registration by then, the student will be able to begin usingALEKS.

In order to authorize registration, log on to your teacher account using the Login Nameand Password received at registration or from ALEKS Corporation. If there are stu-dents in the class awaiting registration, you will come to the Authorization page withinstructions and a list of students needing authorization (Fig. 3.6). If you simply wishto authorize all students, there is a checkbox at the top of the list to do this; otherwiseyou can authorize each student individually by clicking the checkbox opposite his or hername (“Authorize”). There is also a checkbox for deleting the account of a student whohas initiated registration (“Delete”). Checking this checkbox will remove the account.

It is noted on the Authorization page that authorizing registration for stu-dents in Grade 8 or below constitutes your assurance that all necessary



parental consents have been obtained for your students’ use of ALEKS.

Some students may initiate registration more than once due to misunderstanding. Thiswill be evident from the repetition of names in the list. (Occasionally there may bemore than one student in the class with the same combination of first name and lastinitial; presumably the teacher will take this into account.) When there is repetition,you should “Authorize” only one account for each student and “Delete” any others, toprevent unnecessary use of purchased subscriptions.

When all necessary boxes have been clicked, click “Done”; a summary of authorizationsand current licensing status will be shown, and you can continue to work in the TeacherModule. You can also defer authorization simply by clicking “Done” on the Authoriza-tion page, without either authorizing or deleting all or any of the students. You canreturn to the Authorization page later by clicking “Authorization” on the ALEKS menubar.

NOTE. When the Authorization page is shown for classes higher than the 8th grade,there is a note advising you that students under the age of 13 should not be authorizedin this way. When students under the age of 13 wish to register in ALEKS for a classhigher than the 8th grade, contact ALEKS Corporation for assistance.

3.9. TUTORIAL 13

3.9 Tutorial

Following Registration, the students enter a brief tutorial on the use of ALEKS inputtools, also called the Answer Editor Tutorial (See Sec. 4.5). There are separateTutorials for different subjects, since the specific tools for them differ somewhat. TheALEKS Tutorial provides ample feedback to ensure that students complete it success-fully.

NOTE. The Tutorial is not intended to teach mathematical knowledge, but rather totrain students in using the system tools. If students need a “refresher” on use of thesystem tools, it is always possible to click on the “Help” button, which gives access tothe sections of the Tutorial (See Sec. 5.2.12).

3.10 First Assessment

Students proceed directly from the Tutorial to their first assessment (See Chapter 4).To reiterate, no help of any kind should be given to students being assessed, not evenrephrasing a problem. Students need to have paper and pencil. Simple calculatorswithout graphic or symbolic functions may be used for Algebra. A basic calculator ispart of ALEKS. No calculators are used for Arithmetic.

The ALEKS assessment is adaptive and variable in length. Some students will have veryshort assessments, whereas others will have assessments that are longer. Consistencyof effort and concentration are the factors most likely to influence the length of anassessment.

NOTE. All students will be assessed upon their first use of the system. This willprovide you with a baseline picture of your class and of each individual student.

3.11 Report Tutorial

At the conclusion of each assessment, the student is given a brief Tutorial on how tointerpret the Assessment Report. This will be in the form of one or more color-codedpie charts, with accompanying textual information (See Sec. 4.13). It is important thatthe students know how to interpret these pie charts correctly. Some teachers have foundit worth the effort to sit with each student individually as he or she concludes his or herassessment. They can then make sure the student understands the parts of the reportand help him or her choose topics for entry into the Learning Mode. Keep clicking“Next” until you get to “MyPie,” where you can choose items for work in the LearningMode.

Explain to students that subsequent assessments will produce only the pie charts. Thepie charts also appear in the Learning Mode each time a new concept is mastered and


“added to the pie.” If the student wishes to choose a new topic, the pie can always beaccessed by means of the “MyPie” button.

3.12 Beginning the Learning Mode

Students enter the Learning Mode by clicking on one of the topics contained in theirpie chart (topics they are completely “ready to learn”). If at all possible, the studentsshould be given sufficient time in their first ALEKS session to use the Learning Modeand, ideally, to begin to “add concepts to their pie.” If they have this experience, theirinterest in using ALEKS is likely to be more favorable. You should also be present toanswer questions regarding the Learning Mode and to assist your students in familiariz-ing themselves with its varied features. This is particularly important in cases in whichtheir subsequent use of ALEKS will be unsupervised.

In some ALEKS course products, students may choose to continue their initial assess-ment for particular pie slices where no topics are yet available to them. In order toinitiate these assessments, the students click a button marked “Assessment” which ap-pears in the place of a list of available topics for the particular slice. Such assessmentsare called “Initial Assessment (continued),” and are generally shorter than other assess-ments. They focus on topics from the slice chosen, and their purpose is to “open” thatslice for work by the student.

Chapter 4

Assessment Mode

The Assessment Mode is the heart of the ALEKS system. Its ability to quickly and accu-rately determine a student’s knowledge enables ALEKS continuously to make availablethe material the student can most readily employ, and thus efficiently guide individuallearning paths. The Assessment and Learning Modes work together closely. In ALEKS,learning is powered and optimized by assessment.

4.1 Assessments in ALEKS

The ALEKS assessment uses open-ended problems (no multiple-choice questions). It isan adaptive assessment; that is, problem types are selected based on all the previousanswers the student has given. It is impossible to predict which types of problems willappear, or in what order. Moreover, the problems themselves are generated algorithmi-cally, with randomly-selected values (as is also the case in the Learning Mode). Thus,one cannot “learn the assessment” or “teach to the assessment,” and cheating is almostimpossible. In the unlikely event that two students sitting next to one another weregiven the same problem-type at the same time, the problem parameters and valueswould almost certainly be different, and so would the correct answer. Despite this, cer-tain assessments must be supervised, such as the initial, interim, and final assessmentsin a class. Without supervision, students could use a textbook, receive systematic help,or have someone else take the assessment in their place. This point is critical whereassessment results are used for purposes other than those internal to the system. (Thereis no reason for a student who has begun using ALEKS to cheat on a “progress” assess-ment, as this will simply cause the system to suggest problems that are too difficult,and thus hinder the student’s own work.)

As noted, the student takes an initial assessment immediately following completionof the Tutorial (See Sec. 3.10). When an assessment begins, the student is clearlyinformed it has begun. Next a series of mathematical problems is posed to the student.The student provides the solution to each problem using the Answer Editor (or clicks

15

16 CHAPTER 4. ASSESSMENT MODE

“I haven’t learned this yet”). In the Assessment Mode, the system does not inform thestudent whether the answer just given was correct or not. The assessment continues untilthe system has determined the student’s precise knowledge of the domain, at which timethe assessment ends and a report is presented to the student. The number of questionsasked cannot be known in advance, although consistency of effort and attention seemto contribute to shorter assessments.

4.2 Rules for Assessments

Assessment in ALEKS is an important and serious event. It is essential that assessmentsbe conducted according to certain guidelines and in the proper spirit. If there is anatmosphere permitting disturbances or distractions, students will not obtain the benefitsthe system is capable of providing. If assessment results are inaccurate, the system willgive the student inappropriate problems and progress will initially be impaired. Thesystem will recover and find the right level, but the student may still experience adegree of frustration. In order to avoid this, it is strongly recommended that the firstassessment be taken under the teacher’s supervision (See Sec. 3.10).

All students being assessed need paper and pencil. No calculators are permitted inassessments for Arithmetic, but simple calculators without symbolic or graphing func-tions should be available for students being assessed in Algebra. A basic calculator ispart of ALEKS. Most important, no assistance may be given—not even to the extentof explaining or rephrasing a problem. Students should be encouraged to use the “Ihaven’t learned this yet” button when they do not know what to do. It is not possibleto return to previous assessment questions; students should not click their browser’s“Back” or “Forward” buttons when using ALEKS.

4.3 Scheduling of Assessments

Initial Assessment. The initial assessment takes place at the outset of students’ useof ALEKS, immediately after Registration and Tutorial (See Sec. 3.10). We stronglyrecommend that this initial assessment, which has the character of an orientation tothe system for student users, take place in a supervised computer lab setting to ensurethat students do not receive help or collaborate. In creating or editing a class account,the teacher can stipulate that the initial assessment be allowed only from school (SeeSec. 7.17.).

In some ALEKS course products, students may choose to continue their initial assess-ment for particular pie slices where no topics are yet available to them. In order toinitiate these assessments, the students click a button marked “Assessment” which ap-pears in the place of a list of available topics for the particular slice. Such assessmentsare called “Initial Assessment (continued),” and are generally shorter than other assess-ments. They focus on topics from the slice chosen, and their purpose is to “open” that

4.4. BUTTONS 17

slice for work by the student.

Automatic Assessments. Additional assessments are scheduled automatically by thesystem based on two factors: overall time spent in the Learning Mode (called “LoginTime Assessment”) and progress made while there (called “Progress Assessment”). Bydefault, a new assessment is triggered after 20 new items have been learned (but nosooner than 5 ALEKS hours after the last assessment) or after 10 hours have beenspent in Learning Mode since the last assessment or after 60 days have passed sincethe last assessment. Some modification of these parameters is possible; please contactALEKS Corporation Customer Support for assistance if you would like to do this. TheLearning Mode itself updates students’ assessment results as it goes along, periodicallydisplaying new pie charts and new choices of concepts they are completely “ready tolearn.” The automatic assessments, however, provide a firmer basis for such guidance.

Completion Assessments. ALEKS also assesses students automatically when theycomplete the syllabus for a course. If the assessment does not confirm the student’smastery of the syllabus materials, they will return to the Learning Mode. More thanone Completion Assessment is thus possible, but as a rule ALEKS will not reassess thestudent if only a small number of topics need to be relearned.

Requested Assessments. Assessments can also be requested by the teacher for indi-vidual students or for entire classes. For example, the teacher, department, or schoolmay wish to have “interim” assessments under supervision to guarantee sound results.ALEKS allows the teacher to schedule the assessment for a particular date and time(See Sec. 6.5.1). Students logging on to ALEKS within the time period specified for theassessment will automatically enter Assessment Mode.

The teacher simply announces the assessment for a certain time and place. Just prior tothis time the teacher prompts the class assessment in the Teacher Module (See Secs. 7.9–7.10). The next time students log on they will automatically enter the assessment.Note that a requested assessment “resets the clock” for automatic assessments, so thatstudents will not be assessed with undue frequency. Also, among the options for arequested assessment is one to prevent automatic assessments within a certain numberof days prior to the requested assessment (See Sec. 6.5.1).

NOTE. In some ALEKS products, there is an option to request the assessment on aparticular slice or slices of the pie chart. When this is done, there will be a note regardingthe estimated number of questions needed for the assessment. Often, assessing on morethan one slice of the pie chart will result in an assessment that is longer than desired;therefore, this feature is usually most effective when only a single slice is selected. Theteacher also has the option of letting ALEKS select an appropriate slice for each student,based on their individual progress.


Figure 4.1: The Answer Editor for Mathematical Expressions (Assessment)

4.4 Buttons

The Assessment Mode (Fig. 4.1) has a reduced set of active menu buttons enabling thestudent being assessed to leave the system (“Exit”) or get help on use of the AnswerEditor (“Help”). Other buttons appear, but they are disabled. All of the ALEKS menubuttons are enabled in the Learning Mode (See Sec. 5.2).

Note that students using ALEKS should not click their browser’s “Back” and “Forward”buttons. Only the navigation tools that are part of the ALEKS interface should be used.

The two aspects of the ALEKS interface relevant to work in the Assessment Mode arethe Answer Editor and the Assessment Report.

4.5 Answer Editor

Input to the ALEKS system is always in the form of proper mathematical expressionsand constructions, never multiple choice. A critical reason for this is to prevent sub-stantial inaccuracies which arise from students’ guessing and trying out the differentchoices.

Another purpose of this approach is to train students in the same skills that are necessaryfor conventional, paper-and-pencil communication of solutions and results. At the sametime, the sophistication of the ALEKS input tools provides certain advantages. Thepresentation of results is always neat and clear. Manual dexterity plays a reduced role indrawing an accurate graph or geometrical construction. Immediate feedback is providedon the formal completeness of solutions.

The general term for the input tools used in ALEKS is the “Answer Editor.” This en-compasses a variety of actual modes for user input: an Answer Editor for mathematicalexpressions, an Answer Editor for the number line, an Answer Editor for graphing in the

4.6. MANIPULATORS FOR MATHEMATICAL EXPRESSIONS 19

Expression Answer Editor keypad button Keyboard equivalent

Square Root [ ]√

[ ] (none)

Fraction [ ][ ] /

Mixed Number [ ] [ ][ ] (none)

Repeating Decimal [ ][ ] (none)Absolute Value [ ] |[ ]| (none)List of Expressions [ ], [ ], . . . ,

Exponent [ ][ ] ∧ (before exponent)Multiplication Expression [ ] × [ ] ∗Percentage % %Greater-Than [ ] > [ ] >Less-Than [ ] < [ ] <Greater-Than-or-Equal-To [ ] ≥ [ ] (none)Less-Than-or-Equal-To [ ] ≤ [ ] (none)Equal-To [ ] = [ ] =Not-Equal-To [ ] 6= [ ] (none)AND AND (none)OR OR (none)

Figure 4.2: Mathematical Expressions Produced by the Answer Editor

Cartesian plane (with x and y coordinate axes), and an Answer Editor for histograms(in Statistics). A student beginning to use ALEKS is thoroughly trained in all featuresof the Answer Editor that are relevant to the subject being studied during the Tutorial(See Sec. 3.9).

In much of what follows, emphasis is on the “Answer Editor for mathematical expres-sions,” as this is the section which involves the greatest degree of interplay betweenmouse, keyboard, and on-screen buttons and icons.

4.6 Manipulators for Mathematical Expressions

The Answer Editor for mathematical expressions consists of two parts: a rectangularfield into which mathematical expressions are entered (the “entry field”) is to the left,and a “keypad” made of buttons with mathematical symbols is to the right (Fig. 4.1).These buttons have labels in the Tutorial, but not afterwards. Mathematical expressionsare entered and edited using the buttons of the Answer Editor keypad, as well as thebasic keyboard, the Left and Right arrow keys, the Tab, Enter, and Backspace keys,and the mouse.

NOTE. Buttons are displayed to correspond with the kind of problem being solved. Theselection is made in such a way as to avoid giving away the correct answer. Keyboardshortcuts (Fig. 4.2) work only when the corresponding button is displayed.


Key Effect

Right arrow -Tab - Enter

moves the cursor one place to the right(ahead)

Left arrow moves the cursor one place to the left (back)

Backspace deletes input immediately preceding (to theleft of) the cursor and moves the cursor oneplace to the left (back) OR deletes selectedinput

Figure 4.3: Using Special Keys in the Answer Editor

Basic Input

When a new page is opened and contains a problem whose solution is a math-ematical expression, the entry field initially contains at least one blue box. Eachblue box represents a mathematical expression that forms part of the completeanswer. To enter a mathematical expression one must first click on a blue box.When this is done, the cursor (or “caret”) appears inside the box. The cursormarks the point at which something is entered. Material can be entered using thebasic keyboard or the buttons of the keypad. Individual digits can be entered onlyfrom the keyboard. Symbols can be entered using the buttons of the keypad and,sometimes, from the keyboard as well (Fig. 4.2).

Basic Editing Tools

The cursor, showing the point at which material is entered, can be moved usingthe Left and Right arrows and the Tab and Enter keys. It can also be positionedusing the mouse. Input can be deleted using the Backspace key (Fig. 4.3).

Selecting Input

It is possible to select a continuous portion of input by dragging the pointer withthe mouse button held down. A segment that has been selected by dragging inthis way can be deleted by pressing Backspace, replaced by typing, or replaced byclicking the buttons of the Answer Editor keypad. It can also be inserted into amathematical expression such as a fraction or a square root (the selected portionis placed in the numerator position or under the square root sign, respectively).

Clear and Undo

After material has been entered, the field can be returned to its empty state byclicking on “Clear.” Clicking on “Undo” cancels the most recent action. Clickingon “Undo” a second time restores the effect of the canceled action (including a“Clear” command).

4.7 Mathematical Expressions

The purpose of the Answer Editor for mathematical expressions is to process user inputin the form of correct mathematical expressions. One important way in which the

4.7. MATHEMATICAL EXPRESSIONS 21

Answer Editor guides the user in constructing such expressions is by means of the blueboxes. If a blue box remains on the screen, you know that the input typed so far is notvalid.

Entering expressions from the keyboard

For expressions that do not require the use of the Answer Editor keypad, the usercan place the cursor within a blue box and enter the mathematical expression fromthe keyboard. For many expressions, however, the Answer Editor keypad must beused. It may be used, as well, for some types of expressions that can also be enteredfrom the regular keyboard (Fig. 4.2).

Using the Answer Editor keypad to structure simple expressions

To form a simple mathematical expression, the user places the cursor in an emptyblue box and clicks on the appropriate button from the Answer Editor keypad.The initial blue box disappears and new blue boxes may appear (depending on thebutton), accompanied by all of the necessary signs. The user can now fill in thenew boxes.

Entering complex expressions

Sometimes it is necessary to enter more complex mathematical expressions. Whathas been written about entering mathematical expressions into a single blue boxholds equally true for entering expressions into any of the blue boxes produced byclicking a button of the Answer Editor keypad. One can place the cursor in one ofthese boxes and enter an expression from the keyboard, or, by clicking on a buttonof the Answer Editor keypad, replace it with the structure of a new mathematicalexpression. Expressions of any degree of complexity can be created in this way.

NOTE. The Answer Editor does not supply parentheses. The user must knowwhen these are necessary. In particular, when there is an expression consisting ofmore than one symbol that must be raised to a power, one may need to enclose itin parentheses, just as in writing; otherwise, only the final symbol (just before theexponent) will be raised to the specified power.

Alternate ways of entering expressions

The buttons of the Answer Editor keypad can be used in other ways as well. Inparticular, one can select some portion of the input in the entry field which consti-tutes a complete mathematical expression, and then click on a keypad button. Thiswill create a new mathematical expression within which the expression selected isone component. The same basic rule applies: the minimum unit of manipulationis a complete mathematical expression.

Other mathematical signs

The following mathematical signs can be entered only from the keyboard:� the plus sign (+);� the minus sign (-), both for connecting the two parts of a subtraction expressionand for designating a negative number;� the period (.) used in decimals;

22 CHAPTER 4. ASSESSMENT MODE� the comma (,) used to punctuate numbers of more than three places.

Please note as well the following special cases:

The asterisk for multiplicationThe “x” character on the keyboard cannot be used to enter a multiplicationsign. Only the asterisk (*) serves this purpose. (The multiplication sign onthe Answer Editor keypad, however, is the traditional x-shaped symbol.)

Mixed numbersAlthough fractions can be entered from the keyboard using the front slashcharacter (/), mixed numbers cannot be entered this way. More precisely,the Answer Editor does not automatically regard a whole number followedby a fraction as a mixed number. The mixed number button on the AnswerEditor keypad must be used to enter mixed numbers.

4.8 Types of Mathematical Expressions

The following set of tips is intended to illustrate the variety of ways in which math-ematical expressions can be entered using the Answer Editor. It is in no way a thoroughdescription of the Answer Editor, which includes many other kinds of mathematical ex-pressions and constructions.

Here, “Button” will always refer to a button on the Answer Editor keypad. By “select”we mean drag the mouse over the expression to be selected with the mouse buttondepressed, so that a red box appears surrounding it.

Percentage 48%

The next example illustrates the possibility, in some cases, of using either theAnswer Editor keypad or the regular keyboard to enter signs:� Enter the expression you wish to express as a percentage and click on the

percent button; OR� Enter the expression you wish to express as a percentage and then enter the(keyboard) percent sign.

Fraction 710

Fractions can be entered conveniently at least three ways:� Enter the numerator, enter a (keyboard) forward slash character, and enterthe denominator; OR� Enter the numerator, click on the fraction button, and enter the denominator;OR� Click on the fraction button, enter the numerator, then click on the blue squarein the position of the denominator and enter the denominator.

4.8. TYPES OF MATHEMATICAL EXPRESSIONS 23

Mixed Number 5 78

Mixed numbers can be entered in more than one way, but they each require use ofthe mixed number button:� Enter the whole number part, click on the mixed number button, enter the

numerator, press Enter, and enter the denominator; OR� Click on the mixed number button, click on the first blue box (for the wholepart), enter the whole number part, press the right arrow, enter the numerator,move the cursor to the denominator position, and enter the denominator (i.e.,fill in the boxes).

Repeating Decimal 1.27� Enter all digits that precede the repeating pattern, including the decimal point(a period on the keyboard) and any decimal places preceding the pattern, clickon the bar button, and enter the repeating pattern; OR� Enter all digits, including the decimal point (a period on the keyboard) andall decimal positions following it, select the repeating pattern only, and clickon the bar button.

Fraction in square root followed by multiplier√

58 × 3

For this example only one input method is given, but others could be suggested:� Click on the square root sign button, click on the fraction button, enter thenumerator, tab, enter the denominator, then tab, enter an asterisk (from thekeyboard), and enter the multiplier.

List 1, 2, 3

For the purposes of the following example, assume that there is a list consisting ofthree components to be entered:� Enter the first expression, click on the list button (or press the keyboard

comma), enter the second expression, click on the list button, enter the thirdexpression, click on the list button, and enter the fourth expression; OR� Click on the list button (or press the keyboard comma) twice, click on the firstblue box, enter the first expression, move the cursor right, enter the secondexpression, move the cursor right, and enter the third expression.

Answers with Units 10 cups

There are also some cases where the Answer Editor does part of the formatting.For example, in problems where answers must be expressed in some kind of units,such as dollars or candies, the unit expression needed may appear in advance.

Square Root√

81� Click on the square root button and enter the expression into the square rootsign; OR

24 CHAPTER 4. ASSESSMENT MODE� Enter the expression you wish to appear under the square root sign, select it,and click on the square root button.

In the simple example just given the second method reverses the sequence of stepsof the first method. Such complementary methods are typical.

Absolute Value | − 6|� Click on the absolute value button and enter the expression whose absolutevalue you wish to express; OR� Enter the expression whose absolute value you wish to express, select it, andclick on the absolute value button.

Exponent 32� Click on the Exponent button, enter the base, then move the cursor to theexponent box and enter the exponent; OR� Enter the expression you wish to raise to a power, click on the exponent button,and enter the exponent.

NOTE. If the number you wish to raise to a power is an expression consisting ofmore than one symbol, it may need to be enclosed in parentheses. The AnswerEditor will not do this for you. If no parentheses are used, only the last symbolwill be raised to a power.

Square Root Preceded by Multiplier 2√

6

With more complex expressions you can use the mouse to place the cursor in theneeded position, as in the second method:� Enter the multiplier, click on the square root button, and enter the expression

you wish to be under the square root sign; OR� Click on the square root button, click to the left of the square root sign, enterthe multiplier, tab (or press the right arrow, or press Enter, or click on theblue box under the square root sign), and enter the expression you wish to beunder the square root sign.

4.9 Advanced Mathematical Expressions

The following types of mathematical expressions occur in more advanced subjects.

To create a matrix, the user clicks on an icon corresponding to the dimensionsdesired (2 × 2, 2 × 3, etc.), then fills in the cells with appropriate values.

For topics involving set notation, there will appear icons for each of the specialsymbols required, such as curly braces, “belongs to,” “such that,” the real numbers,the integers, and so forth.

4.10. THE ANSWER EDITOR FOR THE NUMBER LINE 25

Figure 4.4: The Answer Editor for the Number Line

4.10 The Answer Editor for the Number Line

The Answer Editor for the number line consists of a number line and tools for placingfull and empty endpoints and segments (Fig. 4.4). To place a segment, mark a pointon the number line with the pencil, then click on that point with either the full orthe empty tool. To place a segment, use the Region tool to click on any point in therelevant part of the number line. If the user clicks between two endpoints, the segmentwill extend to each of them. When the user clicks between an endpoint and an extremityof the number line, the segment will appear with an arrow to indicate that it continuesto infinity. Click with the eraser to remove any part of the construction.


Figure 4.5: The Answer Editor for Graphing

4.11 The Answer Editor for Graphing

The Answer Editor for graphing consists of a Cartesian plane with x− and y− coordinateaxes and a selection of other tools for graphing lines and regions of the plane (Fig. 4.5).

To graph a line, use the pencil tool to plot two points. Then, align the straightedge(ruler) on the two points (it is a “grabby” tool and will jump to a point when itis near it). Then use the pencil tool to draw the line. Note that the effect of thestraightedge continues past its ends, so there is no need to move it to make a linegoing from edge to edge of the depicted plane. The line should be started withinthe graph area, however.

To fill in a region, use the region tool and click in the desired region of the plane.One must draw all lines defining the region before filling it in. In order for oneor more of the lines defining a region to be dotted (as in the graph of a systemcontaining one or more strict inequalities), click on the line with the dotted linetool. This may be done before or after the region is filled.

4.11. THE ANSWER EDITOR FOR GRAPHING 27

To place a point where coordinates are not both integers: use the input field to enternumerical values (fractions and mixed numbers can be placed using the icons beneaththe field), then click on the icon with horizontal broken line (for the y-coordinate)or vertical broken line (for the x-coordinate). A broken line will appear on theplane for each given coordinate. Use the pencil to mark the desired point at theirintersection. Another method is the click on the ordered pair icon (with a commaseparating two boxes in parentheses), enter a pair of coordinates (in terminatingdecimal, fractional, or mixed-number form), then click on the icon with a smallCartesian plane and a point marked by “X.” This will place the point directly onthe plane without using the pencil.

To draw a graph requiring an asymptote, use the asymptote tool (broken horizontalor vertical line) to place the asymptote as needed. A slanted asymptote may beplaced by first drawing two points and then using the tool with a broken diagonalline. Plot the additional points needed for the graph, and then click on the graphbutton (curved line connecting “X”s).

For each type of conic section, there is a special tool allowing the construction of itsgraph. Normally, the user clicks once with the tool to establish the center or vertexof the graph, and then one or more additional times to determine its final form.

As with the number line, select the eraser tool and click on any part of a line, arc,or other component to remove it.


Figure 4.6: The Answer Editor for Histograms

4.12 The Answer Editor for Histograms

The Answer Editor for histograms consists of a space for drawing histograms and icons(buttons) permitting the creation and adjustment of bars (Fig. 4.6).

Initially, the histogram appears with a small number of bars (e.g., two). The heightof the bars is adjusted by clicking on the top edge of each and holding the mousebutton down while dragging to the desired height. To add bars, click on the iconwith the plus sign; to subtract bars, click on the icon with the minus sign. Each barhas a space beneath it where an appropriate label can be typed in.

Any bar may be set to any integer height by dragging. To set the height of a barat a non-integer value, enter the value in the white area to the upper right of thehistogram, then click on the icon with the broken horizontal line. This will place abroken line on the histogram at that height. Any bar may then be dragged to theheight of any broken line that has been placed.

4.13. ASSESSMENT REPORT 29

Figure 4.7: Assessment Report

4.13 Assessment Report

At the conclusion of an assessment, the Assessment Report is presented. The interpre-tation of this report is the same as for pie chart displays found in other places withinALEKS (such as in “MyPie”).

4.13.1 Standard Report Format

The standard report format is used for all assessment reports. This format consists ofone or more pie charts (Fig. 4.7).

4.13.2 Interpreting the Pie Charts

Pie Charts express the results of a given assessment. They contain the following typesof information:� which mathematics topics are part of the program;� the relative importance of the parts of the mathematics program; and

30 CHAPTER 4. ASSESSMENT MODE� to what extent the student has attained the knowledge for each part of the math-ematics program, according to the assessment.

Each color-coded slice of the pie chart refers to a particular part of the program, suchas “Whole Numbers” or “Proportions and Percents.” Each slice is marked with anabbreviation. The meanings of these abbreviations and of the chart’s color-coding aregiven in the legend immediately following the pie chart. If the abbreviation next to theslice is underlined, it means this topic contains concepts the student is most “ready tolearn.”

A pie chart will show only those topics that are part of the math curriculum for the classindicated. The portion of the chart taken up by any one topic reflects the importanceof that topic relative to others in the given program.

The progress a student has made toward satisfying the program for knowledge in agiven topic is expressed by the degree to which the slice corresponding to that areais shaded (i.e., filled in with solid color). The measure of progress given by the piecharts is dependent on the standards for a particular class and is set by teachers andadministrators (See Chapter 8).

When a user places the pointer over one of the slices of the pie charts, the slice popsout of the pie. A list of the items for that topic the student is currently best readyto learn will appear. Not every slice necessarily contains such a list, even if the topichas not yet been fully mastered. If the slice contains concepts, its label is underlined.This is because a student may not be ready to learn a concept in a given topic (slice)before concepts in another topic (slice) have been mastered. Clicking on any one ofthese concepts takes the user into the Learning Mode, beginning with that concept.

State standards report. In some states, there will also be an entry in this displaygiving access to the state standards report for this student. For a complete descriptionof this feature, see Sec. 6.4.16.

4.14 Multiple Pie Charts

For courses in Arithmetic in ALEKS it is normal to have separate pie charts for thegrade level preceding that assigned to the class, the grade level assigned to the class, andthe subsequent grade level (labeled “Readiness,” “Mastery,” and “Above and Beyond”).The reason for this is that students are very likely to be working on material that spansat least three grade levels. For early or late grade levels the number of pie charts shownmay be fewer, depending on how the curriculum has been set up for a given school.

4.15. READY TO LEARN 31

4.15 Ready to Learn

The concepts given as most “ready to learn” do not represent a casual selection ofconcepts that the student has not yet mastered. By resuming study with one of theseconcepts, the student is following the most efficient path to mastery of the completedomain (See Chapter 11).

4.16 Progress Bars

Another graphic expression of the student’s progress is given by the bar graphs at thebottom of the report (“History”). These represent the general extent of the student’smastery: the blue portion of each bar represents material that was learned as of thegiven assessment, the green portion material mastered in the Learning Mode since thatassessment, and the yellow portion material belonging to the curriculum for the givenlevel that has yet to be learned. When the bar is entirely blue, the student has completedthe curriculum for a level or levels.

Chapter 5

Learning Mode

5.1 The ALEKS Learning Mode

The purpose of the Learning Mode is to assist students in mastering mathematicalconcepts. Students using ALEKS choose which concepts they wish to work on in theLearning Mode from the list of concepts the system has determined they are mostprepared to learn. This happens either as the result of an assessment or through thecontinuous update of assessment results that is performed by the Learning Mode. Stu-dents in the Learning Mode work on those concepts they are best prepared to learn, sothat the benefit of their work is maximized.

In the Learning Mode students always work on one concept at a time. The LearningMode provides them with a rich array of resources to help in mastering the concept. Thisincludes explanations, practice problems, diagnostic feedback on problem solutions, andaccess to a student mathematical Dictionary. Moreover, the Learning Mode is designedto monitor the progress made by students toward mastery of a given concept and advisethem on continuing or changing concepts. A student is required to solve an appropriatenumber of practice problems correctly before the system will conclude that the concepthas been mastered. At this point the student is encouraged to choose a new conceptfrom the (updated) pie chart, but the opportunity to continue to work on this conceptis available if the student wishes. If the student makes mistakes, a greater number ofcorrect solutions may be required.

If the student has difficulty, the system may suggest closer attention to the explanationsor offer the name of a classmate who has recently mastered this concept. A new selectionmay also be encouraged.

The student continues to work in the Learning Mode until a new assessment is ordered,either by the teacher or automatically when a certain amount of time has been spentor a certain amount of progress has been made since the last assessment (See Sec. 4.3).

33

34 CHAPTER 5. LEARNING MODE

Figure 5.1: The Options Page

5.2 Buttons

5.2.1 Exit

One can end a session with ALEKS in either of two ways: click on the “Exit” buttonat the upper left-hand corner of the browser window or simply close the window inone of the ways provided by the browser. Also, if no input is supplied to the systemfor 30 minutes the session is terminated automatically. No matter which way youexit, ALEKS will return you to the same place when you next log on.

5.2.2 English

The Language menu can be used to switch back and forth between English andSpanish versions of ALEKS. The Spanish translation of ALEKS is complete forcourses used in Grades 3 through 11.

5.2.3 Options

The “Options” button opens a page containing the user’s current registration infor-mation (with a link for changing the Password), course and instructor (with a linkfor changing the course), a checkbox for joining “Ask a Friend” (See Sec. 5.7), and

5.2. BUTTONS 35

the beginning and expiration dates of the account (Fig. 5.1). “Report” connects to amenu of all assessment reports (See Sec. 5.2.5.). “History” displays a list of conceptsthe student has worked on recently, indicating the level of mastery achieved and pro-viding the opportunity to return to that concept for further practice. Clicking on“Done” returns to the Learning Mode.

5.2.4 Print

To print the contents of the ALEKS display, click the “Print” button on the menubar. This transforms the display into a form suitable for printing. Next, click onthe browser’s “Print” button, or use whatever keyboard equivalent is provided. Theprocedure is the same as for printing any web page. To return to the LearningMode, close or minimize the window that was printed.

5.2.5 Report

Clicking on the “Report” button displays a menu of all past assessments, with themost recent displayed by default. Any assessment can be selected (by date) fromthe menu. Then click “OK” to see the results of that assessment. This will includeone or more pie charts, a list of concepts recently learned, a list of concepts mostready to be learned, and the progress bar graphs (See Sec. 4.16). To return to theLearning Mode, click “Done.”

NOTE. Click on the link “and many other more elementary concepts.” to see a com-plete list of topics mastered.

5.2.6 Dictionary

Clicking on the “Dictionary” button produces a new browser window with an indexof entries in the online student mathematics Dictionary. Click on any entry to viewthe definition. Remember that the Dictionary can also be accessed by clicking onunderlined words (hypertext links) anywhere in the Learning Mode. Dictionarydefinitions are designed to present concepts in their simplest form first, moving intogreater depth as the definition proceeds (See Sec. 5.3.5). Close or minimize theDictionary window to return to the Learning Mode.

5.2.7 Calculator

The Calculator button will light up (become enabled) on topics where ALEKS per-mits use of a calculator. Click on this button to use the online calculator.


5.2.8 Review

The “Review” button gives a list of concepts the student has recently worked onin the Learning Mode (See Sec. 5.5). One can click any of these concepts to getfurther practice on it. There is also an option for “more extensive review.” Clickon “Done” to return to the Learning Mode.

5.2.9 Worksheet

The student may obtain an individualized, printable homework sheet by clicking“Worksheet.” The questions on the worksheet are based on that student’s mostrecent work in ALEKS (See Sec. 5.6).

5.2.10 Quiz

The student can take a quiz assigned by the teacher or check the results of quizzesalready taken by clicking “Quiz.” If a quiz has been “scheduled” by the teacher,however, the student does not need to use this button; when the student logs onduring the time the quiz has be taken it will begin automatically (See Sec. 7.11).

5.2.11 Message

The student can use the “Message” button to check for messages from the teacheror administrator, and send or respond to messages if this has been enabled (SeeSecs. 7.12, 7.13). It is also possible to send messages directly to ALEKS Corporation.Click on “Done” to return to the Learning Mode.

5.2. BUTTONS 37

Figure 5.2: The Help Menu

5.2.12 Help

The “Help” button in the Assessment and Learning Modes provides detailed assist-ance with use of the Answer Editor (Fig. 5.2). The Help Menu contains a list ofquestions on how to use the various icons of the Answer Editor; clicking any one ofthese leads to a brief refresher tutorial on the use of the icon.

5.2.13 MyPie

Clicking on “MyPie” produces a pie chart display reflecting the current state of thestudent’s mastery in the Learning Mode (See Sec. 4.13). The student can use thisbutton to select a new concept to work on from among those currently most “readyto learn.”


Figure 5.3: Item Page

5.3 The Learning Mode Interface

5.3.1 Item Page

After clicking on the name of an item from their pie chart, the student comes to anitem page containing the title of the current item, such as “Absolute Value of a NegativeInteger,” followed by a problem or instance of that item (Fig. 5.3). Mathematical termsare underlined and set off as hyperlinks (clicking on these will open the Dictionary).There is, however, no Answer Editor: the answer to the problem must be given on thePractice page.

Underneath the problem are two buttons, “Practice” and “Explain.” Clicking on “Ex-plain” goes to a detailed explanation of the item with additional Dictionary links. Click-ing on “Practice” goes to a page containing the Answer Editor and provides the oppor-tunity to attempt solving the problem.

5.3. THE LEARNING MODE INTERFACE 39

Figure 5.4: Explanation Page

5.3.2 Explanation Page

Like the item page, the explanation page (Fig. 5.4) begins with the title of the currentitem and an instance of that item. The answer to the problem is supplied at the end ofthe explanation.

Here again, mathematical terms are linked to Dictionary definitions. The system maysuggest looking up certain key terms to help with the explanation (especially if the ex-planation has already been visited). At the bottom of the page is the “Practice” button.Clicking on this button produces a new instance of the same problem-type. Sometimesthere may also be a button for “Additional Explanation” or “Detailed Explanation.”

You can always return to the pie chart to choose a different topic by clicking on the“MyPie” icon.

5.3.3 Practice Page

This page displays an instance of the problem, followed by the Answer Editor. This iswhere a solution to the problem can be attempted (Fig. 5.5). All practice problems aregenerated by algorithms with random selection of numerical values values so that thevariety of problem instances for any item is very great.

Underneath the Answer Editor are buttons labeled “Next” and “Explain.” Clickingon “Next” has the same effect as described for the Assessment Mode: it submits the


Figure 5.5: Practice Page

answer. Here, however, the user finds out immediately whether the answer is right orwrong. If it was correct, a new problem is presented or (if the system believes this topichas been mastered) a choice of new items is offered. Wrong answers will return thepresentation of the original problem (on the Wrong Answer page) with feedback on thestudent’s error. Students can then click on “Explain.”

5.3. THE LEARNING MODE INTERFACE 41

Figure 5.6: Wrong Answer Page

5.3.4 Wrong Answer Page

The wrong answer page appears only after an incorrect answer has been submitted onthe practice page (Fig. 5.6). It is identical to the previous page except that the systemexplains the answer is wrong, and offers advice on what went wrong and which wordsmight be looked up in the Dictionary.

The old, incorrect answer appears in the Answer Editor, where it can be corrected andresubmitted. Again, clicking on “Explain” is an option that leads to an explanation ofthe problem.

5.3.5 Dictionary

The online mathematics dictionary is always available in the Learning Mode. In additionto the Dictionary menu (button), links to the Dictionary appear in explanations, itemdescriptions, and in the feedback.

Clicking on a link to the Dictionary creates a new window on top of the ALEKS in-terface. At the top of the window is a bar with an Index button and text entry field(Fig. 5.7). The “Index” button gives access to an index of all the Dictionary’s head-ings and subheadings. Beneath this bar is the Dictionary entry, with links to otherentries and graphic illustrations as appropriate. The window can be closed after use orminimized for quicker access the next time needed.


Figure 5.7: Dictionary

5.4 Feedback in Learning Mode

In the Learning Mode feedback is integrated into a sophisticated system of guidancefor the student. Some errors prompt ALEKS to give specific hints and suggestions(Fig. 5.6). For example, it may say that a fractional answer needs to be reduced or thata list of expressions is incomplete. After a right answer the system will ask a limitednumber of questions for the same concept before judging that it has been mastered.If an item is missed too many times, however, a new topic will be suggested. If aconcept has been left without mastery being attained, however, the system may suggestreturning to it after one or two other topics have been covered.

5.5 Review

A student using ALEKS can review topics recently worked on in the Learning Modeby using the “Review” button (Fig. 5.8). Clicking on any of these topics provides thechance for additional practice; this is particularly useful when the student knows that anew assessment is imminent. When the student has not yet worked in Learning Modesince a new assessment, this list may be empty. “More Extensive Review” gives acomprehensive list of all topics mastered by the student for brief, summary review.

The Review page also contains a link to the Worksheet (See Sec. 5.6).

NOTE. The system will sometimes automatically offer a student the option of reviewing

5.6. WORKSHEET 43

Figure 5.8: Review

past material at the time of login.

5.6 Worksheet

A student using ALEKS can obtain an individualized, printable homework sheet (in.pdf format) containing 16 practice questions based on the student’s most recent workin ALEKS by clicking the “Worksheet” button (or the “Review” button) (Fig. 5.9).When the student does this, a sheet containing answers for this individual worksheet(labeled with the student’s name and the date) is sent to the teacher via the ALEKSmessage system (See Sec. 7.13). The teacher may set the option for this feature so thatthere are 12 review questions and 4 “Extra Credit” questions (See Sec. 7.17).

A record will be kept on the Worksheet page of all worksheets produced by the student.The student can click on the link for any past worksheet in order to obtain that work-sheet again. If the teacher has permitted access to worksheet answers, there will alsobe links on this page to answer keys for each of the worksheets (See Sec. 7.17).

NOTE. In order to view or print documents in .pdf format, such as the ALEKS work-sheet, Adobe Acrobat or Adobe Acrobat Reader must be installed on your computer.Most computers have this software. If for any reason your computer does not, there isa link on the ALEKS Worksheet page to download it. Also, because the worksheet isopened in a new browser window, it may be necessary to disable your popup blockertemporarily in order to produce the ALEKS worksheet.


Figure 5.9: Worksheet

5.7 Ask a Friend

Under some circumstances, a button marked “Ask a Friend” will appear at the bottomof the page in the Learning Mode, next to the “Explain” button. Clicking on thisbutton enables the student to ask for help from another student using ALEKS in thesame class.

The button appears only if (1) the teacher or school administrator has made this featureactive, (2) the student was unsuccessful in answering this concept, and (3) there isanother student who has successfully answered the concept and who has chosen toparticipate in the “Ask a Friend” component.

Chapter 6

Teacher Module: Basic Interface

The basic interface to the ALEKS Teacher Module was designed for the greatest possibleease of use. Although all parts of ALEKS can be used without training or documenta-tion, the wealth of features in the Teacher Module is not easily grasped by a first-timeuser. The basic interface, to address this need, has been constructed to be a fully func-tional, menu-driven gateway to the ALEKS Teacher Module. Once common operationsare familiar, the teacher may prefer to bypass the basic interface and work directly inthe advanced interface, which is somewhat more powerful, especially in the fewer stepsneeded to accomplish tasks and in the possibilities for combining tasks and workingwith groups.

Wherever possible in this chapter, descriptions of operations in the basic Teacher Mod-ule are cross-referenced to descriptions of similar operations in the Advanced TeacherModule.

The essential method of the basic interface is what software designers call the “wizard.”This method breaks a task down into steps and leads the user through those steps,asking questions and confirming the accuracy of information and decisions as it goes.The wizard minimizes the likelihood that the user will become lost or confused or takean unintended action while using the system. The use of the wizard interface involvesa tradeoff between the number of steps required for a given action and the degree offamiliarity expected of the user.

Throughout the Teacher Module (as we will call the basic interface in this chapter)there is a left-hand sidebar with links to the major areas of the Teacher Module: “Howdo I,” “Class Admin,” “School Admin” (available to users with Administrator status),“Reporting,” “Taking Actions,” and “Advanced” (Fig. 6.1). The links are all activewhen the user has selected a class for the focus of Teacher Module functions. Theseareas will be explained in the following sections. Also, each page of the Teacher Modulecontains a link to the Message Center, which can be used at any time to send queriesor messages to ALEKS Corporation Customer Support.

Like the Advanced Teacher Module, the basic Teacher Module offers different capacities

45

46 CHAPTER 6. TEACHER MODULE: BASIC INTERFACE

Figure 6.1: Teacher Module

to users who are registered in ALEKS with Administrator status, as opposed to thosewith Teacher status. Essentially, a Teacher has control only over those classes for whichshe or he is the teacher; an Administrator has control over all classes for all teachers inthe school, exactly as though he or she were the teacher for each of those classes.

In the following, the parenthetical notation “(Administrator)” indicates which areas,operations, and parts of operations are available only to users with Administrator status.

6.1 How do I

The first page to appear when you log on to your Teacher Module account is a list ofthe classes currently set up in your Teacher account. Click on one of these classes toindicate that it will be the focus of your next actions. You can change the class youare working with at any time by using a menu of current classes just at the top of yourTeacher Module page (labeled “My Class”). It is also possible to create a new classfrom this initial page, using the link at the bottom marked “Create a new class.”

The first thing you will notice on the home page of the Teacher Module (called “Howdo I”) is a brief list of the most common actions that you may wish to take (e.g.,

6.1. HOW DO I 47

Figure 6.2: How do I Questions

“Customize this class’). Click any one of these items to initiate the action.

Underneath this list is menu of questions. These questions correspond to a longer listof the most frequently performed operations in the Teacher Module, such as “Howdo I change someone’s password?” or “How do I create a new teacher account?” Bychoosing the last item, “More,” in the menu, or clicking “full list,” you can see the entirelist of questions, arranged by category (Fig. 6.2). These categories are also includedin the links featured in the left-hand sidebar of the Teacher Module: “Class Admin,”“School Admin” (Administrator), “Reporting,” “Taking Actions,” and “Advanced.”Along with “How do I” (for the home page), these are available from anywhere in theTeacher Module.

The questions on “How do I” are simply a way of getting quickly to the tutorial de-scriptions found in the Teacher Module. For example, clicking on “How do I move astudent from one class to another?” brings you to the page for “Move a student fromone class to another,” which can also be found by clicking the sidebar link for “ClassAdmin.”

The “How do I” page contains an email link and telephone number for contactingALEKS Corporation Customer Support. Questions and messages can also be sentdirectly to ALEKS Corporation Customer support using the Message Center links found


Figure 6.3: Class Admin

on each page of the Teacher Module.

6.2 Class Admin

Class Admin is concerned with the creation and management of classes in ALEKS, andis available to all teachers for ALEKS in a given school (Fig. 6.3). This area of theTeacher Module will be needed especially around the beginning of a new term or class,and also as the term proceeds, when students complete domains in ALEKS and needto be moved up to new ones.

6.2.1 Create a new course

See also Section 7.17.� (Administrator) click on a name from a list of existing teachers;� enter name of class, choose topic, and click “Save”;� receive Class Code for new class, with option for further customization (below).

6.2. CLASS ADMIN 49

6.2.2 View all your courses and course codes

This command is useful for obtaining an overview of the classes you are teaching.� for each class (Administrator: for each teacher), view name, topic, teacher (Ad-

ministrator), number of students, and Class Code.

6.2.3 Customize a course

See also Section 7.18.� click “Course name or topic taught; edit name and topic of class and click “Save”;� click “Textbook used for teaching”; choose textbook to be linked to class in ALEKSand click “Next”; set dates for completion of textbook chapters and click “Save”;� click “Content editor”; click boxes to remove topic areas from class coverage andclick “Save” (see also Section 7.24);� click “Content List”; view list of topics currently included in class coverage; clickindividual topics to see sample problems;� click “Worksheet”; check options for access to Worksheet answers and click “Save”;

ALEKS has powerful features for organizing the content of courses according to thetextbook being used. Please see Sec. 7.19 for a complete description.

6.2.4 Password issues

See also Section 7.21.� click on name from list of students in class;� enter new password twice and click “Save.”

6.2.5 Account preferences

See also Section 7.16.� edit own title, name, status options, email, and email/message options and click“Save.”

6.2.6 Student Account preferences

See also Section 7.21.� click on name from list of students in class;� edit name, email, and active status of student and click “Save.”


6.2.7 Move a student from one class to another

See also Section 7.20.� click on name from list of students in class;� click on name from list of classes (Administrator: for each teacher) to move studentto that class.

NOTE. This procedure is fine for moving one student at a time. If groups of studentsneed to be moved, see Section 7.20.

6.2.8 Unenroll a student from a class

See also Section 7.20.� click “Select All” if all students are to be unenrolled, or click “Select None” tocancel section, or click the names of students to select them individually, and thenclick “Next”;� click “Confirm” to confirm unenrollment of student or students.

6.2.9 Delete a class

See also Section 7.18.� click “Confirm” to confirm deletion of empty class.

Note that a class must be empty (contain no students) before it can be deleted. Seeabove, “Unenroll a student from a class.”

6.3. SCHOOL ADMIN (ADMINISTRATOR) 51

Figure 6.4: School Admin

6.3 School Admin (Administrator)

School Admin allows the ALEKS Administrator(s) for a given school to create andmanage the accounts of teachers using ALEKS, and is accessible only to users with Ad-ministrator status (Fig. 6.4). In most cases, teachers, once they are enrolled in ALEKS,will be able to manage their own accounts, and will require little or no assistance fromthe Administrator.

6.3.1 Create a new teacher account

See also Section 7.15.� fill in title, name, and administrator status (Administrator) and click “Next”;� edit Login Name, set Password, and click “Save”;� option to create classes for new teacher (below).

6.3.2 Password issues

See also Section 7.16.� click on a name from a list of existing teachers (including self);� enter new password twice and click “Save.”


6.3.3 Teacher account preferences

See also Section 7.16.� click on a name from a list of existing teachers (including self);� edit title, name, status options, email, and email/message options and click “Save.”

6.3.4 Move a class from one teacher to another

See also Section 7.18.� click on a name from a list of existing teachers (including self) to transfer class tothat teacher.

6.3.5 Delete an Teacher Account

See also Section 7.16.� click on a name from a list of existing teachers (including self);� click “Confirm” to confirm deletion of teacher account (possible only if the teacherdoes not currently have classes in ALEKS).

6.4. REPORTING 53

Figure 6.5: Reporting

6.4 Reporting

Reporting should be used frequently during a class taught with ALEKS to monitor thestudents’ use of and progress in the system.

After you click on the link for “Reporting,” a series of options for reporting will beshown (Fig. 6.5).

6.4.1 Class Progress options

The rows in the “Progress” views contain bar graphs showing students’ performanceon and following dated assessments. You can use the students’ Login Names or id’srather than their names as the identifier in the left-hand column; simply click on thecorresponding link at the top of that column. This may be useful when the data fromthis page needs to be downloaded and stored in a particular format for administrativepurposes.

Each student’s name is linked to their individual Progress page (See Sec. 6.4.17).


6.4.2 Download Excel spreadsheet

A link at the top of the page allows you to download the data in Excel spreadsheetformat.

6.4.3 Sorting

The information in the Class Progress page can be sorted on any of the columns. Simplyclick on the header or footer of a column to sort on that column; a second click switchesbetween ascending and descending order.

6.4.4 Statistical information

Most display options provide additional types of statistical information on studentprogress in the right-hand part of the display. Their significance varies according tothe display option, and is indicated in the column headings. One or more fields maybe blank if the information gathered for that student is not sufficient at a particulartime. It is also possible to choose “Time to Completion”; this indicates the estimatedtime necessary for individual students to complete the course goals based on averageprogress for the period chosen. Where the Intermediate Objectives are in use, this alsoshows “Time to Current Objective” (See Sec. 7.23).

6.4. REPORTING 55

Figure 6.6: State standards report

6.4.5 State standards report

State standards report analyzes the current progress of the class in terms of thestrands and substrands of the applicable state standards. For each strand, a verticalbar graph at the top of the display shows the satisfaction of that strand as measuredby ALEKS; the numbers beneath each bar indicate the proportion of substrands underthat strand which have been satisfied by the students, according to the parameters setbeneath the bars. The options appearing beneath the bars enable the teacher to choose:� what percentage of ALEKS items supporting a substrand must be completed by a

student for the student to be considered as having satisfied that substrand;� how the students’ mastery of items will be determined: by initial assessment, bymost recent assessment, or by most recent work in the Learning Mode;� which students will be used to calculate levels of achievement: all students in theclass, or students who have spent certain amounts of time (10, 20, 40, or 60 hours)using their ALEKS accounts.

Further down the page, the display provides complete detail on standards-based achieve-


ment by the class. The teacher can choose to see this detail organized by student (whichsubstrands have been mastered by each student) or by substrand (what the preciselevel of satisfaction is for each substrand, with lists of ALEKS items supporting thesubstrands and how many of them individual students have mastered).

This report is also available in the Advanced Teacher Module (See Sec. 7.8).

6.4. REPORTING 57

Figure 6.7: Individual learning progress since latest assessment

6.4.6 Individual learning progress since latest assessment

Individual learning progress since latest assessment displays a list of the studentsin the class, each with a single bar graph showing the most recent assessment andprogress made since that assessment (Fig. 6.7). All students who have completed atleast one assessment have bar graphs. The blue portion of the bar graph shows masteryas of the most recent assessment, and the green portion shows progress in the LearningMode since that assessment.


Figure 6.8: Individual detailed progress history

6.4.7 Individual detailed progress history

Individual detailed progress history displays a list of the students in the class, eachwith a series of bar graphs for each assessment taken to date (Fig. 6.8). For each studentwho has taken at least one assessment, there is a bar graph shown for each assessmenttaken in the last 6 months (other periods may also be chosen). The blue part of thebar shows mastery on the assessment, and the green part additional mastery achievedin Learning Mode following that assessment (but before any subsequent assessment).

6.4. REPORTING 59

Figure 6.9: Individual overall progress in assessment

6.4.8 Individual overall progress in assessment

Individual overall progress in assessment displays a list of the students in theclass, each with a single bar graph showing the progress made between that student’sfirst and most recent assessments (Fig. 6.9). All students who have completed at leasttwo assessments have bar graphs. The blue portion of the bar graph shows mastery asof the first assessment, and the light blue portion shows progress made between thatassessment and the most recent assessment taken.


Figure 6.10: Scheduled Assessment Report

6.4.9 Scheduled assessment report

Scheduled assessment report shows the results of an assessment that has been sched-uled for the class in the form of a series of bar graphs (Fig. 6.10). The blue portion ofeach bar graph shows the student’s knowledge as measured by the assessment; subse-quent progress in Learning Mode is not shown in this view. Grades for the assessmentare shown if the teacher has chosen to grade the assessment (See Sec. 6.5.1). A menuat the top of the display can be used to choose earlier scheduled assessments.

6.4. REPORTING 61

Figure 6.11: Average report (pie chart)

6.4.10 Average report (pie chart)

Average report (pie chart) displays one or more combined pie charts for the class,showing its average progress toward mastery of the curriculum (Fig. 6.11).

6.4.11 Display options for Average Report

Beneath the pie charts there are other kinds of analysis available for class assessmentdata. Choose “Average,” “Ready to learn (learning),” “Ready to learn (assessment),”“What students can do (learning),” or “What students can do (assessment)” from the“Display Mode” menu and click on “OK” to display results.

6.4.12 Average

This option produces a list of the specific concepts mastered by a percentage of thestudents, as of their most recent assessment. The list is organized by general categories(Fig. 7.6). For each concept, the percentage of students in the class who demonstratedmastery is given.


6.4.13 Ready to learn

This option also shows a list of specific concepts, organized by general categories. Foreach concept, it shows the number of students in the class who are ready to learnthat concept in the Learning Mode (learning) or as of their most recent assessment(assessment). Clicking on the number of students will display a list of their names;there also appears a link for sending a message to all the students in the group sodefined (See Secs. 7.12, 7.13). The button “Open All” displays all students’ names ineach group (with links).

6.4.14 What students can do

This option also shows a list of specific concepts, organized by general categories. Foreach concept, it shows the number of students in the class who have recently masteredthat concept in the Learning Mode (learning) or as of their last assessment (assessment).Clicking on the number of students will display a list of their names; there also appearsa link for sending a message to all the students in the group so defined (See Secs. 7.12,7.13). The button “Open All” displays all students’ names in each group (with links).

6.4. REPORTING 63

Figure 6.12: Quiz results for all the students

6.4.15 Quiz results for all the students

Quiz results for all the students shows the results on any given quiz for all studentsin the class who took the quiz (Fig. 6.12). Clicking on the Date Submitted for anyparticular quiz will give the individual results of that quiz by question. It will also bepossible to see the individual questions and the answers that the student submitted forthem. Please also note the option to view quiz results on a per-question basis, whichcan be useful in identifying the specific class strengths and weakness shown by the quizresults.


Figure 6.13: State standards report for a single student

6.4.16 State standards report for a single student

State standards report for a single student analyzes the student’s current progressin terms of the substrands of the applicable state standard. For each substrand, thepage indicates how many ALEKS items supporting that substrand have been masteredby the student, with detail available on the specific items mastered and not mastered.

This report is also available in the Advanced Teacher Module (See Sec. 7.6) and in thestudent’s own account (See Sec. 4.13.2).

6.4. REPORTING 65

Figure 6.14: Progress report for a single student in this class

6.4.17 Progress report for a single student in this class

Progress report for a single student in this class displays a list of bar graphs forthe single student chosen. There is one row for each assessment that the student hastaken, with dates (linked to the Report page for that assessment) (Fig. 6.14). Each rowcontains one to three bar graphs, depending on the student’s grade. Each bar graphmeasures the student’s mastery as of the given assessment as seen by the blue portionof the bar. Progress made in the Learning Mode subsequently to that assessment (butbefore the next assessment, if there is one) is measured by the green portion of the bar.There are also percentage values given beneath the bar for the blue and green portionsof the bars; for example, 57+9% means that the last assessment showed 57% mastery,and that subsequent work in the Learning Mode added another 9% mastery. If thereis more than one bar per row, they will correspond to the programs for the previousgrade, the current grade, and the subsequent grade.

Information on each assessment, total hours and weeks spent subsequently in the Learn-ing Mode (up to the time of the next assessment) with average numbers of items gainedper hour and per week is also provided (optionally, this shows the time left to completionof course goals).


Figure 6.15: Report for a single student in this class

6.4.18 Report for a single student in this class (pie chart)

Report for a single student in this class (pie chart) displays one or more piecharts for the single student chosen, showing the student’s current progress towardmastery of the curriculum (Fig. 6.15). There is also a menu giving access to earlierpoints in the student’s progress.

Beneath the pie charts is a list of concepts that the student has mastered recently(“What Name Can Do”) and another list of concepts that the student is currently (asof the given assessment) most ready to begin learning (“Ready to Learn”). There mayalso be a summary of the student’s history in ALEKS (“History”) and a log of work inthe Learning Mode following that assessment (“Learning Log”). There are also buttonsallowing the teacher to request or cancel an assessment for that student and to editIntermediate Objectives (See Sec. 7.23).

6.4.19 Complete list of topics mastered

Click on the link “and many other more elementary concepts.” to see a complete list oftopics mastered by the student.

6.5. TAKING ACTIONS 67

Figure 6.16: Taking Actions

6.4.20 Quiz results for a particular student

Quiz results for a particular student shows the results for any given student onany quizzes taken by that student.

6.5 Taking Actions

Additional class management features are available under “Taking Actions” (Fig. 6.16).Many of these are ways of providing assignments to the students in the class.

6.5.1 Schedule a new assessment

See also Section 7.10.� provide name and date for assessment and click “Next” (Fig. 6.17);� provide start time for assessment with option for more detailed scheduling (preventautomatic assessment up to 7 days in advance, trigger assessment on specified dayonly, restrict assessment to school; assign grading scale to assessment) and click“Save.”

In order to schedule a class assessment, the teacher is asked to specify the name of theassessment (by default, a scheduled assessment is called “Requested Assessment” plus its


Figure 6.17: Schedule a new assessment

number), a date (by default the current date), and a time (by default the current time)(Fig. 7.8). “Detailed scheduling options” permit the teacher to restrict the assessmentto campus and to limit the time when it can be begun. When this information has beengiven, the teacher schedules the assessment by clicking “Save.” If all the defaults areleft, the students will immediately enter Assessment Mode at their next login. If a laterdate and/or time are chosen, the students will enter Assessment Mode the next timethey log in after that date and time. The calendar graphic provides a quick and easyway to choose the date of an assessment (click on the calendar thumbnail to use thisfeature).

NOTE. A Progress Assessment will tend to focus its questions on the material mostrecently learned by the student, and will be shorter than a Comprehensive Assess-ment. A Comprehensive Assessment is a bit longer, but will question the student morecomprehensively on material covered in the course product. If an assessment is beinggiven to determine students’ overall mastery at the end of a course, the ComprehensiveAssessment should be used.

NOTE. In some ALEKS products, there is an option to request the assessment on aparticular slice or slices of the pie chart. When this is done, there will be a note regardingthe estimated number of questions needed for the assessment. Often, assessing on morethan one slice of the pie chart will result in an assessment that is longer than desired;therefore, this feature is usually most effective when only a single slice is selected. Theteacher also has the option of letting ALEKS select an appropriate slice for each student,based on their individual progress.


Figure 6.18: Grading with Scheduled Assessment

6.5.2 Detailed scheduling options

You can block automatic assessments for up to 7 days prior to a scheduled assessment(useful to avoid having some students assessed twice in a row); limit the effect of ascheduled assessment to the day it is assigned to or control the period of time duringwhich it is in effect. If an assessment is limited to the assigned day, a student loggingon to ALEKS on that day (after the start time) will be assessed, but if the studentdoes not log on that day that student will not be assessed until the next automaticor scheduled assessment. The period during which the assessment is in effect can beextended for a number of days.

6.5.3 Grading with Scheduled Assessments

You can assign a grading scheme to this assessment only. The Grades feature uses achart with sliders (Fig. 6.18). The grades received by students on scheduled assessmentscan be seen under “Scheduled Assessment Report” (See Sec. 6.4.9).

The three buttons under the graph determine the use of the evaluation: if “Disabled,”no one sees it; if “Private,” the teacher sees it but the students do not; if “Public,” theteacher sees it and each student sees it for their own work.

The graph has sliders, with labels referring to the intervals they define. Additionalsliders may be placed by dragging the right-hand or left-hand sliders, or sliders may beremoved by dragging them off to the right or left. The sliders may be set and the labels


edited as the teacher desires. To change the label on a new or existing slider, select thetext of the current label, retype as desired, and then press “Return.”

6.5.4 Cancel an assessment

See also Section 7.10.� click on name from list of scheduled assessments;� click “Save” to confirm cancellation of assessment.

6.5.5 Change the name, date, grading scale of an assessment

See also Section 7.10.� click on name from list of scheduled assessments, with option to schedule newassessment;� click link to modify grading scale, name, date, or other property of assessment;� modify settings and click “Save” (possible option for more detailed settings).

6.5.6 Create a quiz

See also Section 7.11.� enter a name for the quiz, or leave the name provided (“Quiz N”), and click “Next”(you can also use the link provided to copy an existing quiz, if there is a quiz inexistence for this kind of class);� select from the list of topics in the left-hand window either by dragging topics intothe right-hand window, or by highlighting topics and clicking “Add”, then click“Save”;� use the links provided to continue editing the topics on the quiz, assign a gradingscale, change how the quiz is made available to your students, or assign the quizto some group of students within the class.

NOTE. Often it is necessary to provide a “makeup” quiz to some students. This caneasily be done by copying the original quiz, then editing it so that it is assigned only tothe students needing the makeup.

6.5.7 Tips for making quizzes

Double-click on the name of any topic to see a sample problem. Topics can be selectedin continuous groups using the Shift key or discontinuous groups using Ctrl; the entirefolder is selected by using Ctrl-a.


The Quiz feature in ALEKS allows teachers to create quizzes for their students usingany topics in the ALEKS domain. These quizzes are administered through ALEKS andscored automatically, with optional use of a grading scale set by the teacher. Quizzesmay be scheduled for particular days and times, or they may be made available for thestudents in a class to take when they are ready (“Homework Quiz”). The results ofquizzes can be seen through the reporting features of ALEKS, but do not influence thestudents’ knowledge states or their guided learning in ALEKS.

6.5.8 Grading with quizzes

The grading scale used with quizzes is like the one used for assessments (See Sec. 6.5.3).As with assessments, grading is not obligatory; if no grading scale is set, the studentsand the teacher will only see the percentage of questions answered correctly.

6.5.9 Availability of quizzes to students.

By default, quizzes are made available to students as “Homework Quizzes.” This meansthat the student is not forced into the quiz by ALEKS; rather, the student clicks the“Quiz” button when they are ready to take the quiz (See Sec. 5.2.10). If this option ischosen, the teacher must indicate a due date for the quiz, after which the quiz will nolonger be available to students. A message can also be sent to students informing themthat the quiz has been assigned.

Quizzes may also be “hidden” for later availability to students (“Don’t make this quizavailable yet”), or they may be scheduled. A graphic calendar is provided for easyscheduling of quizzes. If the quiz is scheduled, the teacher will have options for specifyingthe time of day it is to begin, the time limit on the quiz, whether students are notified,how many days the quiz should be in effect (“Window of time to take the quiz”), whetherthe quiz is restricted to the school, and prevention of automatic assessments up to fivedays before the quiz is scheduled.

The quiz may be assigned to all the students in the class or, optionally, to some groupwithin the class.

6.5.10 Edit a quiz

See also Section 7.11.� click on name from a list of existing quizzes;� modify the quiz using the features described above.

6.5.11 Delete a quiz

See also Section 7.11.

72 CHAPTER 6. TEACHER MODULE: BASIC INTERFACE� click on name from a list of existing quizzes;� click on “Confirm” to delete the quiz, or “Cancel” to leave it.

6.5.12 Authorize a student account

See also Section 7.22.

NOTE. If there are students waiting for authorization, there will be a notificationappearing to the teacher immediately upon login. You can click on the link in thisnotification to go directly to the authorization page (See Sec. 3.8).� if there are any students waiting for authorization, check the “Authorize” box next

to their names, or use the option “Authorize every account below”;� click the “Delete” box for any duplicate names, then click “Next”;� check the availability of licenses for new students, then click “Next” to completethe authorization process. Clicking “Back” will enable you to modify your selectionof students for authorization.

6.5.13 View/Create Worksheets for a single student

See also Section ??.

This link lets you view all worksheets generated for particular students in your class,and also generate worksheets for particular students.

6.6 Advanced

On clicking this link, the user is shown a brief explanation of how the Advanced TeacherModule differs from the standard one (Fig. 6.19).

Teachers using ALEKS should not be intimidated about trying the advanced interface.It is a visual or graphic (“point and click”) interface based on a model of directories, files,and actions applied to files and directories, which is essentially shared by all moderncomputer systems. With even slight familiarity, most users will have no difficulty usingit (See Chapters 7-8).

6.6.1 Show me a tutorial for the “Advanced” Teacher Module.

The Tutorial for the Advanced Teacher Module is a complete guide to the most commonly-used features of this area (See Sec. 7.2). From within the Advanced Teacher Module,it is possible to retake the Tutorial at any time or to review parts of it by using the“Help” button.� click “Next” to enter the Tutorial for the Advanced Teacher Module.

6.6. ADVANCED 73

Figure 6.19: Advanced

6.6.2 Enter the “Advanced” Teacher Module now.

When a teacher has achieved a certain level of familiarity with the Teacher Module,she or he may wish to try using the advanced interface, or even to use the advancedinterface exclusively. As noted, the Advanced Teacher Module has certain advantagesof efficiency and flexibility, especially in operations affecting groups of students.� click “Next” to enter the Advanced Teacher Module (optionally, set your prefer-

ences to log directly into the Advanced Teacher Module when using this account).

Chapter 7

Advanced Teacher Module: Results &Progress

7.1 The ALEKS Advanced Teacher Module

The Advanced Teacher Module interface provides an array of features enabling teachershaving some familiarity with ALEKS to carry out management and monitoring of theirclasses with more efficiency and power. The Advanced Teacher module is entered fromthe basic Teacher Module by clicking “Advanced”; teachers may also choose to makethe advanced interface their default interface for the ALEKS Teacher Module. Teachersusing the Advanced Teacher Module can return to the basic Teacher Module at anytime by using the link, “Go to the Basic Teacher Module,” located at the top of theAdvanced Teacher Module window.

7.2 Teacher Tutorial (Advanced Teacher Module)

The Tutorial for the Advanced Teacher Module is designed to parallel the function ofthe Tutorial taken by all student users of ALEKS when they first register with thesystem. It introduces the teacher to the features of the ALEKS Advanced TeacherModule in a brief, but thorough, interactive way, and will give teachers who choose thisinterface confidence in carrying out the operations needed to effectively monitor andmanage their ALEKS classes.

The Tutorial for the Advanced Teacher Module reproduces the advanced ALEKS inter-face and poses the teacher a series of tasks involving the interface tools (Fig. 7.1). Theteacher proceeds to the next page by carrying out the current task; feedback is providedto guide the teacher through all needed actions.

Teachers will normally take the Tutorial at the time that they begin to explore or use theAdvanced Teacher Module interface. The Tutorial can be skipped; a teacher who has

75

76 CHAPTER 7. ADVANCED TEACHER MODULE: RESULTS & PROGRESS

Figure 7.1: Tutorial for the Advanced Teacher Module

skipped part of the Tutorial can return to where they left off or restart from scratch.Also, the Help page contains an index, which links to every section of the Tutorial.Current teachers may take the Tutorial at any time by clicking the link marked “Showme a Tutorial” at the top of the Advanced Teacher Module window. (An teacher whohas chosen to skip all or part of the Tutorial sees “Return to the Tutorial.”)

7.3. ACCESS TO THE ADVANCED TEACHER MODULE 77

Figure 7.2: The Results and Progress Directory (Advanced Teacher Module)

7.3 Access to the Advanced Teacher Module

When you enter the Advanced Teacher Module with teacher status, you will see adirectory containing only your own classes. If you have an administrator account youwill see all of the teacher directories for your school. If you have a root administratoraccount you will see directories for all schools under your administration (Fig. 7.2).

NOTE. The directory window is called the “Selector.” It is the chief graphic navigationtool of the Advanced Teacher Module. You can always return to the Selector by scrollingyour browser window up. Similar Selector windows are used in other areas of theAdvanced Teacher Module for special purposes.

If you have a teacher account, the system features at your disposal can affect only yourclasses and the students under your supervision. If your account is that of a schooladministrator, your privileges are similar, but extend to all the classes and all of thestudents in the school. If your account is that of a root administrator (e.g., over anentire school district), your privileges extend to all schools under your administration.In the following, we assume that your account is that of a school administrator.

The Advanced Teacher Module has two parts: “Results & Progress” and “Standards& Programs.” When you enter the Advanced Teacher Module, you are automaticallyplaced in “Results & Progress.” Use the ALEKS menu bar to change the part of theAdvanced Teacher Module in which you are working (See Chapter 8).

“Results & Progress” is used for most administrative tasks, such as monitoring individ-


ual and group progress. Teachers using ALEKS with one or more classes will probablywish to check into this part of the Teacher Module on a daily basis. This allows theteachers to verify the rate of progress achieved by the students. The features also enableteachers to set up additional classes if they need to.

The following sections describe the various actions that can be carried out by teacherswith appropriate levels of privilege in the Advanced Teacher Module.

7.4 Online Help in the Advanced Teacher Module

Context-sensitive online help in the Advanced Teacher Module can be obtained byclicking on “Help” in the bar at the top of the window (next to the “Message” button).

Bulletin Board and Mailing List. The “Help” button also gives access to theALEKS bulletin board and mailing list for teachers. The purpose of these features isto allow teachers using ALEKS to exchange information and viewpoints on teachingmethods, strategies, and the like. They can also be accessed from the ALEKS websiteby registered teachers (click on “Help”).

7.5. VIEW STUDENT PROGRESS 79

Figure 7.3: Student Progress (Advanced Teacher Module)

7.5 View Student Progress

To view student progress, select the name of the student and click on the “Progress”button. A chart will appear below the directories window with one or more rows ofinformation (Fig. 7.3). There is one bar graph for each assessment that the studenthas taken, with dates (linked to the Report page for that assessment). Each bargraph measures the student’s mastery as of the given assessment as seen by theblue portion of the bar. Progress made in the Learning Mode subsequently to thatassessment (but before the next assessment, if there is one) is measured by thegreen portion of the bar. There are also percentage values given beneath the barfor the blue and green portions of the bars; for example, 57+9% means that thelast assessment showed 57% mastery, and that subsequent work in the LearningMode added another 9% mastery. If there is more than one bar per row, theywill correspond to the programs for the previous grade, the current grade, and thesubsequent grade.

A variety of other information, clearly labeled, is provided on the Progress page: dateof last login, enrollment date, total hours spent on the system. Information on eachassessment, total hours and weeks spent subsequently in the Learning Mode (up tothe time of the next assessment) with average numbers of items gained per hour andper week is also provided (optionally, this shows the time left to completion of coursegoals). There are also buttons allowing the teacher to schedule or cancel an assessment


for that student and to edit Intermediate Objectives (See Secs. 7.9, 7.23), and a link fordownloading this information to the teacher’s computer.

Downloading. Information from the Student Progress page can be downloaded intwo formats. “Spreadsheet Format” is comma-separated values (CSV), which can beimported into a variety of applications but is raw in appearance. “Excel Format” is inMicrosoft Excel format, and has a legible, professional appearance, suitable for printing.

Monitoring progress. When a student has spent enough time on ALEKS to havehad two or more assessments, the sequence of bar graphs appearing on the StudentProgress page begins to tell a clear story of the student’s success in moving towardmastery. There may be considerable difference among individual students in the speedand smoothness of their progress. When one bar graph appears above another bargraph, the uppermost one represents a later assessment, in which the student seeksto confirm knowledge of material tentatively mastered in Learning Mode. For somestudents, progress in assessments is slower than that in Learning Mode. This can beseen when the green portion of one bar graph extends further to the right than theblue portion of the bar graph above it (not everything covered in Learning Mode wasconfirmed subsequently in the assessment). For other students the opposite is true:progress in assessments is faster than that in the Learning Mode. This can be seenwhen the green portion of one bar graph does not extend so far to the right as the blueportion of the bar graph above it (more knowledge was confirmed in the assessment thanhad been covered previously in Learning Mode). When a student is frustrated, this willbe obvious from the bar graphs; in such cases the teacher may need to provide extrahelp or encouragement. It is well worth the teacher’s time to check daily on individualand class progress in ALEKS.

7.6. VIEW STUDENT ASSESSMENT REPORT 81

Figure 7.4: Student Report (Advanced Teacher Module)

7.6 View Student Assessment Report

Select the name of the student for whom you wish to observe a report and clickon the “Report” button. A display containing one or more pie charts will appearbeneath the directories window (Fig. 7.4). Its interpretation is the same as for thereports received by students following all assessments (See Sec. 4.13.1). By default,the Report page shows the most recent assessment or the most recent knowledgeattained in the Learning Mode. Other assessments or other Learning Mode reportsmay be chosen by selecting dates from the menu at the top of the chart and clickingon “OK.”

Dates. Each report in the menu at the top of the Student Report page is dated. Ifan assessment is begun on one date and finished on another, the begin and end datesare shown on the Student Report page, along with the amount of time spent in theassessment (the menu shows only the begin date). The date for a Learning report isthe last date on which the student worked in the Learning Mode before any subsequentassessment.


Figure 7.5: Class Progress (Advanced Teacher Module)

State standards report. In some states, there will also be an entry in this displaygiving access to the state standards report for this student. For a complete descriptionof this feature, see Sec. 6.4.16.

Beneath the pie charts is a list of concepts that the student has mastered recently(“What Name Can Do”) and another list of concepts that the student is currently (asof the given assessment) most ready to begin learning (“Ready to Learn”). There mayalso be a summary of the student’s history in ALEKS (“History”) and a log of work inthe Learning Mode following that assessment (“Learning Log”). There are also buttonsallowing the teacher to request or cancel an assessment for that student and to editIntermediate Objectives (See Secs. 7.9, 7.23).

Complete list of topics mastered. Click on the link “and many other more elemen-tary concepts” to see a complete list of topics mastered by the student.

7.7 View Class Progress

Select the class for which you wish to observe progress and click on the “Progress”button. A chart will appear below the directories window with a series of rows, onefor each student enrolled in the class (Fig. 7.5). The rows contain bar graphs (Seeinterpretation in “View Student Progress,” Sec. 7.5). By default, only the bar graphfor the most recent assessment is shown (the students’ names are linked to their

7.7. VIEW CLASS PROGRESS 83

individual Progress pages, while the assessment dates are linked to their individualReport pages). You can use the students’ Login Names or ids rather than their namesas the identifier in the left-hand column; simply click on the corresponding link atthe top of that column. This may be useful when the data from this page needs tobe downloaded and stored in a particular format for administrative purposes.

Report Style. A range of options providing variations on this format are accessiblethrough a menu at the top of the chart. Choose the desired format from the menu andclick on “Compute” to view results.

Of these options, the following have been found particularly useful by a wide rangeof users: “Progress in learning mode” (for frequent checks on progress and time spentin ALEKS), “Total progress” (for viewing the overall effectiveness of students’ use ofALEKS over a longer period of time, such as a term or semester), and “Full progressover last 6 months” (for convenient examination of the learning patterns followed bystudents in a class).

Progress in learning mode

All students who have completed at least one assessment have bar graphs. Theblue portion of the bar graph shows mastery as of the most recent assessment, andthe green portion shows progress in the Learning Mode since that assessment.

Total progress

All students who have completed at least two assessments have bar graphs. Theblue portion of the bar graph shows mastery as of the first assessment, and thelight blue portion shows progress made between that assessment and the mostrecent assessment taken.

Most recent progress

All students who have completed at least two assessments have bar graphs. Theblue portion of the bar graph shows mastery as of the assessment immediatelypreceding the most recent one, and the light blue portion shows progress madebetween that assessment and the most recent assessment taken.

Progress over last 6 months

All students who have completed at least two assessments within the last sixmonths have bar graphs. The blue portion of the bar graph shows mastery asof the first assessment taken within the last six months, and the light blue portionshows progress made between that assessment and the most recent one taken.

Progress over last 3 months

All students who have completed at least two assessments within the last threemonths have bar graphs. The blue portion of the bar graph shows mastery as ofthe first assessment taken within the last three months, and the light blue portionshows progress made between that assessment and the most recent one taken.

Progress over last month

All students who have completed at least two assessments within the last monthhave bar graphs. The blue portion of the bar graph shows mastery as of the first


assessment taken within the last month, and the light blue portion shows progressmade between that assessment and the most recent one taken.

Most recent assessment only

All students who have completed at least one assessment have bar graphs. Theblue portion shows mastery as of the most recent assessment.

Full progress over last 6 months

For each student who has taken at least one assessment, there is a bar graph shownfor each assessment taken in the last 6 months. The interpretation is the same asfor “Progress in learning mode”; that is, the blue part of the bar shows mastery onthe assessment, and the green part additional mastery achieved in Learning Modefollowing that assessment (but before any subsequent assessment).

Full progress over last 3 months

For each student who has taken at least one assessment, there is a bar graph shownfor each assessment taken in the last 3 months. The interpretation is the same asfor “Progress in learning mode”; that is, the blue part of the bar shows mastery onthe assessment, and the green part additional mastery achieved in Learning Modefollowing that assessment (but before any subsequent assessment).

Full progress over last month

For each student who has taken at least one assessment, there is a bar graph shownfor each assessment taken in the last month. The interpretation is the same as for“Progress in learning mode”; that is, the blue part of the bar shows mastery onthe assessment, and the green part additional mastery achieved in Learning Modefollowing that assessment (but before any subsequent assessment).

Scheduled Assessment

Underneath the “Report Style” menu is a second menu listing assessments thathave been scheduled for this class. To view the results of that assessment, selectthe name (with date) of the assessment and click “Compute” (See Sec. 7.10).

Buttons at the bottom of the page allow the teacher to schedule an assessment for allthe students taking the class and to download information from the page in a formatsuitable for spreadsheet display (See Sec. 7.10).

Statistical Information. Most display options provide additional types of statisticalinformation on student progress in the right-hand part of the display. Their significancevaries according to the display option, and is indicated in the column headings. One ormore fields may be blank if the information gathered for that student is not sufficientat a particular time. It is also possible to choose “Time to Completion”; this indicatesthe estimated time necessary for individual students to complete the course goals basedon average progress for the period chosen. Where the Intermediate Objectives are inuse, this also shows “Time to Current Objective” (See Sec. 7.23).

Assign Learning Rates. A link at the top of the Class Progress page provides accessto the learning rates feature (See Sec. 7.25).

7.7. VIEW CLASS PROGRESS 85

Sorting. The information in the Class Progress page can be sorted on any of thecolumns. Simply click on the header or footer of a column to sort on that column; asecond click switches between ascending and descending order.

Grouping. It is possible to create arbitrary groups within the class and generateProgress pages for these groups. Simply select the names of the students in the Selector:hold Shift to select a continuous range, or Ctrl to select a discontinuous group. Thenclick the “Progress” button.

Downloading. Information from the Class Progress page can be downloaded in twoformats. “Spreadsheet Format” is comma-separated values (CSV), which can be im-ported into a variety of applications but is raw in appearance. “Excel Format” is inMicrosoft Excel format, and has a legible, professional appearance, suitable for printing.


Figure 7.6: Class Report (Advanced Teacher Module)

7.8 View Class Report

Select the class for which you wish to view a report and click on the “Report”button. A display containing one or more pie charts will appear beneath the direc-tories window (Fig. 7.6). Its interpretation is the same as for the reports receivedby students following all formal assessments, except that it represents an analyticsummary of reports received by all students in the class. The period summarizedmay be changed using the menu at the top of the chart (click on “OK” to displayresults).

State standards report. In some states, there will also be a tab in this display givingaccess to the state standards report for this class. For a complete description of thisfeature, see Sec. 6.4.5.

Display options. Beneath the pie charts there are other kinds of analysis availablefor class assessment data. Choose “Average,” “Ready to learn (learning),” “Ready to

7.8. VIEW CLASS REPORT 87

learn (assessment),” “What students can do (learning),” or “What students can do(assessment)” from the “Display Mode” menu and click on “OK” to display results.

Average

This option produces a list of the specific concepts mastered by a percentage ofthe students, as of their most recent assessment. The list is organized by generalcategories (Fig. 7.6). For each concept, the percentage of students in the class whodemonstrated mastery is given.

By default, items are not listed if they have been learned by fewer than 5% or bymore than 95% of the students in the class. For a comprehensive list (0%-100%),click the link “Display full list.”

Ready to learn

This option also shows a list of specific concepts, organized by general categories.For each concept, it shows the number of students in the class who are readyto learn that concept in the Learning Mode (learning) or as of their most recentassessment (assessment). Clicking on the number of students will display a list oftheir names; there also appears a link for sending a message to all the students inthe group so defined (See Secs. 7.12, 7.13). The button “Open All” displays allstudents’ names in each group (with links).

What students can do

This option also shows a list of specific concepts, organized by general catego-ries. For each concept, it shows the number of students in the class who haverecently mastered that concept in the Learning Mode (learning) or as of their lastassessment (assessment). Clicking on the number of students will display a list oftheir names; there also appears a link for sending a message to all the students inthe group so defined (See Secs. 7.12, 7.13). The button “Open All” displays allstudents’ names in each group (with links).

Focusing instruction. These tools can be used to focus instruction for classes andgroups of students. The “Average” display shows very clearly which specific conceptsand general areas within the program need the most work for the greatest number ofstudents. Consequently, it can be used to prioritize topics for lectures and lesson plans.The “Ready to learn” display, on the other hand, makes it possible to break a largeclass up into small groups, each focused on the concept or concepts that it is workingon currently in Learning Mode. The “What students can do” display mode can be usedto form groups of students for special discussions and exercises designed to expand anddeepen their understanding of a concept they have all recently mastered. Where thereis not sufficient teaching staff to coach several groups simultaneously, the teacher maycall out small groups during their use of ALEKS for brief, pointed “chalk talks.”

At the bottom of the Class Report page there are buttons allowing the teacher toschedule an assessment for all the students in the class or to edit Intermediate Objectives(See Secs. 7.10, 7.23).

Grouping. It is possible to create arbitrary groups within the class and generateReport pages for these groups. Simply select the names of the students in the Selector:


Figure 7.7: Student Assessment (Advanced Teacher Module)

hold Shift to select a continuous range, or Ctrl to select a discontinuous group. Thenclick the “Report” button.

7.9 Schedule Student Assessment

Assessments for individual students may be requested or canceled using buttons on theProgress or Report pages for those students (Fig. 7.7). If more than one student nameis selected before clicking “Progress” or “Report,” the assessment will be requested forthat group of students. When the teacher has requested an assessment, the student orstudents will immediately enter the Assessment Mode at the next login. The teachercan specify whether the assessment is to be taken from any location or only from theschool.

NOTE. In some ALEKS products, there is an option to request the assessment on aparticular slice or slices of the pie chart. When this is done, there will be a note regardingthe estimated number of questions needed for the assessment. Often, assessing on morethan one slice of the pie chart will result in an assessment that is longer than desired;therefore, this feature is usually most effective when only a single slice is selected. The

7.10. SCHEDULE CLASS ASSESSMENT 89

Figure 7.8: Class Assessment (Advanced Teacher Module)

teacher also has the option of letting ALEKS select an appropriate slice for the student,based on that student’s individual progress.

NOTE. If an assessment is scheduled, whether by the teacher or automatically by thesystem, and the student is required to take the assessments at the school, the studentwill be unable to use the system from locations other than school until the assessmentis completed (See Sec. 7.17). Teachers wishing to constrain assessments in this wayshould contact ALEKS Corporation for assistance in determining the domain addressesused by their school.

7.10 Schedule Class Assessment

Assessments for entire classes may be scheduled using buttons on the Progress or Reportpages for those classes, or on the Edit page under the tab “Advanced.”

In order to schedule a class assessment, the teacher is asked to specify the name of theassessment (by default, a scheduled assessment is called “Requested Assessment” plus anumber), a date (by default the current date), and a time (by default the current time)(Fig. 7.8). The teacher can also specify whether the assessment can be taken anywhere(the default) or is restricted to campus. When this information has been given, theteacher schedules the assessment by clicking “Save.” If all the defaults are left, thestudents will immediately enter Assessment Mode at their next login. If a later dateand/or time are chosen, the students will enter Assessment Mode the next time they


Figure 7.9: Grading with Scheduled Assessment (Advanced Teacher Module)

log in after that date and time. The calendar appearing to the right of the input fieldsprovides a quick and easy way to choose the date of an assessment. The calendar alsoshows the dates of all currently scheduled assessments and days on which automaticassessments have been blocked.

At the bottom of the Class Assessment page all currently scheduled assessments arelisted. Clicking any of these links brings up the scheduled assessment for modificationor deletion. Use the “Delete Assessment” button to delete a scheduled assessment, orthe “Create New Assessment” button to add a new assessment from this page.

The tabs “Slices” (for some products), “Message,” “Grades,” and “Advanced” provideaccess to additional features affecting scheduled assessments.

Slices

In some ALEKS products, there is an option to request the assessment on a par-ticular slice or slices of the pie chart. When this is done, there will be a noteregarding the estimated number of questions needed for the assessment. Often,assessing on more than one slice of the pie chart will result in an assessment thatis longer than desired; therefore, this feature is usually most effective when only asingle slice is selected. The teacher also has the option of letting ALEKS select anappropriate slice for each student, based on their individual progress.

Message

Add a special message to accompany the automatic message which students receiveinforming them that they are entering a scheduled assessment. If you prefer thatthe students not receive a message, cancel the automatic message.

Grades

Assign a grading scheme to this assessment only. The Grades feature uses a chart

7.11. CREATE, EDIT, VIEW QUIZZES 91

with sliders (Fig. 7.9). The grades received by students on scheduled assessmentscan be seen under Class Progress using the “Scheduled Assessment” menu (SeeSec. 7.7).

The three buttons under the graph determine the use of the evaluation: if “Dis-abled,” no one sees it; if “Private,” the teacher sees it but the students do not; if“Public,” the teacher sees it and each student sees it for their own work.

The graph has sliders, with labels referring to the intervals they define. Additionalsliders may be placed by dragging the right-hand or left-hand sliders, or slidersmay be removed by dragging them off to the right or left. The sliders may beset and the labels edited as the teacher desires. To change the label on a newor existing slider, select the text of the current label, retype as desired, and thenpress “Return.”

Advanced

Block automatic assessments for up to 7 days prior to a scheduled assessment(useful to avoid having some students assessed twice in a row); limit the effect of ascheduled assessment to the day it is assigned to or leave it in effect until the nextscheduled assessment. If an assessment is limited to the assigned day, a studentlogging on to ALEKS on that day (after the start time) will be assessed, but if thestudent does not log on that day that student will not be assessed until the nextautomatic or scheduled assessment. The period during which the assessment is ineffect can be extended for a number of days.

NOTE. If an assessment is scheduled, whether by the teacher or automatically by thesystem, and the student is required to take assessments at the school, the student willbe unable to use the system from locations other than school until the assessment iscompleted (See Sec. 7.17). Teachers wishing to constrain assessments in this way shouldcontact ALEKS Corporation for assistance in determining the domain addresses usedby their school.

Grouping. It is possible to create arbitrary groups within the class and request assess-ments for these groups. Simply select the names of the students in the Selector: holdShift to select a continuous range, or Ctrl to select a discontinuous group. Then clickthe “Progress” or “Report” button, and request the assessment as you normally wouldfor an entire class.

7.11 Create, Edit, View Quizzes

To create, edit, or view quizzes, select the name of the class for which you wish todo this and click “Quiz.” You will see a list of students in the class with results forthe most recent quiz. A menu above the list allows you to select a previous quiz(then click “OK” to view the quiz results). To see detailed results for any particularstudent on that quiz, click on the date of the quiz opposite the student’s name.It will also be possible to see the individual questions and the answers that the


Figure 7.10: Creating a Quiz (Advanced Teacher Module)

student submitted for them. To see all quiz results for a particular student, clickthat student’s name in the main display. This list can be resorted on any of theheadings by clicking on that heading. Links at the top of the page enable you to seea breakdown of quiz results by question and to assign a grading scale for the quiz.

The Quiz feature in ALEKS allows teachers to create quizzes for their students usingany topics in the ALEKS domain. These quizzes are administered through ALEKS andscored automatically, with optional use of a grading scale set by the teacher. Quizzesmay be scheduled for particular days and times (“Scheduled”), or they may be madeavailable for the students in a class to take when they are ready (“Homework”). Theresults of quizzes can be seen through the reporting features of ALEKS, but do notinfluence the students’ knowledge states or their guided learning in ALEKS.

Create New Quiz. To create a new quiz, click on the button to lower right, “CreateNew Quiz.” On the page that follows, you will see various options for the quiz. Enter aname for the quiz in the box to upper left, or leave the name provided (“Quiz 1”, etc.).Next, select from the list of topics in the left-hand window either by dragging topics intothe right-hand window, or by highlighting topics and clicking “Add.” Click “Save” to

7.11. CREATE, EDIT, VIEW QUIZZES 93

create the quiz. To set the availability of the quiz, use the radio buttons at the bottomof the page and the “Scheduling” button. When the quiz is properly configured, click“Save.”

Other buttons enable you to create a different quiz (“Create New Quiz”) or delete thisone (“Delete Quiz”). There are links at the bottom to edit any existing quiz. Also, anew quiz can be created by duplicating an existing quiz (“Copy Quiz”).

The tabs at the top can be used to schedule, send a message to announce the quiz, orset a grading scale.� The Schedule tab generally features an interactive calendar for scheduling quizzes.

For “Scheduled” quizzes, this is the date (and time) when students are put intothe quiz by ALEKS; for “Homework” quizzes, it is the date on which the quiz isdue (at midnight of the date indicated).� The Assign To tab allows the teacher to assign any quiz to particular studentsin the class (including a single student, or no students). By default, any quiz isassigned to all students in the class.� The Message tab allows the teacher to customize the simple message normallysent to students announcing a quiz, or to cancel the message. By default, a messageis sent to all students indicating that a quiz has been scheduled (for “Scheduled”quizzes) or posted (for “Homework” quizzes).� The Grades tab allows the teacher to set a grading scale for the quiz. By default,the grading scale is “Disabled,” meaning that neither teacher nor students see anygrades. If it is set to “Private,” only the teacher sees the grades for all students. Ifit is set to “Public,” the teacher sees the grades for all students, and each studentsees their own grade.

NOTE. Often it is necessary to provide a “makeup” quiz to some students. This caneasily be done by copying the original quiz, then editing it so that it is assigned only tothe students needing the makeup.

Tips. Double-click on the name of any topic to see a sample problem. Topics can beselected in continuous groups using the Shift key or discontinuous groups using Ctrl;the entire folder is selected by using Ctrl-a.

Grading with quizzes. The grading scale used with quizzes is like the one usedfor assessments (See Sec. 7.10). As with assessments, grading is not obligatory; if nograding scale is set, the students and the teacher will only see the percentage of questionsanswered correctly.

Availability of quizzes to students. By default, quizzes are made available tostudents as “Homework Quizzes.” This means that the student is not forced into thequiz by ALEKS; rather, the student clicks the “Quiz” button when they are ready to


take the quiz (See Sec. 5.2.10). If this option is chosen, the teacher must indicate a duedate for the quiz, after which the quiz will no longer be available to students (HomeworkQuizzes are always due on midnight of the due date specified). A message can also besent to students informing them that the quiz has been assigned.

Quizzes may also be “hidden,” meaning that the students do not have any access tothem (pending the teacher’s decision to “release” the quiz), or they may be scheduled(“Scheduled Quiz”). A graphic calendar is provided for easy scheduling of quizzes. Ifthe quiz is scheduled, the teacher will have options for specifying the time of day it is tobegin, the time limit on the quiz, whether students are notified, how many days the quizshould be in effect (“Window of time to take the quiz”), whether the quiz is restrictedto the school, and prevention of automatic assessments up to seven days before the quizis scheduled.

Edit Quiz. To edit an existing quiz, click on the button to the lower right, “EditQuiz.” The quiz may be modified using the features described above for the creation ofquizzes, or it may be deleted.

Downloading. Information from the Quiz page can be downloaded in two formats.“Spreadsheet Format” is comma-separated values (CSV), which can be imported into avariety of applications but is raw in appearance. “Excel Format” is in Microsoft Excelformat, and has a legible, professional appearance, suitable for printing.

Makeup Quizzes. The easiest way to create makeup quizzes is to duplicate the quizneeding to be made up, then give it a new due date and “assign” the quiz to only thosestudents needing to make it up. When doing this, either turn off the Message notificationor make sure that the quiz has been assigned to the necessary students before clickingthe “Save” button. Attention to this detail will spare your other students from anunintended notification of the new quiz!

7.12. SEND MESSAGE 95

Figure 7.11: Send Message (Advanced Teacher Module)

7.12 Send Message

Select the student or class to whom you wish to send a message, and click onthe “Compose Message” button. A full-featured editor will appear beneath thedirectories window with fields for a subject and a message and a “Send Message”button (Fig. 7.11). The student or students to whom the message is being sentwill see it at their next login (See Sec. 5.2.11). It is also possible to send messagesdirectly to ALEKS Corporation.

ALEKS Message Center. The ALEKS Message Center resembles an email pro-gram in most of its features, although the exchange of messages takes place within theALEKS system. Also, the Message Center is equipped with special symbols and toolsappropriate to communication about the subject-matter used in ALEKS. Optionally,you can have copies of your students’ messages sent to your email account as well (SeeSec. 7.15).

Mathematical Expressions. The ALEKS Message Center contains a full range oftools for using mathematical symbolism, constructions, and expressions in your mes-sages. The tools are like those used by ALEKS itself in the Answer Editor (See Sec. 4.5).Moreover, students sending you messages in the Message Center can attach a graphicrepresentation of the problem they are currently working on, to facilitate posing andanswering mathematical questions.


Figure 7.12: Server Statistics (Advanced Teacher Module)

Grouping. It is possible to create arbitrary groups within the class and send messagesto these groups. Simply select the names of the students in the Selector: hold Shiftto select a continuous range, or Ctrl to select a discontinuous group. Then click the“Compose Message” button.

7.13 Check Messages

Click on the “Message” button at the top of the Teacher Module window. You canreceive messages from students in a class only if this has been enabled in the teacheraccount (See Sec. 7.15.).

7.14 Check Server Usage

Click on the “Server Stats” button. A table will appear beneath the directorieswindow (Fig. 7.12). The type of information shown in the table can be changed byselecting a heading from the menu at the top of the table and clicking the “Com-pute” button. The options for display are: Enrollment/Activity, Class Activity,Assessment/Performance, Enrollment List, Server Use: Page Hits, Server Use: UserHours.

7.15. CREATE TEACHER ACCOUNT 97

Figure 7.13: Teacher Account (Advanced Teacher Module)

NOTE. The information provided by this feature is of interest to system administrators,teachers, and educational administrators seeking general statistical information on theuse of ALEKS.

7.15 Create Teacher Account

Select the directory for the school where you wish to create a teacher account (orthe directory “All teachers”) and click on the “New Teacher” button. A form forthe new account will appear beneath the directories window (Fig. 7.13). Supply theteacher’s first and last names, a title (“Mr.,” “Mrs.,” “Ms.,” etc.), a Login Name,and a Password. By default, the new account is set for a teacher. If you are anadministrator, you can make another administrator account by checking “Teacherand Administrator.” The “id” field is optional and may be left blank. “Messagefrom student” should be enabled if you wish the account holder to receive messagesfrom students (See Sec. 7.13). “Status” must be enabled if the teacher is to haveclasses assigned (if “Status” is enabled, you will see here how many classes areassigned to the teacher).


When you are finished filling in the form click on “Save.” This creates the account. Tostart over, click “Reset.” To cancel the account, click “Delete File.”

Other settings may be changed for the teacher by using the additional tabs “Mail” and“Advanced.”

Mail

This tab contains options for entering an email address, forwarding ALEKS mes-sages to this address, and permitting students to send the teacher messages throughALEKS (See Sec. 7.13).

Advanced

This tab contains a button for “Cleanup Tools.” These tools permit the teacherto unenroll and delete students and to modify database records in other ways.

NOTE. Deleting a student removes that student’s records permanently from theALEKS system.

NOTE. Under the “Cleanup Tools,” “Records” refers to information in the databaseconcerning student knowledge as shown on assessments and in the Learning Mode.Clear Records will remove all such information. “Stats” refers to information inthe database concerning the hours students have spent in ALEKS. Clear Stats willremove all such information.

7.16 Edit Teacher Account

Select the teacher whose account you wish to edit and click the “Edit” button. Thesame form will appear as described in “Create Teacher Account” (Fig. 7.13). Theaccount may be deleted (“Delete File”) only if there are no classes and no studentsenrolled for this teacher (“Advanced”).

7.17. CREATE CLASS ACCOUNT 99

Figure 7.14: Class Account (Advanced Teacher Module)

7.17 Create Class Account

Select the teacher for whom you wish to create a class and click on the “New Class”button. A form for the new account will appear beneath the directories window(Fig. 7.14). Select a grade or level for the class. Provide a name (e.g., “Aleks”) andchoose a category. At this point, you have the option of choosing a teacher otherthan the one initially selected (if others are available). This will transfer the classto that teacher. The “id” field is optional and ordinarily left blank.

The Class Code for the newly-created Class appears in the upper right-handcorner of the screen.

When you are finished filling in the form click on “Save.” This creates the account. Tostart over, click “Reset.” To cancel the account, click “Delete File.”

Other settings may be changed for the class by using the additional tabs “Status,”“Assessment,” “Learning,” “Content,”

Status

Under “Status” you can close the class for enrollment (by default it is open) and re-strict students’ access to their account (“assessment only” or “denied”—no access).Also, you can request to be notified by ALEKS (through the Message Center) whenany student in the class assesses at 100% of your syllabus.


Assessment

The students’ assessments can be restricted so that either the initial assessment,or subsequent assessments, or both, can be taken only from the school. For thissetting to be effective, a valid domain name must be entered in the school account.Teachers wishing to constrain assessments in this way should contact ALEKS Cor-poration for assistance in determining the domain addresses used by their school.

Learning

If the “Ask a friend” option is checked, students in the class will be able to requestthe name of a classmate for help with a topic that is causing difficulty. “Novice”means the system will choose a classmate who has mastered the concept veryrecently. “Expert” means that the system will choose a classmate who masteredthe concept earlier than others in the group. The teacher may pick any point onthe continuum between “novice” and “expert.”

This tab also contains options for the use of the ALEKS Worksheet (See Sec. 5.6).The teacher may enable or disable the worksheet, choose between 16 review ques-tions or 12 review plus 4 extra credit, remind students to print a worksheet whenexiting ALEKS, and have answer sheets sent through the Message Center eachtime a student downloads a new worksheet. The teacher can also choose to makethe answers to the worksheets directly available to students on their Worksheetpage.

Other options here concern the availability of the calculator and of the “Time toCompletion” data to students on their Report page (See Secs. 5.2.5, 7.5, 7.7).

Content

Clicking the “Content” tab gives access to the ALEKS Content Editor (See Sec. 7.24).This feature lets the teacher quickly and easily modify the content for a course.If the teacher clicks in the checkbox for any content area, that content area isremoved from the curriculum of the course; it will also not appear in assessments.To see exactly which items are contained in this content area, click on the title ofthe content area.

Advanced

Under “Advanced” it is possible to find a range of class management features.“Cleanup Tools” permit the teacher to unenroll and delete students and to modifydatabase records in other ways. The “Class Program” button is equivalent to the“Select Class Program” button (See Sec. 7.19). “Assign Learning Rates” opens theLearning Rates feature (See Sec. 7.25). “Edit Int. Objectives” gives access to theIntermediate Objectives feature (See Sec. 7.23). “Schedule Assessment” permitsthe teacher to schedule an assessment for the class (See Sec. 7.10.). If the user hasAdministrator privileges, there is also a button for scheduling upgrades of ALEKScourse products. If QuickTables are in use for this class, there are also buttons forsetting QuickTables options (See Sec. 9).

NOTE. Under the “Cleanup Tools,” “Records” refers to information in the databaseconcerning student knowledge as shown on assessments and in the Learning Mode.

7.18. EDIT CLASS ACCOUNT 101

Figure 7.15: Textbook Integration (Advanced Teacher Module)

Clear Records will remove all such information. “Stats” refers to information inthe database concerning the hours students have spent in ALEKS. Clear Stats willremove all such information.

7.18 Edit Class Account

Select the class you wish to edit and click on the “Edit” button. The same form willappear as described in “Create Class Account” (Fig. 7.14). The account may bedeleted (“Delete File”) only if there are no students currently enrolled in the class(“Unenroll Students”).

The Class Code for the Class being edited appears in the upper right-handcorner of the screen.

7.19 Textbook Integration

Select the class for which you wish to choose the class program and click on the“Select Class Program” button. (This feature can also be used in the Basic TeacherModule; see Sec. 6.2.3 You will be shown a menu of textbooks available for integra-


tion with this course. If you wish to organize the content of your course on the basisof an available textbook, select the name of the textbook and click “Next.” (Thereis also a checkbox which you can uncheck if you wish to have the precise textbookcoverage and textbook references, but not full integration.)

There may also be a choice in the textbook menu labeled “ALEKS Curriculum.” Thisorganizes the class material on the basis of the slices of the ALEKS pie chart ratherthan any particular textbook.

The page that follows contains a list of chapters in the textbook with menus for assigningdates to each of them. For each chapter, assign the date on which you require yourstudents to complete that material. If the date is left blank, no date will be assigned forthat material; this does not mean it will be skipped, but rather that it will be includedin the material for the next chapter to which a completion date is assigned. When youare done assigning dates, click “Save,” and the dates chosen will go into effect. Theycan be modified at any time.

The textbook integration feature in ALEKS presets both syllabus and intermediate ob-jectives for the course. During the time that the students are supposed to be completinga particular chapter, they will see dotted lines on their pie charts showing how far theyneed to fill in, and the date by which they need to do it; if they complete the chapterthere will be a congratulatory message and they will be moved to the next chapter. Theteacher will also see which students in the class have completed the current chapter (SeeSec. 7.23).

If a student does not complete the chapter by the completion date, there will be nocongratulatory message, and the dotted lines on that student’s pie chart will move outto their new positions. The student will still have to complete any prerequisite materialfrom unfinished chapters while working on the current one.

Another effect of textbook integration is that references will appear on the ALEKSExplain pages, indicating the specific place in the textbook where the current conceptis covered (See Sec. 5.3.2).

When textbook integration is in effect, the quiz feature in ALEKS is also customizedso that quizzes can easily be created on the basis of textbook chapters (See Sec. 7.11).

If you do not wish to use full integration of an available textbook with this course, clickthe button “No Integration.” You will then have a choice of programs for the class.You may also have the option of choosing a textbook to be used with ALEKS (this willgenerate textbook references on the Explain page, but will not provide full textbookintegration). When you are finished filling in the form click on “Save.” To start over orrestore defaults, click on “Reset.”

NOTE. The “class program” is a set of topics or items used as a goal for mastery bythe students in a given class (See Chapter 8.). In school classes one program is usuallyset for the class. “Standards” are collections of programs covering a range of grades.ALEKS always contains ready-made standards set to appropriate defaults. Thus, inmost cases the school teacher need not select the class program.

7.20. ENROLL AND UNENROLL STUDENTS 103

7.20 Enroll and Unenroll Students

Select the class for which you wish to enroll or unenroll students and click on “Enrollin Class.” A display will appear beneath the directories window showing the namesof all students who may be enrolled. The students currently enrolled in this classappear with their names highlighted in gray; those enrolled in some other classare highlighted in yellow. The names of students can be highlighted (enrolled) ordehighlighted (unenrolled) by clicking on them. When all desired changes have beenmade, click on the “Save” button.

Drag and drop. Students may be moved between classes more easily by draggingand dropping their names. Simply select the names of students to be moved in theright-hand side of the directories window and drag them to the target folder on the left.The entire class can be selected by using Ctrl-A; a continuous range by holding Shiftand clicking; or a discontinuous group by holding Ctrl and clicking. You will see thetarget folder become highlighted when the student or students are ready to “drop.”


Figure 7.16: Student Account (Advanced Teacher Module)

7.21 Edit Student Account

To edit a student account, select the name of the student and click on the “Edit”button. A form will appear beneath the directories window containing the student’saccount information: name, login name, id, email, and current enrollment status(Fig. 7.16). The student’s Password is not shown in a readable form, but it can bechanged to provide a student with a new Password when one has been forgotten.Corrections or changes may also be made to the student’s name, login name, id,and email. The student’s id and email are optional, though it may be useful to havethese on record.

Advanced. Under “Advanced,” “Cleanup Tools” permit the teacher to unenroll anddelete the student and to modify database records in other ways. “Records” refers toinformation in the database concerning student knowledge as shown on assessments andin the Learning Mode. Clear Records will remove all such information. “Stats” refersto information in the database concerning the hours the student has spent in ALEKS.Clear Stats will remove all such information.

Account Information. The begin and expiration dates of the student’s current ac-count are also shown on this page. Similar information is available to the student onthe Options page (See Sec. 5.2.3).

7.22. AUTHORIZE STUDENT ACCOUNT 105

Figure 7.17: Intermediate Objectives List (Advanced Teacher Module)

7.22 Authorize Student Account

A detailed account of the authorization procedure can be found in Sec. 3.8.

To begin the authorization process in the Advanced Teacher Module, click on the “Au-thorization” button in the menu bar at the top of the ALEKS window. If there are anystudents waiting for authorization, check the “Authorize” box next to their names, oruse the option “Authorize every account below.” Then, click the “Delete” box for anyduplicate names, and click “Done” at the bottom of the page.

On the page that follows, check the availability of licenses for new students, then click“Next” to complete the authorization process. Clicking “Back” will enable you tomodify your selection of students for authorization.

7.23 Intermediate Objectives

The Intermediate Objectives feature was created to address the needs of teachers us-ing ALEKS in conjunction with a planned sequence of topics for classroom instruction


Figure 7.18: Intermediate Objectives (Advanced Teacher Module)

(Fig. 7.18). It enables teachers to prioritize certain groups of topics for specified seg-ments of time, when these topics will be at the focus of class discussion. When inter-mediate objectives have been set, students will be directed to work on these objectivesas soon as they are available in the domain and guided through their prerequisites inthe most direct way possible. Both students and teacher will receive clear informationon current progress toward completion of scheduled objectives.

To create or edit intermediate objectives, select the name of the class for which youwould like to set or modify objectives and click “Edit.” On the Edit page, click the tabmarked “Advanced.” On the page that follows, click “Edit Int. Objectives.”

The page that follows shows you a list of any intermediate objectives currently set foryour class (or a note that none is currently set) and buttons for adding and copyingintermediate objectives (Fig. 7.17). The dates for existing intermediate objectives canbe changed by using menus in the list and clicking “Update.” If you wish to copy one ormore intermediate objectives that have been set for another class or section, click “CopyInt. Objectives.” Also, you can choose to prevent automatic assessments for studentsin this class for up to five items before fulfillment of your intermediate objectives. Tocreate a new set of intermediate objectives, click “Add Int. Objectives.” To edit anexisting set of intermediate objectives, click on their link in the list.

7.23. INTERMEDIATE OBJECTIVES 107

Here you will see a vertically divided selector window (Fig. 7.18). This window displaysthe topics available to be selected for the set of intermediate objectives. To view asingle, scrolling list of topics, click on “Open All,” then on the tiny “X” in the upperright-hand corner of the window. Select and unselect items for inclusion by clicking onand off the little checkmarks in the boxes that precede them.

NOTE. ALEKS always maintains the coherence of its intermediate objectives; any setof intermediate objectives must contain all of the items within the domain needed tolearn the items it contains. If an item being added to the objectives has prerequisiteitems not currently also belonging to the objectives, these will be automatically addedas well; conversely, if an item being removed from the objectives is a prerequisite itemfor some items presently in the objectives, these will also be removed. The editor warnswhen this is occurring (See Sec. 8.4.3).

Every set of intermediate objectives is assigned to a particular date, which is the dateby which the students are to have completed this set of objectives. The date is set ina pair of menus directly below the selector window, one for month, one for day. Theset of objectives will be in effect through the date to which it is assigned, after whichthe next set of objectives will take effect. If no date is assigned, the objectives will takeeffect following the last set of objectives to which a date has been assigned, and remainin effect to the end of the class (“final” objectives).

The name of a set of objectives appears at the top of the list of topics. Click on thisname to edit it. When you have picked a name, selected topics, and set a date, click“Save” to enter the objectives into the system for this class.

When a set of objectives is in effect, both teacher and student will receive informationabout progress toward their fulfillment. The teacher will see notations on the ClassProgress page indicating which students have fulfilled the current objectives, and whichare close to doing so. The student will see dotted lines on their pie chart showing howfar each slice will need to be filled in to achieve the current objectives. The teacher willsee the same dotted lines when they view the pie charts for the class and for individualstudents.

When a student uses MyPie to choose a topic for work in the Learning Mode, the itemsshown as available are those which the student is “Ready to Learn,” excluding any itemswhich do not lead directly to fulfillment of the current objective. Once the student hascompleted the intermediate objective, she or he will move immediately into the nextobjective, whether or not the completion date has passed. If the completion date passeswithout the student’s completion of that objective, the new intermediate objective willtake effect in terms of the student’s guidance, but unfinished prerequisite material fromthe earlier objective will still have to be completed before moving on.


Figure 7.19: Content Editor (Advanced Teacher Module)

7.24 Content Editor

The ALEKS Content Editor is a quick and easy way to modify the content of a course(Fig. 7.19). Select the name of the course and click “Edit,” then click on the tab for“Content.” You will see a list of content areas, each preceded by a checkbox. To seewhat is contained in any of these areas, click on its title. To remove the area fromthe course, click on the checkbox to place an “x” in the box. This indicates that thearea has been removed from the course content; it will also not appear in assessments.Then click “Save” to put your changes into effect, or “Reset” to undo them.

NOTE. The Content Editor is far more convenient, though somewhat less powerful,than the Program Editor (See Sec. 8.4). Keep in mind that while a program createdor modified by the Program Editor can be used by any number of classes within theschool, the Content Editor acts on only one course at a time.

7.25. ASSIGN LEARNING RATES 109

Figure 7.20: Assign Learning Rates (Advanced Teacher Module)

7.25 Assign Learning Rates

The purpose of the Assign Learning Rates feature in ALEKS is to provide teachers witha highly flexible tool for interpreting and evaluating the work of students in ALEKS.One possible use of the information provided by this feature is as a component in thegrading system used for a class, or in some other method of motivation or reinforcementfor student success.

In the Advanced Teacher Module, select the name of the class for which you wish toassign learning rates and click the “Progress” button. At the top of the Class Progresspage you will see a link marked “Assign Learning Rates.” Clicking on this link producesa page with four rectangular graphs (Fig. 7.20). Each of the graphs refers to a particularway of evaluating a student’s work: by the percentage of course objectives that they havemastered (Grading), by the total number of hours spent on ALEKS (Time on Task),by the average number of items gained per hour (Hourly Progress), and by the averagenumber of items gained per week (Weekly Progress). The vertical bars appearing in thegraphs indicate the distribution of students relative to the given scales. Any combinationof these scales may be used. The three buttons to the right of each graph determinethe use of the evaluation: if “Disabled,” no one sees it; if “Private,” the teacher sees


it but the students do not; if “Public,” the teacher sees it and each student sees it fortheir own work.

Each graph has sliders, with labels referring to the intervals they define. Additionalsliders may be placed by dragging the right-hand or left-hand sliders, or sliders may beremoved by dragging them off to the right or left. The sliders may be set and the labelsedited as the teacher desires. To change the label on a new or existing slider, select thetext of the current label, retype as desired, and then press “Return.”

The function of the sliders is as follows: a student’s evaluation on a given scale is thelabel of the interval within which that student is currently located. For example, if oneslider is set to 80 on the “Grading” graph and another slider to 90, with the intervalbetween them labeled “B,” a student who has mastered 82% of the class goals will havethe evaluation “B.” To take another example, if a slider under “Time on Task” hasbeen set to 10 hours and another to 20 hours, with the label for their interval set to“Enough,” a student who has spent 11 hours on ALEKS will receive the evaluation“Enough.” When the desired settings have been made, click “Save.” Now the labels setto “Private” will appear in the Progress page.

If any of these charts are set to “Public” the students will see their ratings according tothose charts when they log on to ALEKS. Explain carefully to the students what themeaning is of the notations that they will see, and how they relate to the overall goalsfor the class. Some charts, such as Weekly Progress, may be more useful to the teacherthan to the students, as an aid to monitoring students’ work and learning. These shouldbe set to “Private.”

Variable Scale. By default, the segments into which values are divided in the “score”graph are at 5-unit intervals. This can be reset to 2 units for greater precision, using alink in the lower right-hand part of the page.

Chapter 8

Advanced Teacher Module: Standards& Programs

By default, the Advanced Teacher Module displays “Results & Progress,” as describedin the preceding sections (See Chapter 7). A second mode, “Standards & Programs,”can be chosen from the menu at the top of the Advanced Teacher Module window(Fig. 8.1). This mode enables the teacher to explore the system of standards and pro-grams currently available in their ALEKS database. Administrators with a sufficientlyhigh level of user privilege may also copy programs and standards, and modify them tosuit the needs of a school.

The “program” is a set of concepts taken from the sum total of concepts defining masteryof a domain (e.g., Arithmetic or Algebra) that has been set as the curricular goal fora particular level of study. That is to say, mastery of this set of concepts is equivalentto completion of the curriculum for that level, and all reports generated by the systemfor students and classes using the program are framed in terms of this program. A“standard” is a collection of programs covering a range of grades.

To view a particular standard or program, use the directories window of “Standards &Programs.” This will open the folder for a particular grade within a particular stand-ard. Normally the program will be organized by topics and subtopics using standardmathematical terminology. There is a list of individual concepts within each of thesetopics, each of which is either marked with a checkmark, indicating that it belongs tothe program, or not so marked. Editing a new standard means adding and removingcheckmarks from individual “items” according to some scheme of curricular progress.

NOTE. In some ALEKS products, the syllabus is maintained internally and is notaccessible for editing. In such products, modification to the scope of the class can beachieved using the Content Editor (See Sec. 7.24).

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112 CHAPTER 8. ADVANCED TEACHER MODULE: STANDARDS & PROGRAMS

Figure 8.1: The Standards & Programs Directory (Advanced Teacher Module)

8.1 Items, Programs, and Standards

In order to understand and use this part of the Advanced Teacher Module effectively,it is necessary to grasp three key concepts. Additional information can be found in thediscussion of Knowledge Space theory (See Chapter 11).

Item

An item is a fundamental unit of knowledge or ability recognized by the system.An example of an item in Arithmetic is “Subtraction of Negative Integers.” Everymathematical subject covered by ALEKS (such as Arithmetic) corresponds to aset of items, each of which can be tested and taught by the system. Mastery ofthe subject means mastery of each of the items making up the subject.

Program

A program is a subset of the set of items belonging to a mathematical subjectthat has been defined as the goal for a particular class. For example, a programfor Arithmetic is a set of items that students completing the class are expected tomaster. All assessment reports by the ALEKS system are based on some programselected by teachers or administrators for use by those students. The ALEKS

8.2. NAVIGATION AND USE 113

Program Editor is provided to permit teachers and administrators to customizeexisting programs (See Sec. 8.4).

Standard

A standard is a set of programs, usually covering the entire range of grades overwhich a particular subject is taught. A standard should organize the teaching of asubject in a coherent and methodical way. That is, items belonging to the programfor one grade should belong to the programs for higher grades, and items shouldbe distributed among the programs according to some well-founded pedagogicalrationale.

Under “Standards & Programs,” users of the Advanced Teacher Module can navigatethrough a hierarchical listing of the standards currently available and the programscontained by them. Standards and programs can be copied. Users with appropriatelevels of privilege can enter the Program Editor to create new programs based on existingones, possibly leading to the creation of new standards.

8.2 Navigation and Use

Access to directories under “Standards & Programs” is the same for all levels of userprivilege, teacher and above. Any user of the Advanced Teacher Module may navigatethrough all directories and make copies of all available standards and programs. Users,however, may change only those standards and directories which they have themselvescreated (by copying existing ones), or those created by users within their authority. Thismeans, for a root administrator, any administrator or teacher under their administra-tion; for a school administrator, it means any teacher in the school. A user not withinthe authority of another given user has independent authority. Standards and programscreated by a user with independent authority may not be changed. The privilege levelof a particular user also determines where the new standards and programs created bythat user will be placed.� On choosing “Standards & Programs,” the user begins with a master directory

entitled “All Standards,” containing a list of all the standards available for thatsystem (Fig. 8.1).� On opening any of the listed standards, the user is presented with a list of thegrades covered by that standard.� On opening any of the grades listed for the given standard, the user will see a listof the (mathematical) subjects covered for that grade. At a minimum, there willbe an element entitled “Basic.” Each element in this list corresponds to a programavailable within the system.


8.3 Buttons

The following buttons appear next to and beneath the navigation display in “Standards& Programs” (Fig. 8.1). The buttons are always visible; which buttons are active atany given moment depends on what is selected in the navigation display.

Edit Standard

The selected standard must have been created (copied from another standard) bythe current user or by one within the authority of the current user. The basicstandards included with ALEKS and programs created by users with independentauthority cannot be changed, but they can be copied and the copies changed.

A standard is defined by designating its name, source (authority), and an optionalid number. The “Enabled” button must be selected if the standard is intended foruse.

Edit Program

This will open the selected program for modification in the Program Editor (SeeSec. 8.4). The selected program must have been created (copied from anotherprogram) by the current user or by one within the authority of the current user.Programs belonging to the basic standards included with ALEKS and programscreated by users with independent authority cannot be changed, but they can becopied and the copies changed.

Copy/New Standard

If a standard is selected, this will make a copy of that standard, usually for thepurpose of establishing a new one based on it. If no standard is selected, it createsa new, empty one.

Copy/New Program

If a program is selected, this will make a copy of that program, usually for thepurpose of establishing a new one. If no program is selected, it creates a new,empty one. If a new standard has been created, the new program will be placedhere.

Drag and drop. The programs may be copied between folders by dragging anddropping them. Simply select the names of programs to be copied in the right-hand side of the directories window and drag them to the target folder on the left.You will see the target folder become highlighted when the program is ready to“drop.”

8.4 Program Editor

In order to make changes to programs that have been copied, users must select the newprogram and click on the “Edit Program” button (or double-click on the icon for that

8.4. PROGRAM EDITOR 115

Figure 8.2: The Program Editor (Advanced Teacher Module)

program). This gives access to the ALEKS Program Editor for that program. Althoughthe Program Editor is always entered under the heading “Standards & Programs,” it hasits own, distinctive interface appearing beneath the “Standards & Programs” directory.

The Program Editor displays items for the given subject, organized in folders by generaltopic. To see items you must open all folders in which they are contained. Items arelabeled by name and topic, and indicate whether or not they belong to the currentprogram by a checkmark (Fig. 8.2). If a new program is created by copying anotherprogram, precisely the same items are selected in it as in the original. If the programis created from scratch, no items in it are selected.

NOTE. If a folder is marked with a large checkmark, this means that all items inthat folder currently belong to the program. A small checkmark means that some ofthe items in that folder belong to the program. No checkmark means no items in thatfolder belong to the program.

Clicking on the tiny “x” in the upper right-hand corner of the directory window createsa single window and makes it possible to view all the items at once (click on “OpenAll”).


8.4.1 Fields

The following fields appear above and below the editor display, and should be filled inas needed in creating or editing a program.

Standard

The standard to which this program belongs.

Status

Should be set to “enabled” if the program is to be available for use.

Parser

The name of the person creating or modifying the program (and so responsible forselection of items). To parse in this sense means to establish functional relation-ships between all elements of a sequence; the parser is making all items for thesubject either members or nonmembers of the program.

id

Optional identification number.

8.4.2 Buttons

The following buttons also appear adjacent to the editor display.

Open All

Shows all folders in the editor display. This gives a complete picture of the topicalstructure of the subject matter.

Undo

Undoes the most recent editing action (the addition or removal of an item).

8.4.3 Using the Program Editor

To define a program, the teacher must first ascertain which of the items in the completelist of items making up the subject matter are to belong to this program. This shouldbe a thoughtful decision, usually made within an appropriate institutional framework.If a particular source is used for defining a program, the source should be recordedin the standard containing the new program, and should be documented externallyas justification for the decision to adopt the given program. If the class is part of asequence, the programs for the other classes in this sequence will normally be definedtogether with it as part of a single progression.

Once the list of items to be included has been established, the teacher responsible forediting the program examines each of the displayed items. There should be a checkmarkbefore each item to be included, and no checkmark before items that are not to be

8.4. PROGRAM EDITOR 117

included. A checkmark is added or removed by clicking once on the checkbox. Followingthis, click on the “Save” button to record the program.

NOTE. ALEKS always maintains the coherence of its programs; any ALEKS programmust contain all of the items within the domain needed to learn the items it contains. Ifan item being added to the program has prerequisite items not belonging to the program,these will be automatically added as well; conversely, if an item being removed from theprogram is a prerequisite item for some items presently in the program, these will alsobe removed. The Program Editor warns when this is occurring.

Chapter 9

QuickTables

QuickTables is a special tool for mastery of Arithmetic facts (Addition, Subtraction,Multiplication, Division), available as part of ALEKS course products for levels 3, 4,and 5 and as an independent ALEKS course product. It uses individually configured,progressive, paced-response drill to develop mastery of the math facts, in a supportive,colorful, child-friendly interactive environment. Among many other features, it containsa series of games which the students “earn” through the progress that they make towardmastery of the various fact tables.

9.1 Setting Up QuickTables for your Class

Although ALEKS QuickTables is available at any time for any Level 3, 4, or 5 class,they will not appear for your students until you have completed a simple configurationprocedure for the tables that you wish to use. In any ALEKS class at levels 3, 4,and 5, you may select any one or any combination of the following tables: Addition,Subtraction, Multiplication, and Division. The selection may be changed at any time;for example, you may start out with only Addition, then add Subtraction and the othersone at a time as the students work their way through these tables.

When you log on to your Teacher account for the first time, you will be prompted toset up QuickTables for your classes. If you elect to skip this, you can return at any timeby clicking “Class Admin” in the upper left-hand part of your Teacher account, then“Customize this class,” then “Edit QuickTables.” Scroll down to see the list of tablescurrently available for this class (Fig. 9.1). To add a table, click the link marked “Adda table.” (Tables currently available can be deleted by clicking the “Delete” button tothe right of the table row.)

When you add a table, you will be prompted to choose the operation for the table(Addition, Subtraction, Multiplication, Division) and the range of numbers to be used(0-9, 1-9, 0-10, 1-10, 0-12, 1-12). You can make the table available to all students inthis class (the default) or only to selected students.

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Figure 9.1: QuickTables Configuration

Other options that you see on the “Edit QuickTables” page apply to all the tablesthat you set up in this class. These are: the maximum length of a session (default15 minutes), maximum number of sessions per week (default 3), maximum number ofgames per session (default 6), minimum length of session before games become available(default 10 minutes). In most cases, you may wish to leave the defaults; if, however,after some experience using QuickTables with your students, you wish to change them,a range of options are available.

Why are there limits on the use of QuickTables by students? From consultationwith experienced educators, it is clear that in most cases the students’ use of QuickTablesshould be limited through the choices mentioned above. This is both to ensure thatstudents for whom QuickTables is only one part of their ALEKS class also spend timeworking in the “regular” ALEKS class, and also because the benefit of using the type ofdrill that QuickTables provides is at its greatest when concentrated in relatively shortand well-spaced sessions. You will notice that your students’ work in QuickTables isbroken up into short “bursts” of drill activity. This is also to maximize benefit bykeeping the students’ concentration sharp.

High score chart. The final option on this page is to reset the “high score chart” atregular intervals. When your students play the games that QuickTables gives them as

9.2. HOW YOUR STUDENTS USE QUICKTABLES 121

Figure 9.2: QuickTables Learning Display

a reward for progress made, they earn numerical scores, which are compared with thescores of other students in the class. The current “high score” is reset at the intervalthat you choose (default weekly). In effect, this interval establishes a regular period ofcompetition among the students for highest game score, for added motivation.

9.2 How Your Students Use QuickTables

When your students log on in an ALEKS class where QuickTables is enabled, they willsee tabs on the right-hand part of their top bar for choosing ALEKS or QuickTables.If they click on QuickTables, they will switch into the QuickTables environment.

The first time a student enters QuickTables, they are given a brief training in how totype numbers quickly and enter them as answers to the problems they will be given inQuickTables. It is parallel to the Tutorial that students experience when using ALEKSfor the first time, but focused exclusively on typing and entering answers smoothly andpromptly. Please note that an answer can be “entered” in QuickTables by using eitherthe Enter button or the Space Bar on the keyboard, whichever the student finds moreconvenient.


Figure 9.3: QuickTables Reporting

NOTE. The drill provided by QuickTables is paced, in the sense that students needto enter their answers within a specified “Target Time.” QuickTables seeks to developquick, “automatic” response to questions on math facts. The actual time period foranswering is subject to customization (see below).

Following the introductory training, the students take a brief test to determine theircurrent knowledge of the math facts in the particular table being used. (Where thereis more than one table, a test will be taken for each new table.) This is parallel tothe Assessment taken in regular ALEKS. When the student completes the test, thecolor-keyed Learning Display is presented, showing them their current knowledge of thetable and permitting them to choose how they will work toward complete mastery ofthe table facts (Fig. 9.2). This display has a function similar to that of the pie chart inregular ALEKS.

To choose a math fact to work on, the student clicks on the corresponding cell in thetable. If the student simply presses Enter or the Space Bar, a fact will be chosen fromthose available. There is a brief introduction to the fact, and then a paced drill sequencein which review of previously-learned facts is mixed in with reinforcement of the newfact. Sequences are kept short so that the student’s concentration remains high. If thereis a mistake, the drill is halted while the student reenters the correct answer, with help

9.2. HOW YOUR STUDENTS USE QUICKTABLES 123

Figure 9.4: QuickTables Advanced Options

from QuickTables; also, if the student takes too long in answering, there is a similar haltwhile the student catches up with the drill. Once the student shows good knowledge ofthe new fact, there is a pause before the next cycle of learning.

As the student progresses in mastery of new facts, the colors in the table flow acrossto show the changing area of mastery. This provides the student with direct, tangibleevidence of progress, building the student’s motivation. At the same time, the ther-mometer graphic to the right of the table also indicates the percentage of the tablecontents that the student has worked through. Gold stars next to the thermometerindicate levels of progress where new games become available to the student. Studentscan click on the Games button in the top bar to take a break from drill and play anyof the games that they have earned, subject to the limits chosen by the teacher (seeabove). The games provided in QuickTables are designed to reinforce the students’knowledge of the math facts that they have just learned.


Figure 9.5: QuickTables Worksheets

9.3 Reporting your Students’ Progress in QuickTables

The Report for QuickTables appears as an option under Reporting for any class whereQuickTables has been enabled. (Click “Reporting” in the left-hand margin, then “Quick-Tables,”, then the tab for the table whose report you would like to see (e.g., “Addition”).The Reporting view for QuickTables shows, for each student, the Target Time (how longthe student has to answer problems), the date they started in QuickTables, the last logindate, and the total hours spent in QuickTables (Fig. 9.3). Then it shows a bar graph;the bar graph displays percent mastery of the table contents in blue for the most recentassessment, with an additional segment in green showing what was added since the lastassessment (blue plus green equals the student’s total current mastery).

To print the Reporting page, use the ALEKS Print button to upper right; to downloadits contents in Excel format, use the link just above the tabs at the right-hand margin.To see separate bar graphs for all of your students’ assessments, use the link beneaththe report marked “Display old Sessions.” To see advanced options accessible throughthe Reporting page, click “Display Advanced Options.”

9.4. ADDITIONAL FEATURES IN QUICKTABLES 125

9.4 Additional Features in QuickTables

Using the link “Display Advanced Options” reloads the Reporting page in a somewhatexpanded format. In this view, it is possible to change the “Target Time” for students’answers, order a new assessment or worksheet for any student or group of students,and activate the Keypad for students who may need it. The Keypad allows students toenter answers by clicking with their mouse, rather than using the computer keyboard.

QuickTables Worksheets. You can also find options for the use of QuickTablesWorksheets under “Taking Actions” (Fig. 9.5). Like other Worksheets in ALEKS,QuickTables Worksheets are individualized to each student’s current progress. It is alsopossible to produce customized Worksheets on selected facts from the tables.

Chapter 10

Teaching with ALEKS

10.1 The ALEKS Educational Paradigm

ALEKS is based on the realization that students learn math in different ways, at differingspeeds. Starting from an accurate assessment of their current knowledge, students inALEKS are only offered what they have shown themselves ready to learn. They thereforeexperience less frustration (from material that is too hard for them) and boredom (frommaterial that is too easy for them). Learning is more efficient and more rapid. Studentshave “ownership” of their learning process, and grow in confidence and independence.If a student forgets what was once learned, ALEKS smoothly and efficiently guides thestudent through all necessary review and reinforcement. The student will not be “lost.”With time and persistence, every ALEKS student will progress toward mastery; thisprogress will be clearly visible to both student and teacher.

It is normal for students to be in disparate knowledge states; this would be the casein any event, but ALEKS puts this information clearly at the teacher’s disposal. Therelative mastery attained by students appears clearly from the “Learning Progress SinceLatest Assessment” Report in the Teacher Module. ALEKS does not require the stu-dents to progress as a unified group. ALEKS will permit a student to work on any topicin the category “ready to learn,” a well-chosen list of topics which the student has notyet learned, but has demonstrated (within ALEKS) the readiness to begin learning.

Students using ALEKS will experience new independence in learning, to which somemay be unaccustomed. Many will find this difference exhilarating. Teachers also mayfind different opportunities for optimizing their role in the learning process, with agreatly expanded ability to accurately monitor and effectively promote their students’learning. The role of the teacher is critical in providing structure, support, and rewardfor the students’ effective use of ALEKS. If ALEKS is used properly, the teacher’sscope for individual coaching and small-group instruction will be greatly expanded, aswill the freedom to teach a broader and richer math culture (to some or all students,time permitting).

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In other words, ALEKS turns the teacher from a footsoldier in the trenches into a fieldcommander, possessed of powerful resources, surveying a broad landscape of informa-tion, able to make effective strategic decisions. The point is that ALEKS puts theteacher in command; among other things, the teacher can take more or less of ALEKS,give it a greater or lesser position among other class requirements and activities. Vari-ous styles of use are possible. The following should be understood as mere suggestions,designed to give teachers a sense of the possibilities offered by ALEKS’s substantiallibrary of tools.

10.2 The Teacher and ALEKS

Not every way of using ALEKS involves supervised classroom sessions. When this issensible, however, it provides a new dimension to the students’ learning.

The teacher in an ALEKS class need not be collecting, correcting, or distributing pa-pers, struggling with discipline issues, organizing groups, managing materials, givinginstructions, or supervising activities. The teacher in an ALEKS class may be just asbusy teaching mathematics to individual learners: getting one student started on a newtopic, checking another student’s work, responding to questions, suggesting alternatemethods and explanations, making or reinforcing connections among concepts, congrat-ulating those who “add an item to their pie.” ALEKS provides comprehensive supportto the student in every phase of its use; yet the teacher will find that the additionaldirect support given this way is unexpectedly welcome and productive. Suddenly the re-lation of teacher and student is based on knowledge and discovery, not management andsanction. No one is “behind” in ALEKS; setbacks are readily addressed and overcome;every student can expect to make progress and be recognized.

It is important, especially in the early stages of an ALEKS class, that the teacher begenerous in recognizing student progress. Students need to understand that when theyadd an item to their pie, or show progress in a new assessment, it is an achievement,and the proper use of ALEKS. Soon this will become second nature and learning will beits own motivation. At the same time, formal rewards for the effective use of ALEKSneed to be built into the class structure and made clear from the outset (See Sec. 10.3.).

Students will be assessed at the beginning of their use of ALEKS (following Registrationand the Tutorial), and at regular intervals thereafter. The teacher does not need tosupervise all ALEKS assessments; normally, students will be using ALEKS outside aswell as in the lab or classroom, and taking assessments at various times and locations.Once the students realize that the purpose of the ALEKS assessment is to provideappropriate material in the Learning Mode, there will be little reason to get help,use the textbook or calculator inappropriately, or in any other way achieve incorrectassessment results.

We recommend that the initial assessment be supervised. The students may needassistance in their first use of the system, they will need to be reassured that theassessment is not for a grade, and it is important that the results of this initial assessment

10.3. PLANNING THE ALEKS CLASS 129

be valid, so that that the students’ work in the Learning Mode be productive from thestart. For the teacher’s own information, other supervised assessments may also be heldat regular intervals to provide accurate “snapshots” of overall progress by the class (SeeSec. 10.11). We suggest that such supervised assessments be scheduled at the midpointand end of the class. Also, any assessment results which may be used as a componentin the students’ grades should, of course, be obtained from assessments performed withthe level of supervision required by the educational institution for final exams (SeeSec. 10.15).

NOTE. In cases where students do not seem to be making adequate progress in ALEKS,the cause may be found in help that the student received on an unsupervised assessmentfrom a person or inappropriately used calculator, skewing the assessment results andleading to inappropriate material in the Learning Mode.

10.3 Planning the ALEKS Class

In some ways, planning a class in which ALEKS is to be used is simpler than planningother kinds of classes. The teacher may assume complete freedom in planning lectures,lessons, and assignments, while ALEKS ensures that students can progress toward mas-tery regardless of their level of preparation. It is neither necessary nor helpful for theteacher to attempt to constrain the interactions of the ALEKS system with individualstudents. To the extent that students will be working independently in ALEKS, thecontent of lab classes is provided by their work in ALEKS, and need not be plannedseparately. Teachers wishing to give their students the greatest possible benefit fromusing ALEKS, however, can use its features to plan focused small-group instructionfrom week to week (See Sec. 10.5).

At the same time, it is extremely important to make ALEKS an integral part of the classrequirements and grading scheme. There is no other single factor which influences thesuccess of students using ALEKS so much as the time that they spend on the system,along with the regularity of their use. This means that the students must be requiredto spend a suitable amount of time in ALEKS on a weekly basis, say 2-4 hours, thatthey must be informed of this at the very beginning of the class, and that the teachermust monitor their fulfillment of this obligation. Moreover, the amount of time requiredmust be carefully determined to be reasonable, and in balance with other requirementsfor the course. The teacher should not simply include an ALEKS requirement withoutreducing in corresponding measure the other requirements that the students would havehad to fulfill without ALEKS. For example, the quantity of homework problems may bereduced, as the students will be solving problems in their ALEKS sessions. In a sense,the ALEKS requirement is stricter than others, since the teacher knows exactly whattime the students have spent, and the students will naturally be sensitive to this. Withtime, students will realize the benefit that they receive from ALEKS, and its effect ontheir overall grades. At first, however, it will be simply another requirement, one whosecommunication requires particular thoughtfulness on the teacher’s part.


Obviously these are only suggestions, and experienced teachers may well choose ap-proaches that will be more effective with their own students. The underlying idea isthat there must be clear, formal support for the use of ALEKS, however that supportis best implemented in a particular setting.

Many teachers have found that in order for the ALEKS requirement to be meaningful,it may beneficially be made part of the grading system or system of rewards for theclass. The simplest approach is to provide a certain number of points toward the finalgrade for each week that the student fulfills their required hours. It is advisable toreward each week, so that the student does not fall into the expectation that all of therequired hours can be done at the end; consistency should be rewarded, along with totalhours. If a student falls short of the specified hours during a particular week, that weekis not rewarded, but neither is the “deficit” carried forward; the next week begins witha clean slate (the primary concern is regular use of the system; for this reason a surplusis also not carried forward). Proportional rewards are also possible; each hour spenthas a point value, up to the required minimum.

In order to effectively monitor the students’ use, the teacher should check the hours onthe “Learning progress since latest assessment” page (under “Reporting”). This pagecan be printed out every week for record-keeping. In very rare cases, students will tryto fool ALEKS by logging on to their accounts and doing something else; this can bedetected by noticing that the number of items gained per hour is far too low (or null).ALEKS will log the student off if there is no activity after a certain amount of time.Teachers can obtain a precise record of a student’s actual work in ALEKS by viewing thestudent’s Report (“Reporting”/“Report for a single student in this class (pie chart)”),under “Learning Log.”

The students’ achievement in ALEKS (as opposed to their use of the system) may alsobe used as a component in their final grade. For information on how to do this pleasesee Sec. 10.15.

10.4 Preparing Your Students

The following considerations may be useful in preparing your students to begin to useALEKS.

Computer Skills

Some students who have had little experience with computers may need assistancewith the use of the mouse and, in particular, with “scrolling” the window of a webbrowser. We recommend that you demonstrate these skills to the students beforebeginning their use of ALEKS. If possible, additional staff should be on hand forthe first session to assist the students as necessary.

Difficulty of Assessment Questions

The ALEKS assessment is always comprehensive in order to achieve the highestdegree of accuracy and reliability. In the course of the assessment, some questions

10.5. FOCUSED INSTRUCTION WITH ALEKS 131

may be too easy or too difficult for some students. The students should be told toclick the “I haven’t learned this yet” button if a question is completely unfamiliarto them, but otherwise that they should do their best to answer. As the assessmentproceeds, the questions will focus more and more closely on the outer limits of thestudent’s actual knowledge. In Learning Mode (following the assessment), studentswill be provided only material that they are ideally prepared to learn.

Length of Assessments

The number of questions asked in an ALEKS assessment varies. Normally anassessment in Arithmetic requires between 15 and 25 questions. Occasionally, thenumber of questions asked may be greater than this.

No Help in Assessments

Explain to the students that they will need to use paper and pencil for answeringassessment questions, but that no help or collaboration whatsoever is permittedduring assessment. If the teacher or anyone else helps the student during as-sessment, even to the extent of explaining or rephrasing a question, assessmentresults may be inaccurate and the student’s learning in ALEKS may initially behindered. Be sure they understand that the purpose of the initial assessment is togive ALEKS a precise, detailed understanding of what a student knows, so as torender learning very efficient by focusing on what the student is ready to learn.It is not a “test” that one can pass or fail. They will not receive a grade on anALEKS assessment unless the teacher deliberately chooses to use grades.

10.5 Focused Instruction with ALEKS

The features of the Teacher Module make it possible to prepare students for specifictopics that they are going to work on, and to reinforce and expand on knowledgethat students have recently acquired. This involves either guiding lectures or focusedinstruction to small groups of students based on data obtained from ALEKS. From theteacher’s viewpoint, these are powerful features of ALEKS, and their use constitutes aproactive integration of ALEKS with the class structure.

The two kinds of “teaching opportunities” cued by ALEKS come from two types ofinformation maintained by the system for students over the entire time that they useit: the set of items a student is “ready to learn” (or “outer fringe” of the student’sknowledge state), and the set of items most recently learned (“what students can do,”the “highest” topics in the student’s knowledge state, called the “inner fringe”) (Seethe Teacher’s Guide under “Inner and Outer Fringes of a Knowledge State,” in thechapter “Knowledge Spaces and the Theory Behind ALEKS”). The items “ready tolearn” are the topics a student may normally choose to work on in ALEKS; the itemsrecently learned (“what a student can do”) are considered the least secure and mostlikely to need review or reinforcement. (These items may be made available for reviewby clicking “Review.”) When the students are logged on to ALEKS these two kinds ofinformation are used automatically to guide and manage their learning. The teacher,


however, can also view the inner and outer fringes in a convenient format to plan focusedinstruction that will parallel, supplement, and enhance the individual work that theirstudents are doing in ALEKS.

To find this information for a class, the teacher should enter the Teacher Module andclick “Reporting,” the name of the class, then “Average report (pie chart).” Thepiechart in Average report represents the average student in the given class, and dis-plays the weaknesses and strengths of the class as a whole. To see the outer and innerfringes of the group we need to use options from the “Display mode” menu: “Ready tolearn,” and “What students can do.”

Suppose we choose the option “Ready to learn (learning)” from the menu “DisplayMode.” This will summarize the topics that all of the students in the class are currentlyready to learn; the parenthesis “(learning)” indicates that the information is based ontheir most recent work in the Learning Mode, and so completely current. For eachtopic the number of students ready to learn that topic appears to the right (e.g., “12students”); clicking on that phrase displays the students’ names, whereas clicking on“Open All” displays all the students’ names for all of the topics. For each topic-list,there is a link to send a message to precisely those students. The purpose of this analysisis that the teacher may pick one or more topics from the list and schedule small-groupsessions preparing the named students to learn them more effectively.

Now suppose we choose “What students can do (learning)” from the menu “DisplayMode.” Another list of topics will be produced; the students listed for these topics,however, are those who have recently worked on and, at least tentatively, learned thetopics. Thus, the teacher can schedule focused sessions with these groups of studentsto reinforce or expand on material that is fresh in the students’ minds, on which theyare likely to have the most questions and ideas.

This gives the teacher the possibility of always teaching to students who are ideallyprepared. It suggests a mode of teaching to the moment of opportunity, and generalizesindividual learning to small groups of learners at specific times; obviously, the dataobtained for this purpose from ALEKS on one day will be of considerably less value ifused a week later.

It may be useful to look at some examples illustrating how these features may be used.If you have not used the ALEKS Teacher Module extensively, it will make more senseas you have more experience using ALEKS as a teaching tool.

Example 1: Basic

On a Friday evening, the teacher sits down to plan lessons for the following week.He or she logs onto ALEKS, selects the reporting feature and the name of a class inArithmetic, and clicks “Average Report.” A pie chart appears showing the averageprofile of mastery in the class.

The “slice” of the pie chart for Whole Numbers is full to about 90 percent; theslices for Fractions, Decimals, and Proportions and Percents are filled much less,ranging between 20 and 40 percent. This indicates that lessons for the week may

10.5. FOCUSED INSTRUCTION WITH ALEKS 133

focus profitably on the most advanced Whole Numbers topics as well as on topicsof moderate difficulty in Fractions, Decimals, and Proportions and Percents.

Example 2: Intermediate

On a weekend afternoon, the teacher logs on to ALEKS, clicks “Reporting,” thenthe name of a class in Arithmetic, and then “Average report (pie chart).” Aftera look at the pie chart, the teacher selects “Ready to learn (learning)” from the“Display Mode” menu, and clicks “OK.” When the list of topics appears, theteacher scans this list for items of particular difficulty. There it is! “OrderingNumbers with Exponents” has 16 students currently able to choose this topic fromtheir pie charts. The teacher notes this topic down for class discussion early in theweek. With the benefit of some timely preparation, the students can be expectedto master this troublesome topic with little or no difficulty.

Example 3: Advanced

On a Monday morning, the teacher logs on to his or her ALEKS account, clicks“Reporting,” then the name of a class in Algebra 1, and then “Average report (piechart).” Following this the teacher switches, first, to the option for “Ready to learn(learning)” and clicks the ALEKS Print button. Even if “Open All” was not clickedthe page will be displayed with all lists of students’ names displayed. Then, theteacher switches to the option for “What students can do (learning),” and, again,clicks the Print button. With these two printouts in hand, the experience andexpertise of the teacher are used to used to plan with this information. Supposethat there is only time in the week’s schedule for two small-group sessions. (TheALEKS class has only one hour in the lab, and ten minutes are set aside to speakwith each small group; the remaining 40 minutes are for helping students in thelab.) The teacher will look over the topics with two questions in mind: whichtopics have the greatest numbers of students, and which are pedagogically mostworth discussing.

For example, looking at the list of topics “Ready to learn,” the teacher sees “Solvinga Linear Equation with Absolute Value: Problem Type 1.” The teacher knows fromexperience that students have difficulty with the concept, and that they are moresuccessful with it if they have had a chance to review. This topic has 12 studentsout of 30 in the class. The teacher uses the message feature to send a note to thesestudents, asking them to meet in the front of the room at the beginning of the lab;the students will receive this note the next time they log on to ALEKS, no laterthan the beginning of that lab.

Looking over the list of topics “What students can do,” the teacher sees “Marking apoint in the coordinate plane,” with 10 students. Although the number of studentsis less than for other topics, this one seems to the teacher richer in its content ofmathematical culture than the others. Students who have just worked on thistopic are using the coordinate plane for the first time, and they are ripe for anintroduction to the vast areas of mathematical thought for which it opens thedoor. Thus this is chosen as the second topic, and a second message is sent tothese students, to meet at the front of the room, ten minutes into the lab.


10.6 Models of Classroom Integration

There are numerous ways in which ALEKS can be and is used in concrete educationalsituations.

1. Supervised Math Lab. Expert supervision can be provided for the students’use of ALEKS in regularly scheduled math lab periods, whether or not these arepart of a conventional class structure. Students benefit from the direct coachingand assistance of qualified teachers in the course of their work with ALEKS.

2. Math Lab in Structured Course. The supervised math lab may be part of astructure of class meetings, combined with conventional and lecture-style classes.The teacher in such a setting need not gear the sequence of topics covered in classesin any way with what the students are doing in ALEKS; the students’ independentwork in ALEKS will increasingly benefit their performance on quizzes and tests,as well as their understanding of lectures, as the class progresses. ALEKS isnot designed to “teach to the test,” although experience has shown that students’performance on comprehensive tests improves dramatically when they have workedwith ALEKS over time.

3. Small-Group Instruction. The recommended use of ALEKS in a classroomsetting makes use of the detailed analysis of individual student knowledge providedthrough the Class Report page to tailor the lectures to the skills of students.

4. Self-Paced Learning. In this scenario students may use the school computerlab on their own, with only informal supervision. ALEKS is used in this case muchas it is for distance learning, except that students have the opportunity for closerconsultation with the instructor.

5. Distance Learning. ALEKS is used with great independence by students whomay never enter the physical classroom, or may enter only on a few occasions fororientation and supervised assessments. ALEKS provides a range of features forcommunication between teacher and student, as well as powerful facilities for themonitoring and evaluation of student work.

Regardless of which approach is used, you can derive more benefit from ALEKS thoughmonitoring the students’ use of ALEKS and communicating with them, whether indirect contact, by email, or by messages through the ALEKS system. As discussedabove, we recommend that a certain number of hours in ALEKS each week be required(See Sec. 10.2); this should be made clear from the start as part of the published coursesyllabus and rewarded appropriately through the grading scheme. Students’ progressin ALEKS should be recognized and reinforced early on by informal, personal praise;conversely, students who do not seem to make adequate progress should be contactedpromptly, the cause of their difficulty determined and remedied.

The following sections of this chapter provide more information on these issues affectingthe classroom use and integration of ALEKS.

10.7. MONITORING STUDENT USE 135

10.7 Monitoring Student Use

In the day-to-day use of ALEKS by a class, a principal concern of the teacher is to mon-itor that students are using the system with the required regularity and for at least theminimum required amount of time. The most convenient place to find this informationis the “Learning progress since latest assessment page” (under “Reporting”). Each stu-dent’s name is displayed on this page with the total number of hours that student hasspent logged on to the system. Students can see this same total in their own accountsby using the button “Report.”

It is also important that critical assessments throughout the class be supervised by theteacher, to ensure that valid results are received (See Sec. 10.2).

10.8 Monitoring the Progress of a Class

The teacher can also use the bar graphs to see how close each student is to mastery ofthe subject matter on the Learning Progress Since Latest Assessment page. It shouldbe kept in mind that the bar graphs displayed on this page show only the students’achievement as of their last assessment (in blue) and any progress made in the LearningMode since that assessment (in green). For a more panoramic view of the progressmade by a group, select the “Overall progress in assessment” report. This displaysthe difference between the students’ knowledge as of their first assessment and thatdemonstrated on their most recent assessment.

To see each of the assessments for a given student, with that student’s progress sub-sequent to each assessment in the Learning Mode, the teacher should view the page“Progress report for a single student in this class” for the student.

10.9 Monitoring Individual Progress

On the page “Progress report for a single student in this class” there is a line foreach assessment taken by a particular student, with bar graphs showing mastery asof that assessment and subsequent progress made in the Learning Mode. The initialassessment is shown in the bottom line, with later assessments “stacked” upward. Byfollowing progression from earlier to later assessments, the teacher can see very clearlyhow a student is progressing toward mastery of the subject matter.

Caution should be exercised in interpreting this information. Students vary widely bothin the smoothness and in the speed with which they master material. Progress madein the Learning Mode (green bar) is not always immediately reflected in the student’slevel of mastery on a subsequent assessment. Some students progress more quickly inassessment than in the Learning Mode. In such cases the “new” blue line is furtherahead than the green line just below it. On the other hand, many students make faster


progress in the Learning Mode than in assessment. In such cases the “new” blue linelags behind the green line below it. It is very common for a student to master the entiresubject matter two or more times in the Learning Mode before that mastery is finallyconfirmed in an assessment. None of these situations is unusual. Part of the power ofthe ALEKS system is that it does not expect students to behave like machines, butmakes allowance for a robust and unpredictable “human factor.”

NOTE. In cases where a student moves backward in his or her mastery, the teachershould make individual contact with the student. This student may be experiencinga personal problem, there may have been third-party help on an initial assessment, orthere may be other external factors affecting the situation.

10.10 Moving a Student to a New Class

A student subscription to ALEKS entitles the student to work through as many subjectsin the sequence as the student masters during the subscription period. When a studentcompletes the objectives of a class, ALEKS will allow the student to continue untilthe subject-matter is exhausted. At this point the student should be moved to a moreadvanced class.

For example, when a student completes the subject matter for a class whose programcorresponds to Arithmetic, the teacher should unenroll that student from Arithmeticin ALEKS and reenroll the student in a new class whose topic is set to Algebra. If nosuch class exists, it should be created so that the student is not prevented from makingfurther progress.

10.11 Ordering Assessments

Following the initial assessment (which should be taken under the teacher’s supervi-sion), the ALEKS system will automatically schedule any other assessments needed forcorrectly informing and guiding a student’s progress. The instructor, however, can orderan individual or group assessment at any time. It is a good practice for the teacher toschedule supervised assessments at regular intervals (interim and end of the class), as“snapshots” of overall class achievement. Assessments may be ordered more frequentlyif the teacher feels that there has been third-party help on some automatic assessments,producing invalid results.

10.12 Independent Study and Distance Learning

The ALEKS system is well suited to use in an independent study or distance learningcontext. ALEKS is self-contained and adaptable to any program or class materials.Students using ALEKS under these circumstances know exactly what the class goals

10.13. THE ALEKS KNOWLEDGE STRUCTURE 137

are, where they stand in relation to those goals, and where to find the instructional andpractice tools to achieve them.

For the teacher administering an independent study or distance learning program,ALEKS solves nearly every problem of management, oversight, evaluation, and commu-nication. All of the information needed to keep track of far-flung independent learnersis at the teacher’s fingertips, through the features of the Teacher Module. The internalmessage system of ALEKS puts the teacher in constant touch with students withoutdependence on telephone or email communication.

10.13 The ALEKS Knowledge Structure

Each ALEKS subject, such as Algebra 1, has a knowledge structure associated with it.The knowledge structure for Algebra 1, for example, is covered by about 300 ALEKSitems (or problem types). A knowledge state is a subset of items which may correspondto the knowledge of an actual student (i.e., there may be a student who has masteredexactly those items, and no others). A knowledge structure is the family of all theknowledge states that we may encounter for a given subject.

An ALEKS structure affects virtually every aspect of ALEKS’s functioning. In theALEKS assessment mode it enables ALEKS to make inferences from student answers,keeping the ALEKS assessments brief, but uncannily accurate.

The structure is also crucial in the ALEKS Learning Mode. Using the structure ofAlgebra 1, for example, the system knows precisely which items are in the inner fringeand outer fringe of each of the knowledge states in ALEKS for Algebra 1. The items inthe outer fringe of a student’s knowledge state are those items that the student is themost ready to learn next. (From a technical standpoint an item is in the outer fringeof a state if adding that item to the state results in a feasible knowledge state.) Theseitems are presented to the student in MyPie when the student moves the mouse pointerover the ALEKS pie chart. Similarly, an item in the inner fringe of a student’s state isan item either recently learned or one whose mastery by the student might be shaky.(Technically, an item is in the inner fringe of a state if removing that item from thestate results in another feasible knowledge state.) They are presented to the studentwhen the student is having difficulty in the ALEKS Learning Mode and during ALEKSreview.

An additional benefit of the proliferation of connections among items in ALEKS is itsextreme flexibility from the students’ viewpoint: for any particular topic, there is a vastnumber of possible approaches, or learning paths, which may lead students to masteryof that topic. This flexibility does not imply, however, that any order is possible. Eachlearning path leading to a particular topic must contain, at a minimum, the items whichare “below” such topic in the ALEKS structure. That is, we may say that the more“advanced,” or “highest,” topics in an ALEKS structure are those for which the ALEKSsystem will require the student to learn the largest number of other items before thoseitems will be presented to the student.


10.14 Modification of Programs

Teachers do not need to create or modify the program in order to use ALEKS. Everysubject has a comprehensive default, which will be in effect without any actions on theteacher’s part.

In some cases it may be desirable to modify the program used for a particular group ofstudents. Extensive creation and modification of Standards and Programs is possible inthe ALEKS Advanced Teacher Module (See the Teacher’s Guide, chapter “AdvancedTeacher Module: Standards & Programs”). Please keep in mind the following pointsregarding the use of programs in ALEKS:� A program in ALEKS implies the existence of a knowledge state, that is, a possible

configuration of a student’s knowledge, defined as the goal of the class. As such,all items in this “final” knowledge state of the program must be learnable withinthe program. This is determined in ALEKS by reference to the ALEKS structure(See above, Sec. 10.13). If an item is added to the program in ALEKS, all otheritems which are “below” that item will also be added. If an item is removed, allother items in the program which are “above” that item in the ALEKS structurewill also be removed. The Content Editor warns when this is occurring.� Thus it is possible to modify a program in ALEKS only by “trimming” the treefrom its branches, not from its roots.

ALEKS also provides a facility for creating multiple sets of programs within a singleclass (See the Teacher’s Guide under “Intermediate Objectives,” in the chapter “Ad-vanced Teacher Module: Results & Progress”). The Intermediate Objectives featuremakes it possible to prioritize particular sets of items for particular periods of time,by constraining the choices available to the students. When Intermediate Objectiveshave been set, students will be guided to these items by the shortest possible path.Items that they are ready to learn, but are not on the shortest path to the IntermediateObjectives, with be “grayed out”; they will appear in the students’ pie charts, but thestudents will not be able to choose them.

10.15 Learning Rates in ALEKS

ALEKS allows teachers to flexibly evaluate and interpret student learning. There arefour criteria, which can be used in any combination: percentage of course goals mastered,total hours spent in ALEKS, average items gained per hour of use, and average numberof items gained per week of use. Each can be set to “Private,” so that only the teachersees the evaluations, to “Public,” so that the teacher sees the evaluations for all students,and each student sees their own, or to “Disabled,” so that no one sees them.

Detailed instructions on the use of the learning rates feature may be found in theTeacher’s Guide under “Assign Learning Rates,” in the chapter “Advanced TeacherModule: Results & Progress.”

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Caution must be exercised in determining which, if any, of these criteria should be setto “Public,” so that they are seen by the students. For example, if the evaluation forpercentage of course goals mastered is set to A for 90 percent, B for 80 percent, C for70 percent, D for 60 percent, and Failure below that, the students will see these lettersin their accounts as long as their percentage mastery is in the ranges given (i.e., D whenit is between 60 and 69 percent). This will only make sense when the students are closeto finishing the course, and may cause confusion if the grades are made “Public” beforethen.

The same proviso applies to the other kinds of evaluations available through ALEKS.The value of using these evaluations in the “Public” mode may be greatly enhanced ifthe teacher decides to set a new scale every week, or at other appropriate intervals. Thismight mean, for example, that A is set to 20 percent for the first week, to 25 percentfor the second week, and so forth, with the other evaluations set accordingly. Such aprocedure requires more work by the teacher, but it certainly gives the students a moremeaningful frame of reference for their progress.

Some of the kinds of evaluations in ALEKS may be more useful for the teacher alonethan for the students. Such evaluations should be set to “Private.” The evaluationbased on average items gained per week, for example, might be set to some minimumvalue like 3 (in an Algebra class requiring 3 hours of work in ALEKS per week). Now,the teacher would not want to send the message to the students that 3 items gainedper week is “Enough,” since many students in the class may be capable of much more.Conversely, a student whose progress falls below this rate might not be helped by thestern notation in their account that their progress is “Not enough”; the reasons forslow progress may be varied. At the same time, a student making slower progress thanthis should be brought to the teacher’s attention for intervention of some kind. If theevaluation is set to “Private,” the teacher will see the flag “Not enough” appearing nextto the names of students whose progress is slower than this, on the Class Progress page,alerting them to the need for special attention.

Chapter 11

Knowledge Spaces and the TheoryBehind ALEKS

11.1 History

Knowledge Space Theory has been under development since 1983 by Professor Jean-Claude Falmagne, who is the Chairman and founder of ALEKS Corporation, and otherscientists (especially, Jean-Paul Doignon from Belgium) in the United States and Eu-rope.

ALEKS is the first computer system to embody Knowledge Space Theory for assessmentand teaching.

11.2 Theory

An exposition of Knowledge Space Theory is not intended here, nor is one necessary forthe purposes of this manual. Knowledge Space Theory is expressed in a mathematicaldiscipline often referred to as “Combinatorics.” The Bibliography contains a number ofreferences for those interested in further details (See Sec. 11.3). What follows here is abrief, intuitive summary introducing certain fundamental terms employed in discussionsof ALEKS.

11.2.1 Domain, Items, and Instances

An academic discipline such as Arithmetic or Algebra is represented as a particular setof problems or questions that comprehensively embody the knowledge of the discipline.That set is called the domain, and the problems are called items. A symbolic repre-sentation of the domain of Arithmetic uses dots standing for items (Fig. 11.1). One of

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142 CHAPTER 11. KNOWLEDGE SPACES AND THE THEORY BEHIND ALEKS

Figure 11.1: Domain of Arithmetic

the items, which might be entitled “Word problem with percentages,” is indicated by aline. The problem in the rectangle is an instance of that item.

Each item, or problem type, has dozens, sometimes hundreds or thousands, of instances.In ALEKS, the domain of Arithmetic is made up of about one hundred items, rangingfrom two-digit addition (without carry), to negative exponents. Algebra has a domaincontaining around two hundred items. Full mastery of the domain implies the abilityto solve problems corresponding to all the items making up the domain.

Determining the set of items that make up the domain is the first step in constructinga “knowledge structure” for that domain. This is done by research in instructionalmaterials and standards and very systematic, painstaking consultation with teachers.Substantial agreement is achieved among expert pedagogues on the choice and defi-nition of items. The set of items finally arrived at and forming the domain must becomprehensive, that is, it must cover all the concepts that are essential in the particularacademic discipline.

11.2.2 Knowledge States

The knowledge state of a student is represented by the set of items in the domainthat he or she is capable of solving under ideal conditions (Fig. 11.2). This means thatthe student is not working under time pressure, is not impaired by emotional turmoil

11.2. THEORY 143

Figure 11.2: Knowledge State

of any kind, etc. In reality, careless errors may arise. Also, the correct response to aquestion may occasionally be guessed by a subject lacking any real understanding of thequestion asked. (This will occur very rarely when using the ALEKS system, becausemultiple choice answers are not used.) In general, an individual’s knowledge state isthus not directly observable, and has to be inferred from the responses to the questions.

11.2.3 Knowledge Structures and Knowledge Spaces

It should be intuitively obvious that not all possible subsets of the domain are feasibleknowledge states. For instance, every student having mastered “long division” wouldalso have mastered “addition of decimal numbers.” Thus, there is no knowledge statecontaining the “long division” item that does not also contain the “addition of decimalnumbers” item. The collection of all feasible knowledge states is referred to as theknowledge structure. In the current implementation of ALEKS for Arithmetic, thenumber of feasible knowledge states is approximately 50,000. Thus, the knowledgestructure for Arithmetic contains approximately 50,000 knowledge states. In order toassess a student in Arithmetic, ALEKS must find out by efficient questioning which ofthese 50,000 states the student is in. This large number of states means that there aremany possible ways of acquiring knowledge, i.e., many learning paths (Fig. 11.3). Inthe ALEKS knowledge structure there are literally billions of such learning paths. A


Figure 11.3: Learning Path

“knowledge space” is a particular kind of knowledge structure.

As in many real-life applications, “noise” and errors of various sorts often creep in,which require the elaboration of a probabilistic theory. The ALEKS System is basedon such a probabilistic theory, which makes it capable of recovering elegantly fromany misconceptions. For instance, ALEKS is capable of deciding that a student hasmastered an item, even though the student has actually made an error when presentedwith a problem instantiating this item. This is not mysterious: a sensible examinerin an oral exam, observing an error to a question about addition would neverthelessconclude that the student has mastered addition, for example, if that student had givenevidence of skillful manipulation of fractions.

11.2.4 Inner and Outer Fringes of a Knowledge State

An item that has not yet been mastered by a student may not be immediately learnableby that student. Learning one or more prerequisite items may be necessary. Considera student in a particular knowledge state K. The set of all items that may be learnedimmediately by a student in that state K is called the outer fringe of the state K.More precisely, an item is in the outer fringe of the state K if the addition of that itemto the state K forms a new, feasible knowledge state (Fig. 11.4). Typically, the outerfringe of a knowledge state will contain between one and several items.

11.2. THEORY 145

Figure 11.4: Outer Fringe of a Knowledge State

Similarly, an item is in the inner fringe of a state K if there is some other knowledgestate to which that item may be added to form state K (Fig. 11.5). The inner fringeof a state K is thus defined as the set of all items which may have been the last onelearned.

These two concepts of inner and outer fringes are used in powerful ways in the LearningMode of the ALEKS system. For example, the system always offers a student problemsto solve that are based on items in the outer fringe of his or her state. If ALEKS judgesthat a student is experiencing difficulties in learning some new item, ALEKS typicallyreviews the mastery of items in the inner fringe of the student’s state that are alsorelated to the new item to be learned.

11.2.5 Assessment

How can ALEKS uncover, by efficient questioning, the particular knowledge state of astudent? While the details of ALEKS’s method for achieving such a goal are technical,the guiding intuition is straightforward. At every moment of an assessment, ALEKSchooses a question to be “as informative as possible.” In our context, this means aquestion which the student has, in the system’s estimate, about a 50 percent chanceof getting right. The student’s response (correct or false) determines a change in allthe likelihood values: for instance, if the question involved a manipulation of fractions,and the student’s response was correct, then all the knowledge states containing thisitem would have their likelihood values increased. The specific way the questions are


Figure 11.5: Inner Fringe of a Knowledge State

chosen and the likelihood values altered makes it possible for ALEKS to pinpoint thestudent’s state quite accurately in a relatively short time. In Arithmetic, for example,approximately 15–25 questions often suffice.

Finally, it should be noted that the assessment report given to students, teachers, andadministrators is a very precise summary of the student’s knowledge state. If thestructure is known, the outer fringe and inner fringe together completely define thestudent’s knowledge state. Internally, the system registers the student’s knowledge ornon-knowledge of each item in the domain.

A comprehensive treatment of Knowledge Space Theory can be found in Doignon andFalmagne, Knowledge Spaces (Springer-Verlag, 1999).

11.3 Selected Bibliography

Albert, D., editor. (1994). Knowledge Structures. Springer Verlag, New York, 1994.

Albert, D. and Hockmeyer, C. (1997). Adaptive and dynamic hypertext tutoring sys-tems based on knowledge space theory. In Benedict du Boulay and Riichiro Mizoguchi,editors, Artificial Intelligence in Education: Knowledge and Media in Learning Sys-

tems, volume 39 of Frontiers in Artificial Intelligence and Applications, pp. 553-555,Amsterdam, 1997. IOS Press.

Albert, D. and Lukas, J., editors. (1999). Knowledge Spaces: Theories, Empirical

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Research, Applications. Lawrence Erlbaum Associates, Mahwah, NJ, 1999.

Albert, H. P. Bahrick, J.-C. Falmagne, C. Witteveen, G. d’Ydewalle, and M. Toda.Representation and assessment of knowledge. (1990) In B. Wilpert, H. Motoaki, andJ. Mitsumi, editors, General Psychology and Environmental Psychology, volume 2, pp.9-98, July 1990. Proceedings of the 22nd International Congress of Applied Psychology.

Baumunk, K. and Dowling, C. (1997). Validity of spaces for assessing knowledge aboutfractions. Journal of Mathematical psychology, 41, 99-105, 1997.

Brandt, S., Albert, D., and Hockemeyer, C. (1999). Surmise relations between tests -preliminary results of the mathematical modelling. Electronic Notes in Discrete Math-

ematics, 2, 1999.

Cosyn, E. (2002). Coarsening a knowledge structure. Journal of Mathematical Psychol-

ogy, 46, 123-139, 2002.

Cosyn, E. and Thiery, N. (2000). A practical procedure to build a knowledge structure.Journal of Mathematical Psychology, 44, 383-407, 2000.

Degreef, E., Doignon J.-P., Ducamp A., and Falmagne J.-C. (1986). Languages for theassessment of knowledge. Journal of Mathematical Psychology, 30, 243-256, 1986.

Doignon, J.-P. (1998). Dimensions of chains of relations. Electronic Notes in Discrete

Mathematics, 2, 1999. Abstract of a Talk presented at the OSDA98, Amherst, MA,September 1998.

Doignon, J.-P. and Falmagne, J.-C. (1985). Spaces for the assessment of knowledge.International Journal of Man-Machine Studies, 23, 175-196, 1985.

Doignon, J.-P. and Falmagne, J.-C. (1987). Knowledge assessment: A set theoreticalframework. In B. Ganter, R. Wille, and K.E. Wolfe, editors, Beitrage zur Begriffs-

analyse: Vortrage der Arbeitstagung Begriffsanalyse, Darmstadt 1986, pp. 129-140,Mannheim, 1987. BI Wissenschaftsverlag.

Doignon, J.-P. and Falmagne, J.-C. (1988). Parametrization of knowledge structures.Discrete Applied Mathematics, 21, 87-100, 1988.

Doignon, J.-P. and Falmagne, J.-C. (1997). Well-graded families of relations. Discrete

Mathematics, 173, 35-44, 1997.

Doignon, J.-P. and Falmagne, J.-C. (1999) Knowledge Spaces. Springer-Verlag, 1999.

Doignon, J.-P. and Falmagne, J.-C., editors. (1991). Mathematical Psychology: Current

Developments. Springer-Verlag, New York, 1991.

Dowling, C.E. (1993). Applying the basis of knowledge space for controlling the ques-tioning of an expert. Journal of Mathematical Psychology, 37, 21-48, 1993.

Dowling, C.E. (1993). On the irredundant construction of knowledge spaces. Journal

of Mathematical Psychology, 37, 49-62, 1993.

Dowling, C. and Hockemeyer, C. (1998). Computing the intersection of knowledgespaces using only their basis. In Dowling, C., Roberts, F., and Theuns, P., editors, Re-

cent Progress in Mathematical Psychology, pp. 133-141. Lawrence Erlbaum AssociatesLtd., Hillsdale, USA, 1998.


Dowling, C. and Hockemeyer, C. (1998). Integrating knowledge spaces obtained byquerying different experts. Electronic Notes in Discrete Mathematics, 2, 1999. Abstractof a Talk presented at the OSDA98, Amherst, MA, September 1998.

Dowling, C. and Hockemeyer, C. (2001). Automata for the assessment of knowledge.IEEE Transactions on Knowledge and Data Engineering, 13(3), 451-461, 2001.

Dowling, C., Hockemeyer, C., and Ludwig, A. (1996). Adaptive assessment and trainingusing the neighbourhood of knowledge states. In Claude Frasson, Gilles Gauthier, andAlan Lesgold, editors, Intelligent Tutoring Systems, volume 1086 of Lecture Notes inComputer Science, pp. 578-586, Berlin, 1996. Springer Verlag.

Dowling, C. and Kaluscha, R. (1995). Prerequisite relationships for the adaptive as-sessment of knowledge. In Jim Greer, editor, Artificial Intelligence in Education, 1995,pp. 43-50, Charlottesville, VA, 1995. Association for the Advancement of Computingin Education (AACE).

Dowling, C., Roberts, F., and Theuns, P., editors. (1998). Recent Progress in Math-

ematical Psychology. Scientific Psychology Series. Lawrence Erlbaum Associates Ltd.,Hillsdale, USA, 1998.

Duntsch, I. and Gediga, G. (1995). Skills and knowledge structures. British Journal of

Mathematical and Statistical Psychology, 48, 9-27, 1995.

Duntsch, I. and Gediga, G. (1996). On query procedures to build knowledge structures.Journal of Mathematical Psychology, 40, 160-168, 1996.

Duntsch, I. and Gediga, G. (1998). Knowledge structures and their applications inCALL. In Sake Jager, John Nerbonne, and Arthur van Essen, editors, Language teaching

and Language Technology, pp. 177-186. Swets and Zeitlinger, Lisse, 1998.

Falmagne, J.-C. (1989). A latent trait theory via stochastic learning theory for a knowl-edge space. Psychometrika, 54, 283-303, 1989.

Falmagne, J.-C. (1989). Probabilistic knowledge spaces: a review. In Roberts, F.,editor, Applications of Combinatorics and Graph Theory to the Biological and Social

Sciences, volume 17 of IMA, pp. 283-303. Springer Verlag, New York, 1989.

Falmagne, J.-C. (1993). Stochastic learning paths in a knowledge structure. Journal of

Mathematical Psychology, 37, 489-512, 1993.

Falmagne, J.-C. (1996). Errata to SLP. Journal of Mathematical psychology, 40, 169-174, 1996.

Falmagne, J.-C. (1998). ALEKS, an application of knowledge space theory. Electronic

Notes in Discrete Mathematics, 2, 1999. Tutorial given at the OSDA98, Amherst, MA,September 1998.

Falmagne, J.-C. and Doignon, J.-P. (1988). A class of stochastic procedures for theassessment of knowledge. British Journal of Mathematical and Statistical Psychology,41, 1-23, 1988.

Falmagne, J.-C. and Doignon, J.-P. (1988). A markovian procedure for assessing thestate of a system. Journal of Mathematical Psychology, 32, 232-258, 1988.


Falmagne, J.-C. and Doignon, J.-P. (1993). A stochastic theory for system failureassessment. In B. Bouchon-Meunier, L. Valverde, and R.R. Yager, editors, Uncertainty

in Intelligent Systems, pp. 431-440. North-Holland, Amsterdam, 1993.

Falmagne, J.-C. and Doignon, J.-P. (1997). Stochastic evolution of rationality. Theory

and Decision, 43, 107-138, 1997.

Falmagne, J.-C. and Doignon, J.-P. (1998). Meshing knowledge structures. In Dowling,C., Roberts, F., and Theuns, P., editors, Recent Progress in Mathematical Psychology,

Scientific Psychology Series, pp. 143-153. Lawrence Erlbaum Associates Ltd., Hillsdale,USA, 1998.

Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J.-P. and Johannesen, L. (1990).Introduction to knowledge spaces: How to build, test and search them. Psychological

Review, 97, 201-224, 1990.

Fischer, G. and Laming, D., editors. (1994). Contributions to Mathematical Psychology,

Psychometrics, and Methodology. Springer–Verlag, New York, 1994.

Fries, S. (1997). Empirical validation of a markovian learning model for knowledgestructures. Journal of Mathematical psychology, 41, 65-70, 1997.

Hockemeyer, C. (1997). Using the basis of a knowledge space for determining the fringeof a knowledge state. Journal of Mathematical psychology, 41, 275-279, 1997.

Hockemeyer, C., Albert, D., and Brandt, S. (1998). Surmise relations between courses.Journal of Mathematical psychology, 42, 508, 1998. Abstract of a talk presented at the29th EMPG meeting, Keele, UK, September 1998.

Kambouri, M., Koppen, M., Villano, M. and Falmagne, J.-C. (1991). Knowledge as-sessment: Tapping human expertise. Irvine Research Unit in Mathematical Behavioral

Sciences. University of California, 1991.

Kambouri, M., Koppen, M., Villano, M., and Falmagne, J.-C. (1994). Knowledgeassessment: tapping human expertise by the QUERY routine. International Journal of

Human-Computer-Studies, 40, 119-151, 1994.

Koppen, M. (1993). Extracting human expertise for constructing knowledge spaces: Analgorithm. Journal of Mathematical Psychology, 37, 1-20, 1993.

Koppen, M. and Doignon, J.-P. (1990). How to build a knowledge space by queryingan expert. Journal of Mathematical Psychology, 34, 311-331, 1990.

Lakshminarayan, K. and Gilson, F. (1998). An application of a stochastic knowledgestructure model. In Dowling, C., Roberts, F., and Theuns, P., editors, Recent Progress

in Mathematical Psychology, Scientific Psychology Series, pp. 155-172. Lawrence Erl-baum Associates Ltd., Hillsdale, USA, 1998.

Lukas, J. and Albert, D. (1993). Knowledge assessment based on skill assignment andpsychological task analysis. In Strube, G. and Wender, K., editors, The Cognitive

Psychology of Knowledge, volume 101 of Advances in Psychology, pp. 139-160. North-Holland, Amsterdam, 1993.


Muller C. (1989). A procedure for facilitating an expert’s judgments on a set of rules.In Edward E. Roskam, editor, Mathematical Psychology in Progress, pp. 157-170.Springer-Verlag, Berlin, 1989.

Rusch, A. and Wille, R. (1996). Knowledge spaces and formal concept analysis. InHans-Hermann Bock and Wolfgang Polasek, editors, Data Analysis and Information

Systems, Studies in Classification, Data Analysis, and Knowledge Organization, pp.427-436, Berlin, Germany, 1996. Springer-Verlag.

Schrepp, M. (1997). A generalization of knowledge space theory to problems with morethan two answer alternatives. Journal of Mathematical psychology, 41, 237-243, 1997.

Schrepp, M. (1999). Extracting knowledge structures from observed data. British

Journal of Mathematical and Statistical Psychology, 52, 213-224, 1999.

Schrepp, M. (1999). On the empirical construction of implications between bi-valuedtest items. Mathematical Social Sciences, 38, 361-375, 1999.

Schrepp, M. (2001). A method for comparing knowledge structures concerning theiradequacy. Journal of Mathematical Psychology, 45, 480-496, 2001.

Schrepp, M. and Held, T. (1995). A simulation study concerning the effect of errors onthe establishment of knowledge spaces by querying experts. Journal of Mathematical

psychology, 39, 376-382, 1995.

Stefanutti, L. and Albert, D. (2002). Efficient assessment of organizational action basedon knowledge space theory. In Klaus Tochtermann and Hermann Maurer, editors, 2ndInternational Conference on Knowledge Management, Journal of Universal Computer

Science, pp. 183-190, 2002.

Strube, G. and Wender, K., editors. (1993). The Cognitive Psychology of Knowledge,volume 101 of Advances in Psychology. Elsevier, 1993.

Suck, R. (1998). Ordering orders. Mathematical Social Sciences, 36, 91-104, 1998.

Suck, R. (1998). The basis of a knowledge space and a generalized interval order.Electronic Notes in Discrete Mathematics, 2, 1999.

Suck, R. (1999). A dimension-related metric on the lattice of knowledge spaces. Journal

of Mathematical psychology, 43, 394-409, 1999.

Taagepera, M., Potter, F., Miller, G., and Lakshminarayan, K. (1997). Mapping stu-dents thinking patterns by the use of knowledge space theory. International Journal of

Science Education, 19, 283-302, 1997.

Theuns, P. (1998). Building a knowledge space via boolean analysis of co-occurrencedata. In Dowling, C., Roberts, F., and Theuns, P., editors, Recent Progress in Math-

ematical Psychology, Scientific Psychology Series, pp. 173-194. Lawrence ErlbaumAssociates Ltd., Hillsdale, USA, 1998.

Villano, M., Falmagne, J.-C., Johannsen, L., and Doignon, J.-P. (1987). Stochasticprocedures for assessing an individual’s state of knowledge. In Proceedings of the In-

ternational Conference on Computer-assisted Learning in Post-Secondary Education,Calgary 1987, pp. 369-371, Calgary, 1987. University of Calgary Press.


Wille, R. (1998). Formal concept analysis. Electronic Notes in Discrete Mathematics,2, 1999. Abstract of a Tutorial given at the OSDA98, Amherst, MA, September 1998.

Wille, R. (1998). Mathematical support for empirical theory building. ElectronicNotes in Discrete Mathematics, 2, 1999. Abstract of a Talk presented at the OSDA98,Amherst, MA, September 1998.

Chapter 12

Frequently Asked Questions

12.1 General

General questions on ALEKS concern what it is, its purpose, and what it contains.

What is ALEKS?

ALEKS is the new way to learn math on the World Wide Web. By knowing exactly whichmath concepts the student has mastered, which are shaky, and which are new but withinreach, ALEKS enables the student to work on those concepts the student is most ready tolearn. ALEKS is a full-time automated tutor, including explanations, practice and feedback.ALEKS closely interacts with the student, continuously updating its precise map of thestudent’s knowledge state. ALEKS combines the advantages of one-on-one instruction andevaluation with the convenience of being on-call, on your computer, 24 hours a day, sevendays a week. The cost of ALEKS is a small fraction of the cost of a human tutor.

What makes ALEKS different?

A great many important differences exist between ALEKS and other kinds of “educationalsoftware,” including its finely individualized instructional features, easy access over the WorldWide Web, its rigorous and comprehensive educational content, and its class-managementmodule for teachers and administrators.

A critical difference is the capacity of ALEKS for efficient, precise, comprehensive, and quali-tative assessment. This not only makes it a valuable tool for monitoring educational progress,but also enables it to provide students with the material they are most able to learn at a par-ticular time. This means that the students are given neither material that they have alreadymastered nor material that they are not well suited to work on yet because some prerequisiteshave yet to be learned.

ALEKS is a self-contained learning environment, with complete sets of practice and explana-tory units needed for the subjects that it covers. There is an online student mathematics

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154 CHAPTER 12. FREQUENTLY ASKED QUESTIONS

dictionary accessed by clicking on underlined mathematical terms (hypertext links), and adiagnostic feedback facility that, in many cases, is able to explain the nature of misunder-standings and errors made by students.

For teachers, ALEKS offers a complete administrative and monitoring facility through whichindividual and group progress can be checked, standards established, enrollment managed,and messages exchanged. ALEKS can be configured for use with diverse educational stand-ards.

ALEKS is not a game or “edutainment.” It is an automated educational tool with robust,carefully-designed features for both learners and educators.

What are the parts or “modules” of ALEKS?

The principal “modules” of ALEKS are the Assessment Mode, in which student knowl-edge is rigorously assessed, the Learning Mode, where students work on mastering specificconcepts, the Teacher Module, in which teachers and administrators are able to monitorstudent progress and carry out administrative functions, and the Administrator Module,which permits management and monitoring of an arbitrary number of separate institutions,such as those making up a school district. There is also a Tutorial (which students takeonce when first registering with the system), online help, a mathematics Dictionary, graphicdisplay of assessment results and learning progress, and many other features.

Why is ALEKS on the Internet?

ALEKS is available on the Internet so that a student who has registered with the systemcan use it from any suitable computer, in a school, at home, or anywhere else. Very littletechnical preparation is required. All you need is a self-installing, self-maintaining “plugin”obtained directly from the ALEKS website. No disks, CD’s, peripherals, or backup facilitiesare required. All data is kept on the ALEKS Corporation servers.

12.2 Technical

The technical information needed to use ALEKS is minimal. These few questions areall that are likely to come up, even in a large number of users.

What are the system requirements for using ALEKS?

[Sec. 3.2] The following table presents the technical requirements for ALEKS insummary form:

Your browser should be configured with Java enabled. Both Netscape and InternetExplorer usually ship with Java. You can also install Sun Microsystems’ Java®VM, version 1.4.1+, which can be obtained from Sun.

Note that any of the kinds of direct connection (cable, ISDN, DSL) that are typicalin computer labs are adequate for use with ALEKS. If your computer lab has secu-rity safeguards in place, you will need the cooperation of your LAN administrator,system administrator, or lab technician to install the ALEKS plugin.

12.3. THEORY 155

PC Macintosh

Operating System Windows MacOS 10.2+(10.3+ for Quick-Tables)

Processor 166+ MHz AnyRAM Memory 32+ MB 32+ MBBrowser Explorer 6.0+, Firefox 1.0+, Netscape 7.1+,

Mozilla 1.6+OS 10.3+: Sa-fari, Firefox 1.0+;OS 10.2: Ex-plorer 5.2

Screen Resolution 800x600 (1024x768 for Chemistry) 800x600 (1024x768for Chemistry)

Modem Speed 28+ kbps 28+ kbps

Figure 12.1: System Requirements

Where can I get more information on ALEKS? How can I try out thesystem?

The ALEKS website provides complete information on the ALEKS system, in-cluding a Quick Tour, Free Trial use, licensing, history and theory, and technicalsupport.

12.3 Theory

For those interested in looking beneath the surface, these questions concern the princi-ples on the basis of which ALEKS is designed and constructed.

What is the theory behind ALEKS?

[Chapter 11] [Sec. 11.3] ALEKS is based on a field of Cognitive Science (Math-ematical Psychology) called “Knowledge Spaces.” The purpose of research inKnowledge Spaces is to model human knowledge in any subject, using mathemati-cal tools such as Set Theory, Combinatorics, and Markovian Processes, so as tomake possible fast and accurate assessment through interactive computer applica-tions. There are numerous scientific publications in the field of Knowledge Spacesdating back to the early 1980’s. A recent, authoritative treatment (with Bibliog-raphy) is Doignon & Falmagne, Knowledge Spaces (Springer-Verlag, 1999).

What is an “item”?

[Sec. 11.2.1] In Knowledge Space theory, an “item” is a concept or skill to belearned, the mastery of which is captured by a “problem type” serving as the basisfor specific assessment and practice problems. Thus the item “addition of two-digitnumbers without carry” might produce the problem (instance) “What is 25 plus11?”


What is a “domain”?

[Sec. 11.2.1] In Knowledge Space theory, a “domain” is the set of all items makingup a particular subject matter, such as Arithmetic. A learner is considered to havemastered the domain when that learner can solve problems corresponding to allthe items in the domain.

What is a “knowledge state”?

[Sec. 11.2.2] In Knowledge Space theory, a “knowledge state” is the set of itemsbelonging to a domain that a learner has mastered at some point in time. We speakof knowledge states in relation to a particular learner and a particular domain.Obviously, a learner’s knowledge state changes in time, and the goal of learning isthat it should eventually include (correspond to) the entire domain.

What is the “outer fringe” of a knowledge state?

[Sec. 11.2.4] In Knowledge Space theory, a learner’s “outer fringe” is the set ofitems, any one of which can be added to the current knowledge state, to make anew, feasible knowledge state. These are the items that the student is consideredmost “ready to learn.” Progress is made from one state to another through one ofthe items in the first state’s “outer fringe.”

What is the “inner fringe” of a knowledge state?

[Sec. 11.2.4] In Knowledge Space theory, a learner’s “inner fringe” is the set ofitems, any one of which can be taken away from the current knowledge state, tomake a new, feasible knowledge state. These are the items that the student mayhave learned recently, and thus whose knowledge might be shaky.

What is a “knowledge structure”? What is a “knowledge space”?

[Sec. 11.2.3] In Knowledge Space theory, “knowledge structure” or “knowledgespace” (the two concepts differ in a technical way) refers to the collection of feasibleknowledge states for a particular domain. It is a key point that not all sets ofitems from the domain (subsets of the domain) are feasible knowledge states. Forinstance, in mathematics there can be no knowledge state containing the item“finding the square root of an integer” that does not contain the item “addition oftwo-digit numbers without carry,” since no one will master the first without havingmastered the second.

How was the structure created?

The knowledge structures (or, briefly, “structures”) used by ALEKS are createdby analysis of the subject matter and extensive, computer-aided querying of expertteachers. When ALEKS assesses a student, it is actually searching the structurefor knowledge states that match the student’s present competence.

What is the educational philosophy behind ALEKS?

The educational use of ALEKS is not tied to any particular theory of education orknowledge acquisition. A key insight underlying ALEKS is the existence of a vastmultiplicity of diverse “learning paths” or sequences of topics by which a field canbe mastered. Based on an inventory of knowledge states that numbers in the tensof thousands (for the subjects currently covered by ALEKS) the specialized tools of

12.4. ASSESSMENTS & REPORTS 157

Knowledge Space theory make it possible for the system to accommodate literallybillions of possible individual learning paths implied by the relations among states.

ALEKS does not embody a particular philosophy of teaching mathematics; rather,it is compatible with any pedagogical approach.

12.4 Assessments & Reports

Much of the power of ALEKS comes from its capacity for accurately and efficientlyassessing the current state of a learner’s knowledge.

What is an ALEKS assessment?

[Chapter 4] An assessment by the ALEKS system consists of a sequence of math-ematical problems posed to the student. The answers are in the form of math-ematical expressions and constructions produced by the system’s input tools (nomultiple choice). The student is encouraged to answer “I haven’t learned thisyet” where this is appropriate. During an ALEKS assessment, the student is nottold whether answers are correct or incorrect. The assessment is adaptive. Eachquestion after the first is chosen on the basis of answers previously submitted.Assessment problems (like practice problems) are algorithmically generated withrandom numerical values. The length of the assessment is variable, between 15and 35 questions. There are no time constraints, but many assessments can takeless than a half-hour and few more than an hour. Students taking an assessmentneed to have paper and pencil.

Calculators are not permitted in assessments for Arithmetic, but simple calcula-tors without graphing or symbolic functions are permitted for Algebra. A basiccalculator is part of ALEKS.

No help whatsoever should be given to students taking an assessment, not evenrephrasing problems. Outside help can easily lead to false assessment results andhinder subsequent work in the ALEKS Learning Mode.

Students are always assessed when they first register with the ALEKS system. It ishighly advisable that all assessments from which the teacher uses data in any way(such as for placement) take place under the teacher’s supervision. At a minimum,the initial assessment must be supervised.

How does the ALEKS assessment work?

[Sec. 11.2.5] In assessing a student’s knowledge, the system is in fact determiningwhich of the feasible knowledge states for that subject corresponds to the student’scurrent knowledge. The assessment is probabilistic, so that it is not fooled bycareless errors. (Lucky guesses are very rare, because multiple choice answersare not used.) Likelihood values (values for the likelihood that the student isin a particular knowledge state) are spread out over the states belonging to thestructure. With each correct answer, the likelihood of states containing the itemfor which a correct answer was given is raised and that of states not containing


the item lowered. The reverse occurs for incorrect answers or “I haven’t learnedthis yet.” At each step of the assessment, the system attempts to choose an itemfor which it estimates (based on current likelihood values) the student has about afifty-fifty chance of success; such questions are maximally informative. When thelikelihood values of a few states are extremely high and those of all the rest areextremely low (in technical terms, when the entropy of the structure is lower thana certain threshold value), the assessment ends and results are produced.

If a student makes a careless error or lucky guess, this will appear inconsistentwith the general tendency of the student’s responses and the system will “probe”that area of knowledge until it is sure. For this reason, inconsistent assessments(often resulting from lack of concentration) may require more questions.

How should I interpret the assessment report?

[Sec. 4.13] The results of an ALEKS assessment are shown in the form of a color-keyed pie chart. A pie chart corresponds to a subject matter (domain) or to thecurriculum of a particular class. Each slice of the pie corresponds to a generaltopic. The degree to which the slice is filled in with solid color shows how closethe student is to mastering that area. Where classes are being taken in sequence,there may be pie charts showing the previous and/or subsequent classes in thatsequence.

An extremely important aspect of the pie charts is their indication of what a stu-dent is currently most “ready to learn” (that is, the “outer fringe” of the student’scurrent knowledge state). These items are listed beneath the pie charts in an As-sessment Report and are also given through the pie charts themselves. When themouse pointer is placed over a slice of the pie, a list pops out showing the conceptsthat the student is most “ready to learn” in that part of the curriculum. Clickingon any of these concepts takes the student into the Learning Mode to work on it.

The pie charts are displayed following assessments, after a concept has been workedon in the Learning Mode, and when a student clicks on “MyPie” to change topics.At any given time, a student can only choose to work on concepts that the studentis currently most “ready to learn.” This number may vary between two and a fewdozen, depending on what part of the structure is involved.

12.5 Learning Mode

Students spend by far the greatest part of their time in ALEKS in the Learning Mode.The features of the Learning Mode are designed to provide a maximum of support tothe student’s growing mastery of course materials.

What is the Learning Mode?

[Chapter 5] The Learning Mode in ALEKS contains features to help studentspractice and master specific mathematical concepts and skills. In the LearningMode, students are always working on a specific concept that they have chosen and

12.6. EDUCATIONAL USE 159

that, in the system’s estimation, they are fully prepared to master. If the learnersuccessfully solves an appropriate number of problems based on that concept, thesystem will tentatively determine that it has been mastered and offer a new choiceof topics. If the student has difficulty, the system will attempt to diagnose andinterpret the student’s errors. It will also provide explanations of how to solveproblems and definitions of mathematical terms. It may suggest the name of aclassmate who can help. If the student is unable to master the concept right now,or if the student wishes to change topics, a new choice of topics will be offered.After a certain time has been spent in the Learning Mode, or after a certain amountof progress has been made, the student will be reassessed automatically (unless theteacher has already requested a new assessment).

What is the relationship between the Assessment Mode and the LearningMode in ALEKS?

The Assessment and Learning Modes work together in a cyclical fashion, beginningwith the initial assessment. A student is assessed, and the results of the assessmentserve as a basis for the student’s entry into the Learning Mode (the student workson concepts that the assessment showed that student most “ready to learn”). Aftera certain time in the Learning Mode, during which the results of the previousassessment are tentatively updated according to whether the student masters orfails to master new concepts, the student is reassessed and the cycle begins again.In this sense, ALEKS is an interactive learning system guided and powered byongoing diagnostic assessment.

12.6 Educational Use

ALEKS also provides a full range of features for successful integration into a variety ofteaching styles and class plans.

What is the best way to use ALEKS with my class?

The greatest factor in successful use of ALEKS is regular, structured use, withclose monitoring of student progress by the teacher. We recommend schedulingregular lab sessions with ALEKS, totalling a minimum of three hours per week,as part of your class requirements. Not every lab session need be supervised bythe teacher, but the initial assessment certainly should be. Any other interim andconcluding assessments scheduled specially by the teacher normally should also besupervised.

This having been said, there has been successful use of ALEKS in a very widevariety of contexts and structures, including independent study. ALEKS Corpo-ration is happy to consult with teachers on the best way to use ALEKS with theirstudents.

Can ALEKS be used with handicapped and learning-disability students?Is ALEKS a remedial tool?


ALEKS is designed to help all students who can read sufficiently to understandwhat it says, and who can use a computer. It has been used successfully with stu-dents exhibiting a range of learning disabilities. Students with reading difficultiescan also use it, provided that there is someone on hand to help them as needed.The system does not currently contain facilities for audio output.

What burden will ALEKS place on our computer lab and Lab Direc-tor/LAN Administrator?

Normally ALEKS requires very little support from local computer technicians,given the automatic installation and maintenance of the ALEKS plugin. Most ofthe time, however, the lab administrator will need to assist with installation inorder to overcome security obstacles (for excellent reasons, school computer labstend to prevent students from installing their own software). In a few cases, thepresence of a “firewall” or other security measures may require some action on thetechnician’s part for successful installation. Again, ALEKS Corporation standsready to assist with problems of this nature.

Does ALEKS need to be used with a particular textbook or curriculum?

ALEKS is designed to be used with any program, curriculum, or textbook. Thesystem may also be referenced or linked to a textbook or online applications forparticular classes. The fundamental idea of the ALEKS system is to allow studentsto pursue individualized paths to mastery of the subject matter. For this reasonteachers may very commonly find their students learning material that has notyet been covered in the class. This should be regarded as a sign of the system’seffective use.

Does ALEKS have special features for educators?

[Chapters 6, 7, 8] Students’ use of ALEKS and their progress toward masterycan be monitored using the facilities of the Teacher Module. The Teacher Module(called Administrator Module when it includes more than one school) also en-ables teachers and administrators to establish the programs and standards usedby ALEKS, to configure accounts, to find statistics on school district use, andto exchange messages. A teacher or administrator who has been registered withALEKS enters the Teacher Module immediately upon login.

What are Results & Progress? What are Standards & Programs?

There are two parts of the Teacher Module, “Results & Progress” and “Standards &Programs.” The former is by far the more commonly used. It contains informationon system use and progress by students and groups, as well as all necessary facilitiesfor account and database management. The latter is used strategically, to definethe standards and programs that will be used over extended periods of time byschools. Actions taken in “Standards & Programs” should be the outcome ofwell-considered school district decisions.

How does ALEKS define standards and programs?

[Chapter 6, 8] In ALEKS, a program is a set of items belonging to a domainthat is determined to be the goal for mastery in a particular class. The program

12.6. EDUCATIONAL USE 161

is, if not equivalent to the entire domain, is defined by selection of a particularsubset of the domain. This is done in the Program Editor by adding and removingcheckmarks next to the names of items. A “Standard” in ALEKS is a group ofprograms considered to constitute a logical, integrated sequence.

How can I use ALEKS Corporation Customer Support?

[Sec. 13] You can contact ALEKS Corporation using the information in Chapter10 of this manual. We request that this information not be given to students.

Students should approach their teacher first with any questions or problems re-garding the use of ALEKS. Questions the teacher is unable to answer can then bebrought to our attention.

Chapter 13

Support

NOTE. Troubleshooting information is found in Appendix A.11 of this Teacher’sGuide. Most problems can be resolved using this brief reference.

Current information on ALEKS is available at the ALEKS website:


Technical support and consultation on the effective use of ALEKS is provided to edu-cators by ALEKS Corporation Customer Support. Please contact the support groupby email:

http://support.aleks.com

by telephone:

(714) 619-7090

or by fax:

(714) 245-7190

NOTE. We ask that students using ALEKS not contact us directly, but approach theirteachers first. It is hoped that the information in this Teacher’s Manual will enableteachers to answer many of their students’ questions.

We also welcome any and all comments and feedback on ALEKS. Here is our mailingaddress:

ALEKS Corporation Customer Support15641 Red Hill Avenue, Suite 150

Tustin, CA 92780

163

164 CHAPTER 13. SUPPORT

Appendix A

ALEKS Student User’s Guide

A.1 Preface

Welcome to ALEKS! You are about to discover one of the most powerful educationaltools available for learning mathematics. Combining advanced learning technology withthe flexibility of the Internet, the ALEKS system provides a “smart” interactive tutoringsystem with unmatched features and capabilities. Richly supplied with illustrations andreference materials, ALEKS constantly challenges you and supplies extensive feedbackon what you have accomplished. ALEKS will always help you select the ideal topic towork on now.

That way you learn concepts in the order that’s best for you. ALEKS provides indi-vidualized, one-on-one instruction that fits your schedule. It is available wherever youaccess the Web.

ALEKS was developed with support from the National Science Foundation. It is basedon a field of Mathematical Cognitive Science called “Knowledge Spaces.” The purposeof research in Knowledge Spaces is to model human knowledge of any subject for quick,precise assessment and efficient guided learning in interactive computer programs.

The ALEKS system is self-explanatory and includes online instructions and feedback.This booklet contains basic information to help you begin using ALEKS. Teachers usingALEKS with their classes are provided with a Teacher’s Guide containing completeinformation on the system’s operation. They should be able to answer any questionsbeyond those dealt with in these pages.

NOTE. ALEKS is designed for use without help from a manual. Your teacherwill assist you in registering with the system and beginning to use it. Ifquestions arise, or if you want to learn more about ALEKS, use this Guide.It is intended as a convenient and concise reference.

Only registered users can keep an account on ALEKS. (Anyone may trythe system as a guest.) Two or more persons cannot use the same ALEKS

165

166 APPENDIX A. ALEKS STUDENT USER’S GUIDE

account. The system will regard them as a single person and give incorrectguidance.

A.2 System Requirements

The system requirements for ALEKS are such that it can be used on nearly any com-puter that is connected to the Internet.

PC Requirements

You can use ALEKS on any PC with a Pentium or equivalent (AMD, etc.) pro-cessor of 166 MHz or more or any Pentium II, III, or later processor. At least 32MB of RAM are required. Your operating system must be Windows 98 / 2000 /ME / XP / NT4.0 or higher.

The following popular web browsers are compatible with ALEKS on PCs: InternetExplorer 6.0 or higher, Firefox 1.0 or higher, Netscape Communicator 7.1 or higher,and Mozilla 1.6 or higher.

Chemistry requires a screen resolution of 1024x768.

Macintosh Requirements

ALEKS can be used on a PowerMac or iMac with at least 32 MB of RAM andoperating system Mac 0S 10.2 or higher (10.3+ for QuickTables). With MacOS10.3 or higher and the latest software updates from Apple, compatible browsersare Safari and Firefox 1.0 or higher. With MacOS 10.2, Internet Explorer 5.2 is asupported browser. Chemistry requires a screen resolution of 1024x768.

Internet Access

ALEKS is used over the World Wide Web. You must have an Internet connectionby dial-up modem (at least 28k) or any other kind of access to the Internet (cable,ISDN, DSL, AOL, etc.).

A.3 Registration and Installation

Before You Begin. In order to register as an ALEKS user you need a Class Codeprovided by your teacher. When you register with the ALEKS system, your name isentered into the database and records of your progress are kept. If the ALEKS pluginhas not been installed on the computer being used for registration, it will be installedautomatically as part of this procedure.

1. Go to the ALEKS website by typing in the following address:


NOTE. If you are typing this URL by hand, pay careful attention to the spelling“aleks.” Also, the other ALEKS websites you might find using a search engine willnot work for you. You will be able to register only at the address given above.

A.3. REGISTRATION AND INSTALLATION 167

Figure A.1: The ALEKS Website

For your convenience, add a “Bookmark” or “Favorite” at this location. This isthe site where you will log on to your account.

2. Click on “SIGN UP NOW” in the upper left-hand corner of the window (Fig. A.1).

3. At the beginning of registration you will be asked for your Class Code. It isprovided to you by your teacher. Enter the Class Code in the spaces provided andclick on “Continue” (Fig. A.2).

4. Answer the questions to complete your registration. Among other questions, youmay be asked to enter your email address. Supplying this information enablesyour site administrator to help you with problems more quickly. You will also beable to enter your Student ID number. (Both email and Student ID are optionalinformation.)

5. At the end of registration you will be given a Login Name and Password. Writethese down and keep them in a safe place. You will need them to return to thesystem (See Sec. A.6). You can change your Password at any time (See Sec. A.5.5).

NOTE. If you do not have a current plugin, one will be installed. Do not interruptthis process until a message appears saying that the installation is complete. Thenyou will need to quit your Web browser (“Exit,” “Close,” or “Quit” under the“File” menu), open your Web browser again, and go back to the ALEKS website(use your Bookmark/Favorite).

NOTE. Your Login Name and Password can be typed with upper- or lower-caseletters. Neither may contain spaces or punctuation. If you forget your Passwordbut you did enter your email address in ALEKS, click on the link underneath the


Figure A.2: Class Code

Password field on the ALEKS home page (“Did you forget your password?”).

6. You will need to wait for your teacher’s authorization before starting to use yournew account. If you need to log off now, you can log back on later using yourLogin Name and Password. As soon as your teacher authorizes your registration,you will be able to start using ALEKS by beginning the Tutorial.

A.4 Tutorial

The ALEKS system avoids multiple-choice questions. Most answers are complete math-ematical expressions and constructions. After registration, the ALEKS Tutorial willteach you to use the simple tools needed for your class (Fig. A.3). There is plenty offeedback to help you complete it successfully.

NOTE. The Tutorial is not intended to teach mathematics. It just trains you to use theALEKS input tool (called the “Answer Editor”). Online help is also available while youare using ALEKS; just click the “Help” button, which gives you access to the sectionsof the Tutorial (See Sec. A.5.5).

A.5. ASSESSMENTS AND LEARNING 169

Figure A.3: The Answer Editor (Tutorial)

A.5 Assessments and Learning

A.5.1 Assessments

Instruction through ALEKS is guided by precise understanding of your knowledge ofthe subject. This information is obtained by assessments in which the system asksyou to solve a series of problems. (The system’s estimate of your knowledge is alsoupdated when you make progress in the Learning Mode.) Your first assessment occursimmediately after the Registration and Tutorial.

NOTE. Your teacher may require that the first assessment be taken under supervision.Don’t try to begin your initial assessment at home until you find out whereyour teacher wants you to take it. Additional assessments may be scheduled foryou by the teacher. These may or may not need to be supervised, depending on theteacher’s preference. The ALEKS system also prompts “automatic” assessments whenyou have spent a certain amount of time on the system or have made a certain amountof progress.

A.5.2 Results

Assessment results are presented in the form of a color-coded pie chart. Slices of thepie chart correspond to parts of the program. The relative size of the slices representsthe importance of each topic area for the program. The solidly colored part of a sliceindicates how close you are to mastering that part of the program.

NOTE. You may see more than one pie chart displayed following an assessment whenyou are progressing through a series of classes or units. (Your knowledge in the previousand/or subsequent units is also displayed.)


Figure A.4: Assessment Report

A.5.3 Learning Mode

Following the presentation of assessment results, the system will display a pie chartnavigation tool (“MyPie”) (Fig. A.4). By placing the mouse pointer over slices of thepie, you can see which concepts you are now most ready to learn.

Not all slices will contain concepts at any given time. They may have been masteredalready, or work may need to be done in other slices before they become available. Theconcept you click on becomes your entry into the Learning Mode. The system will helpyou in seeking to master that concept and “add it to your pie.”

A.5.4 Progress in the Learning Mode

In the Learning Mode, you are given practice problems based on the chosen topic. Inaddition, you receive explanations of how to solve this kind of problem and have accessto a dictionary of mathematical concepts. Underlined mathematical terms are links tothe dictionary. Click on any term to get a complete definition. The system will requirea number of correct answers before it assumes that you have mastered the concept.Then it “adds it to your pie.” At this point, a revised pie chart will be shown reflectingyour new knowledge. You will be able to choose a new concept to begin. If you makemistakes, more correct answers may be required. If you tire of this topic and wish tochoose another, you can click on “MyPie” near the top of the window. This will makeyou exit the topic and you will return to your pie chart for a new choice. If you make

A.6. LOGGING ON TO YOUR ACCOUNT 171

repeated errors on a given concept, the system will conclude that the concept was notmastered. It will offer you a new choice of other concepts.

A.5.5 Additional Features

All buttons described below are available in the Learning Mode. In the AssessmentMode, only the “Options,” “Exit,” and “Help” buttons are active.

Options

If you want to change your Password, click on the “Options” button. This pagealso shows the total number of hours you have spent using ALEKS.

Report

Any time you wish to look at your assessment reports, click on “Report.”

Choose any date from the menu and click “OK.”

Dictionary

To search the online dictionary of mathematical terms, click “Dictionary.”

Review

To review past material, use the “Review” button.

Worksheet

To print out an individualized homework sheet based on your most recent work inALEKS, use the “Worksheet” button.

Quiz

To see the results of quizzes you have taken in ALEKS or to begin a quiz assignedto you by your teacher, use the “Quiz” button.

Messages

Your teacher can send you messages via ALEKS. You see new messages when youlog on. You can also check for messages by clicking on the “Message” button. Yourteacher can choose to let you reply to messages as well.

Help

For online help with the use of the Answer Editor, click “Help.”

MyPie

Clicking “MyPie” gives you a pie chart summarizing your current mastery. Youcan use this pie chart to choose a new concept.

A.6 Logging on to Your Account

Here are concise instructions for accessing your ALEKS account.

1. You always log on from the ALEKS website:



Use the “Bookmark” or “Favorite” for this site if you made one (See Sec. A.3).Remember that you may find other ALEKS websites via a search engine, but thisis the only one with your account.

2. On the login page, enter your Login Name and Password provided at the time ofregistration (See Sec. A.3). Be sure to type these correctly, without any spaces orpunctuation.

3. If you enter your Login Name and Password correctly, your browser will beginaccessing the plugin to start ALEKS. This takes a few seconds. You will thencome to the place you left off in your previous ALEKS session, or begin usingALEKS as a first-time user.

NOTE. If you forget your Login Name or Password, use the link on the ALEKShome page marked “Did you forget your password?” If you entered an emailaddress at registration time and you remember your Login Name, your Passwordwill be sent to you by email. Otherwise, please contact your teacher. It is a goodidea to change your Password to one you will remember easily but is difficult forothers to guess (See Sec. A.5.5).

A.7 Installation on Additional Machines

Before You Begin. Installing ALEKS means installing the ALEKS plugin. This isthe software used by your web browser to access and run ALEKS. You can access yourALEKS account from any computer that meets the system requirements and has hadthe ALEKS plugin installed. You cannot use ALEKS without the ALEKS plugin thatis installed over the World Wide Web.

1. Go to the ALEKS website:


Add a “Bookmark” or “Favorite” at this location.

2. Use your Login Name and Password to log on (See Sec. A.3).

3. When you log on to ALEKS, the system will automatically check to see if yoursystem is compatible and if you have the most recent version of the ALEKS plugin.If you do not have a current plugin, it will download the plugin and ask yourpermission to install. After you grant permission, it will install the (new) plugin.Do not interrupt the installation process until a message appears stating thatthe installation is complete and asks you to restart your browser. You will needto quit your Web browser (“Exit,” “Close,” or “Quit” under the “File” menu),open your Web browser again, and go back to the ALEKS website (use yourBookmark/Favorite).

A.8. GUIDELINES FOR EFFECTIVE USE 173

A.8 Guidelines for Effective Use

Please take note of the following important suggestions for successful use of ALEKS.

Supplementary Materials

You should have pencil and paper ready for all assessments and for use in theLearning Mode. Basic calculators should be used only when you are instructed todo so. (A basic calculator is part of ALEKS.)

Assessments

You should not ask for, nor receive any help during assessments. Not even expla-nations or rephrasing of problems are permitted. If you receive help, the systemwill get a wrong idea of what you are most ready to learn, and this will hold upyour progress. If you think you don’t know the answer, you should click “I haven’tlearned this yet.” (Don’t guess!)

Learning Mode

You should learn to use the special features of the Learning Mode, especially theexplanations and the mathematical dictionary.

A button marked “Ask a Friend” may also appear from time to time. Clicking onthis button will prompt the system to suggest the name of a classmate who hasmastered the concept.

Regular Use

Nothing is more important to your progress than regular use of the system. Threehours per week is a recommended minimum.

A.9 QuickTables

QuickTables is a special tool in ALEKS for learning the math facts of Addition, Subtrac-tion, Multiplication, and Division. It is available as part of ALEKS classes for Grades3 through 5, or as a separate class in ALEKS.

In classes where QuickTables has been enabled, you can access the tool by clicking onthe tab marked “QuickTables” in the upper right-hand corner of your student account.Then, click the round “OK” button under the Welcome message (Fig. A.5).

The first time you use QuickTables, you will have a short training session before startingto practice. The purpose of the training is to make sure that you are comfortable typingand entering numbers in the system. There will be a series of quick drills in which youare asked to type numbers that appear on the screen. If you make a mistake, that is noproblem; QuickTables will stop to let you correct it before moving on. You can enterthe numbers by pressing either your computer’s “Enter” key or the Space bar (the longbar at the bottom of the keyboard).


Figure A.5: ALEKS QuickTables

You will need to enter the numbers pretty quickly; QuickTables wants you to learn themath facts so well that you can answer easily and smoothly. If it is easier for you toclick numbers on a keypad, this can be turned on for you.

After this training, you begin a “test” or assessment of what you know now about themath facts. Do not be anxious about this test; just relax and do your best. The resultsof the test will tell QuickTables where you should start off in your math facts table.

You may have more than one table set up. If so, you will see different tabs on yourscreen with the names of the tables: Addition, Subtraction, Multiplication, Division.Simply click on the tab for the table you wish to work in. You will need to take a brieftest when you first start working in any table.

Once you finish the test, you will see a colored display that shows all the facts in thetable (Fig. A.6). The colors in the cells show whether you have learned that fact, andhow well you know it. In general, you will see that the colors fill in through the tablediagonally, from the top left corner down. The “hardest” facts are the ones you get toat last, down in the lower right-hand corner. You will have fun filling in this table!

Also, to the right of the table is a thermometer that gives your overall percentage of thetable. Notice that there are gold stars on the thermometer. Every time you fill in toone of these stars, there will be a new game for you to play. You earn the games by theprogress that you make filling in your table. Any time you want to play a game thatyou have earned, click on the green button marked “Games” at the top of the window.These are fun games that give you extra practice on the math facts that you have been

A.10. FREQUENTLY ASKED QUESTIONS 175

Figure A.6: QuickTables Learning Display

learning.

NOTE. You will only be able to use QuickTables for a certain amount of time on anyday, and only a certain number of times per week. These limits are set for the bestpossible progress in learning and remembering math facts.

A.10 Frequently Asked Questions

For further information on any of these questions, follow the references provided toother sections of this Guide.

What are the rules for taking an assessment in ALEKS?

[Sec. A.8] You must have paper and pencil when taking an assessment in ALEKS.

A basic calculator should be used only when you are instructed to do so. A basiccalculator is part of ALEKS. No help whatsoever is permitted, not even to theextent of rephrasing a problem.

During the assessment, you are not told if your answer is right or wrong. In theLearning Mode, however, you are always told if you made a mistake, and oftenwhat that mistake was. The assessment is not a test. Its main purpose is todetermine what you are most ready to learn and help you make the best progresspossible toward mastery.

How do I add concepts to my pie?


[Sec. A.5.4] You fill in your pie and achieve mastery in the subject matter byworking in the Learning Mode on concepts and skills that the assessment hasdetermined you are most “ready to learn.” When you master a concept in theLearning Mode by successfully solving an appropriate number of problems, youwill see that your pie chart has been changed by the addition of that concept. Thegoal is to fill the pie in completely.

Why is it that I mastered all the concepts in the Learning Mode, but myassessment still says I have concepts to learn?

In the Learning Mode, you are always working on one concept at a time, whereasassessments are cumulative and evaluate you on everything in the given subjectmatter. It may be more difficult to show mastery of concepts you have recentlyworked on, when you are being quizzed on many different topics at the same time.For this reason, your assessment results may not exactly match what you hadmastered in the Learning Mode. This is normal and simply means that you shouldkeep working in the system. (Sometimes the opposite also occurs. That is, progressin the assessment turns out to be faster than in the Learning Mode.)

Why doesn’t my pie chart show any concepts from a category if I haven’tfilled in that category yet?

[Sec. A.5.3] You are completely “ready to learn” a set of concepts or skills whenyou have mastered all the prerequisite concepts or skills that they demand. Totake an elementary example, in order to learn “addition of two-digit numbers withcarry” you might have to first learn “addition of two-digit numbers without carry”and nothing else. Your pie chart will not offer you concepts to work on if you arenot ideally ready to begin learning them, that is, they have prerequisites you havenot yet mastered.

For this reason, your pie chart may show that you have only mastered 8 out of 10concepts for a particular slice of the pie (a particular part of the curriculum), butthe pie chart says you have no concepts available from that slice to work on. Thismeans that the concepts you have left to master have prerequisites in other areasof the curriculum that you must master first.

Keep working in the other slices, and eventually the concepts in that slice will“open up.”

What is the difference between “Explain” and “Practice”?

When you begin working on a particular concept in the Learning Mode, you will beshown the name of the concept, a sample problem, and a choice between “Practice”and “Explain.” If you think you know how to solve the problem, you can click“Practice.” You will be given a chance to solve the same problem that was initiallydisplayed. If you are not sure, you can click “Explain” to produce an explanationof how to solve the displayed sample problem.

At the bottom of the Explanation page you have the “Practice” button, and some-times other options for more detailed explanations and help. If you click the“Practice” button following an explanation, you are offered a different problemof the same type, not the one whose solution was explained. In order to master


the concept and add it to your pie, you must successfully solve a certain numberof “Practice” problems. If you wish to choose a new concept, you can click the“MyPie” button on the ALEKS menu bar.

You should not use your browser’s “Back” and “Forward” buttons while loggedon to ALEKS. Doing so will not help you make progress and may cause temporarysoftware errors.

How can I best use the Learning Mode to help me learn?

[Sec. A.5.4] In the Learning Mode, you should do your best to solve the problemsthat are offered to you. You should not lightly change topics or stop before thesystem tells you that you are done or suggests choosing another concept.

You should get to know the features of the Learning Mode, especially the expla-nations and the mathematical dictionary. The Learning Mode will always tell youif your answer is correct or not. In many cases it will provide information on thekind of error you may have made. You should pay attention to this feedback andbe sure to understand it.

Keep in mind that ALEKS is always giving you material that, in its estimation, youare ideally ready to learn. It does not offer material you have already mastered,except in the Review mode. To go back to concepts you have already worked on,click the “Review” button on the ALEKS menu bar.

How does ALEKS create practice problems?

ALEKS creates both Assessment and Practice problems by means of computeralgorithms, based on the definition of a particular concept or skill to be mastered.Thus, a particular concept or problem-type may serve as the basis for a very largenumber of specific problems, each with different numerical values and sometimes(as in the case of applied problems) differing in other ways as well. With ALEKS,you cannot “learn the test” or “teach to the test.”

What happens if I don’t learn a concept (or I get tired of working on aconcept)?

[Sec. A.5.4] You must answer what the system judges to be an appropriate numberof Practice problems correctly to add a concept to your pie. If you make mistakes,you must answer more. ALEKS will always tell you when you have mastered theconcept. If you wish to stop working on a concept and choose another one, youcan click on “MyPie.” It is usually better to master the concept you are workingon, unless the system tells you to switch. If you are clearly not making progress,ALEKS will suggest that you work on something else.

Why is ALEKS giving me a new assessment?

[Sec. A.5.1] New assessments may be prompted automatically by ALEKS whenyou have spent sufficient time in the Learning Mode or when you have madeadequate progress. Your teacher may also request an assessment for you personally,or for everyone in the class. In this case it may be stipulated that the assessmentmust be taken at school. (If you attempt to work at home when an assessment hasbeen ordered to be done at school, ALEKS will deny access and tell you that youneed to log on from school.)


Why do I need to take a Tutorial to use ALEKS?

[Sec. A.4] The Tutorial is a brief interactive training program that teaches youto use the ALEKS input tools, or “Answer Editor.”

ALEKS avoids multiple-choice questions. It almost always requires that answersbe given in the form of numbers, mathematical expressions and geometrical andother constructions. The Answer Editor is a flexible set of tools enabling you toprovide such answers. Although the Answer Editor is easy to use, the Tutorialwill make sure you are completely proficient with it before beginning the ALEKSsystem. The Tutorial guides you through every step of learning to use the AnswerEditor.

What can I do if I make a mistake entering an answer?

If you make an error entering an answer with the Answer Editor, you should clickon “Undo” to go back one step, or on “Clear” to start over. You can also use the“Backspace” key on your keyboard in the usual way.

NOTE. You cannot use “Undo” or the “Back” button on your browser to go backif you have submitted an answer by clicking on “Next.” If you realize that theanswer you submitted is incorrect, you should not be concerned; the system willmost likely recognize this as a careless error based on your other answers and makeallowances for it.

What are the icon buttons for?

The icon buttons are used to enter mathematical symbols and to create forms formathematical expressions. In some cases the keyboard equivalents for icon buttonscan be used.

Why doesn’t anything appear when I type?

[Sec. A.11] In order to type input in the Answer Editor, you must first clickon a blue box. Each blue box in the input area corresponds to a mathematicalexpression. When you click on an icon button for a complex expression, it mayplace more than one blue box in the space, one for each part of the expression.Each blue box must be filled in for a complete expression. For instance, when youclick on the “Exponent” icon button, you get two blue boxes. The big one is forentering the base, and a smaller one that is raised and to the right is used to enterthe exponent.

How do I get help while using ALEKS?

[Sec. A.5.5] You can get help using the Answer Editor by clicking the “Help”button on the ALEKS menu bar.

Can my teacher or friend help me (or can I use a calculator) in the LearningMode?

[Sec. A.8] Help and collaboration are allowed in the Learning Mode. Keep inmind, however, that if you get too much help, the system will start giving youproblems that you are not prepared to solve. As a general rule, you can get helpwith one Practice problem, but you should solve the others yourself. There shouldbe no help whatsoever on assessments, however.


You need paper and pencil for the Learning Mode, just as you did for the as-sessment. ALEKS provides a calculator when appropriate; when the Calculatorbutton is active, the use of the calculator is permitted (See Sec. A.5.5).

Why are some of the words I see underlined?

[Sec. A.5.5] Underlined words in the Learning Mode are links to the online math-ematical dictionary. You can click on any underlined word to see its definition.You can also access the Dictionary by clicking the “Dictionary” button on theALEKS menu bar. The Dictionary is not available during assessment.

Note that the Dictionary is opened in a new window. When you are finishedreading the definition, you can close or “Minimize” the window, and you will seethe previous screen. Clicking “Back” on the browser won’t work.

What is the “Ask a Friend” button for?

[Sec. A.8] The “Ask a Friend” button sometimes appears when you are havingdifficulty with a particular concept. When you click on the button, the systemsuggests the name of a classmate who has mastered the concept and may be ableto help you.

How can I change my Password?

[Sec. A.5.5] You can change your Password by clicking the “Options” button onthe ALEKS menu bar.

How can I review material I have already worked on?

[Sec. A.5.5] You can click on the “Review” button to work on material you havealready spent time on.

How can I see the reports from previous assessments?

[Sec. A.5.5] To see any of your assessment reports, click on “Report” (on theALEKS menu bar).

How can I choose a new topic to work on?

[Sec. A.5.5] To see your current pie chart and choose a new concept in the Learn-ing Mode, click on “MyPie” (on the ALEKS menu bar), move around on the pie,and choose a new concept in the Learning Mode.

How can I print something in ALEKS?

[Sec. A.11] To print the contents of the screen, you can click on “Print” in theALEKS menu bar. This produces a new, printable window (ALEKS output is notnormally printable). Depending on your browser, you may also have to click thebrowser’s “Print” button. When you are done, you can close the new window.

What should I do if it’s taking too long for a new page to load (or if theprogram freezes)?

[Sec. A.11] It shouldn’t take more than a few seconds for ALEKS to respondwhen you click on any button. If you experience delay, freezing, or crashing, yourfirst step is to click on the small “A” button in the upper right corner. If thisdoesn’t work, you can click your browser’s “Reload” or “Refresh” button. If thisdoesn’t work, you can close your browser and restart it. In extreme cases, use


Ctrl-Alt-Delete (Cmd-Opt-Esc on Macintosh). You will come back to the exactplace you left off after you log back on to ALEKS.

How do I exit the ALEKS program?

To leave ALEKS, you can click the “Exit” button on the ALEKS menu bar orsimply close your browser. ALEKS always remembers where you left off and bringsyou back to that place.

Why do I have to log on to ALEKS?

[Sec. A.1] The fact that ALEKS is used over the Internet means that you canaccess it from your school or from home. As a registered user of ALEKS, you havean account on the server that contains a record of all the work you have done.

Your teacher and administrators at your school have access to these records. Theycan monitor your progress and use of the system as well as carry out administrativefunctions. Web access also means that there is almost no maintenance or technicalpreparation required—no disks, CDs, peripherals, or backup procedures.

What if I have a question or problem using ALEKS?

If you have a question or problem using ALEKS that is not answered here, pleasecontact your teacher. Your teacher has been provided with extensive informationon the operation of ALEKS and should be able to answer almost any question youmay have.

What if I forget my Login Name or Password?

If you forget your Login Name or Password, you can use the link on the ALEKShome page marked “Did you forget your password?” If you entered an emailaddress at registration time and you remember your Login Name, the passwordwill be sent to you by email. Otherwise, please contact your teacher.

How do I extend or renew my ALEKS account?

Wait for your account actually to expire. Don’t worry: your records and progresswill not be lost. Obtain the correct Class Code from your teacher. When youraccount expires, you will be unable to access your account; instead, you will geta message indicating that the account has expired. On this page, click on theleft-hand button. (Do not use the right-hand button.) Enter the 10-charactercourse code and other information as prompted. You will now be able to continueusing your ALEKS account.

A.11 Troubleshooting

Difficulties in using ALEKS can very often be resolved by following the suggestionsgiven in this section.

Login Not Successful

First of all, be careful to type your Login Name and Password correctly, withno spaces or punctuation. Then, be sure you have accessed the correct ALEKS

A.11. TROUBLESHOOTING 181

website. There is more than one ALEKS website, and only the one at which youregistered contains your account. Use the URL provided in this booklet ratherthan looking for “aleks” via a search engine.

Typed Input Does Not Appear

If you have trouble entering numbers or symbols in the Answer Editor, be surethat you have clicked on a blue box and that the pointer is within the answer area(the rectangle containing the blue boxes).

NOTE. It is not always possible to use the number keys on your keyboard’s right-hand “keypad” (check that “Num Lock” has been pressed).

Mixed Number Difficulties

The Answer Editor is easy to use. One warning, however: mixed numbers mustbe entered using the Mixed Number icon, not by entering the whole part and thenusing the Fraction icon.

Freezing and Slow Response

If you are logged on to ALEKS and the program is either not responding or takingtoo long to load a new page, one of the following three actions may help (try themin the order given):

1. click on the small “A” in the upper right-hand corner of the ALEKS window;

2. click on your browser’s “Reload” (or “Refresh”) button;

3. close the browser and log on again (the system will bring you back to whereyou left off); if you cannot close the browser use Ctrl-Alt-Delete (PC) or Cmd-Opt-Esc (Macintosh) and end the task (or reboot, if all else fails).

Open applications, other than the web browser that you are using to accessALEKS, are another cause of slowness. Closing these applications may correctthe problem.

If slowness persists, it is most likely due to a problem in the local network. Bringthis to the attention of your teacher.

Lengthy Assessment

It is impossible to know how many questions will be asked in an assessment. Thenumber of questions asked does not reflect your knowledge of the subject matter.It may reflect the consistency of your effort or concentration.

Reduction of Pie Chart

You may observe a loss of concepts in your pie chart following an assessment.This is not a malfunction in the system, but results from errors made by youon material you had previously seemed to master. Don’t worry: that is the waythe system works. In particular, it is not unusual to have a “bad” assessment,one that, for external reasons (bad mood, distractions, etc.), does not reflect youractual knowledge. ALEKS will quickly bring you back to where you belong.

Repeated Final Assessments

You may need to take more than one final assessment even after you have filled inyour pie (in the Learning Mode). This is normal, since mastery is determined by


the assessment, not by the Learning Mode. The system needs to confirm (in theassessment) that the entire curriculum has been mastered.

Printing Problems

To print ALEKS output (for instance, an Assessment Report) you must press theALEKS “Print” button (on the ALEKS menu bar). This opens a new browserwindow containing the contents of the previous window in the form of a “PrintPreview.” When this page has been printed it should be closed to return to thenormal ALEKS interface.

Appendix B

Programs in ALEKS

B.1 Mathematics - LV3

Place Value and Money

arith066 Expanded formarith643 Expanded form with zerosarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith651 Introduction to inequalitiesarith652 Comparing a simple numerical expression with a numberarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith660 Finding the value of a collection of coinsarith661 Finding the value of a collection of bills and coins

Addition and Subtraction

arith633 Single digit addition with carryarith634 Addition of 3 or 4 single-digit numbersarith635 Adding a 2-digit number and a 1-digit number with carryarith001 Addition without carryarith050 Addition with carryarith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith636 Subtracting a 1-digit number from a 2-digit numberarith007 Subtraction without borrowingarith006 Subtraction with borrowing

183

184 APPENDIX B. PROGRAMS IN ALEKS

arith682 Subtraction with multiple regrouping stepsarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith101 Estimating a sumarith102 Estimating a differencearith653 Fact families for addition and subtractionarith655 Introduction to properties of additionalge284 Evaluating a simple algebraic expression: Problem type 1alge009 Additive property of equality: Problem type 1

Multiplication and Division

arith008 One-digit multiplicationarith679 Multiplication by 10, 100, and 1000arith675 Understanding multiplication of a one-digit number with a larger numberarith003 Multiplication without carryarith004 Multiplication with carryarith632 Multiplication with trailing zeros: Problem type 1arith639 Using multiplication to find the number of squaresarith640 Using addition and multiplication to count the objects on a gridarith641 Multiples: Problem type 1arith642 Multiples: Problem type 2arith075 Simple divisionarith052 Division without carryarith005 Division with carryarith680 Division with trailing zeros: Problem type 1arith650 Division involving quotients with intermediate zerosarith644 Word problem on quotient and remainderarith614 Basic word problem using multiplication or divisionarith677 Estimating a productarith678 Estimating a quotientarith645 Introduction to parenthesesarith658 Filling in missing operations to make an equationarith654 Fact families for multiplication and divisionarith656 Introduction to properties of multiplicationalge683 Evaluating a simple algebraic expression: Problem type 2alge813 Solving simple equations with multiplication or divisionarith056 Factorsarith646 Even and odd numbersarith647 Divisibility rules for 2, 5, and 10alge807 Finding the next terms of a simple sequencealge281 Function tables with one-step rules

B.1. MATHEMATICS - LV3 185

Geometry, Measurement, and Graphs

geom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom303 Acute, obtuse, and right anglesgeom306 Acute, obtuse, and right trianglesgeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom019 Area of a square or a rectanglegeom354 Volume of a solid made of unit cubesgeom348 Vertices, edges, and faces of a solidgeom219 Nets of solidsgeom359 Introduction to congruencegeom360 Introduction to similaritygeom357 Identifying transformationsgeom334 Drawing lines of symmetrymstat033 Measuring length to the nearest inchmstat034 Measuring length to the nearest quarter or half inchunit005 Customary unit conversion with whole number valuesmstat035 Conversions involving measurements in feet and inchesunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuestime010 Telling timetime008 Reading a calendarunit012 Time unit conversion with whole number valuestime009 Introduction to adding timealge278 Reading a point in quadrant 1alge279 Plotting a point in quadrant 1mstat005 Bar graphs for non-numerical datamstat024 Interpreting bar graphsmstat037 Line plotsmstat007 Interpreting line graphsmstat042 Venn diagrams with two setsmstat026 Introduction to probability of an event

Fractions and Decimals

arith623 Introduction to fractionsarith665 Introduction to equivalent fractionsarith212 Equivalent fractionsarith666 Introduction to reduced fractionsarith662 Introduction to mixed numbers and improper fractionsarith044 Ordering fractions with same denominator


arith091 Ordering fractions with same numeratorarith618 Addition or subtraction of fractions with the same denominatorarith079 Product of a unit fraction and a whole numberarith220 Decimal place valuearith608 Ordering decimalsarith670 Introduction to writing a decimal as a fractionarith671 Introduction to converting a fraction to a decimalarith624 Addition of aligned decimalsarith668 Addition with moneyarith625 Subtraction of aligned decimalsarith669 Subtraction with moneyarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2


Number sense, Addition and Subtraction

arith066 Expanded formarith643 Expanded form with zerosarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith651 Introduction to inequalitiesarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith633 Single digit addition with carryarith634 Addition of 3 or 4 single-digit numbersarith635 Adding a 2-digit number and a 1-digit number with carryarith001 Addition without carryarith050 Addition with carryarith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith636 Subtracting a 1-digit number from a 2-digit numberarith007 Subtraction without borrowingarith006 Subtraction with borrowingarith682 Subtraction with multiple regrouping stepsarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith101 Estimating a sumarith102 Estimating a differencearith653 Fact families for addition and subtraction


arith655 Introduction to properties of addition

Multiplication and Division

arith008 One-digit multiplicationarith679 Multiplication by 10, 100, and 1000arith675 Understanding multiplication of a one-digit number with a larger numberarith003 Multiplication without carryarith004 Multiplication with carryarith632 Multiplication with trailing zeros: Problem type 1arith639 Using multiplication to find the number of squaresarith640 Using addition and multiplication to count the objects on a gridarith641 Multiples: Problem type 1arith642 Multiples: Problem type 2arith615 Introduction to multiplication of large numbersarith638 Multiplication with trailing zeros: Problem type 2arith014 Multiplication of large numbersarith075 Simple divisionarith052 Division without carryarith005 Division with carryarith680 Division with trailing zeros: Problem type 1arith650 Division involving quotients with intermediate zerosarith644 Word problem on quotient and remainderarith614 Basic word problem using multiplication or divisionarith649 Division with trailing zeros: Problem type 2arith023 Word problem using divisionarith677 Estimating a productarith678 Estimating a quotientarith645 Introduction to parenthesesarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith657 Introduction to the distributive propertyarith652 Comparing a simple numerical expression with a numberarith654 Fact families for multiplication and divisionarith658 Filling in missing operations to make an equationarith656 Introduction to properties of multiplicationalge807 Finding the next terms of a simple sequencearith646 Even and odd numbersarith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9arith056 Factorsarith033 Greatest common factor


arith070 Least common multiplearith034 Prime numbersarith035 Prime number factorization

Fractions, Time, and Customary Measurement

arith623 Introduction to fractionsarith665 Introduction to equivalent fractionsarith212 Equivalent fractionsarith666 Introduction to reduced fractionsarith067 Reduced fractionarith044 Ordering fractions with same denominatorarith091 Ordering fractions with same numeratorarith092 Ordering fractionsarith667 Plotting fractions on a number linearith618 Addition or subtraction of fractions with the same denominatorarith664 Introduction to addition or subtraction of fractions with different denomina-torsarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith079 Product of a unit fraction and a whole numberarith086 Product of a fraction and a whole numberarith662 Introduction to mixed numbers and improper fractionsarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith215 Addition or subtraction of mixed numbers with same denominatorarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingtime010 Telling timeunit012 Time unit conversion with whole number valuestime008 Reading a calendartime009 Introduction to adding timetime006 Adding timetime007 Subtracting timemstat033 Measuring length to the nearest inchmstat034 Measuring length to the nearest quarter or half inchmstat035 Conversions involving measurements in feet and inchesmstat036 Adding customary units of lengthunit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversion

Decimals, Money, and Metric Measurement


arith660 Finding the value of a collection of coinsarith661 Finding the value of a collection of bills and coinsarith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith670 Introduction to writing a decimal as a fractionarith087 Converting a decimal to a fractionarith671 Introduction to converting a fraction to a decimalarith672 Introduction to writing a decimal as a mixed numberarith624 Addition of aligned decimalsarith668 Addition with moneyarith625 Subtraction of aligned decimalsarith669 Subtraction with moneyarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith674 Introduction to percentunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number values

Geometry

geom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom001 Sum of the angle measures of a trianglegeom310 Classifying quadrilateralsgeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom078 Sides of polygons having the same perimetergeom353 Perimeter of a piecewise rectangular figuregeom019 Area of a square or a rectanglegeom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom340 Area of a piecewise rectangular figuregeom347 Introduction to circle: diameter, radius, and chordgeom311 Volume of a cube or a rectangular prismgeom354 Volume of a solid made of unit cubesgeom348 Vertices, edges, and faces of a solidgeom219 Nets of solids


geom359 Introduction to congruencegeom360 Introduction to similaritygeom355 Introduction to translationsgeom356 Introduction to reflectionsgeom357 Identifying transformationsgeom334 Drawing lines of symmetry

Algebra, Graphs, and Probability

mstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat037 Line plotsmstat024 Interpreting bar graphsmstat044 Double bar graphsmstat007 Interpreting line graphsmstat031 Interpreting a stem-and-leaf plotmstat003 Mode of a data setmstat028 Mean and median of a data setmstat041 Tree diagramsmstat040 Introduction to the counting principlemstat026 Introduction to probability of an eventmstat039 Understanding likelihoodmstat010 Probability of an eventmstat042 Venn diagrams with two setsmstat038 Reading the temperature from a thermometeralge286 Plotting integers on a number linealge284 Evaluating a simple algebraic expression: Problem type 1alge683 Evaluating a simple algebraic expression: Problem type 2alge285 Evaluating a simple algebraic expression: Problem type 3alge009 Additive property of equality: Problem type 1alge813 Solving simple equations with multiplication or divisionalge008 Multiplicative property of equality: Problem type 1alge281 Function tables with one-step rulesalge282 Function tables with two-step rulesfun005 Finding a function rule: Problem type 1alge278 Reading a point in quadrant 1alge279 Plotting a point in quadrant 1alge283 Graphing whole number functionsalge280 Graphing a line in quadrant 1



Whole Numbers

arith066 Expanded formarith643 Expanded form with zerosarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith633 Single digit addition with carryarith634 Addition of 3 or 4 single-digit numbersarith635 Adding a 2-digit number and a 1-digit number with carryarith001 Addition without carryarith050 Addition with carryarith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith660 Finding the value of a collection of coinsarith661 Finding the value of a collection of bills and coinsarith636 Subtracting a 1-digit number from a 2-digit numberarith007 Subtraction without borrowingarith006 Subtraction with borrowingarith682 Subtraction with multiple regrouping stepsarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith641 Multiples: Problem type 1arith642 Multiples: Problem type 2arith008 One-digit multiplicationarith679 Multiplication by 10, 100, and 1000arith675 Understanding multiplication of a one-digit number with a larger numberarith003 Multiplication without carryarith004 Multiplication with carryarith615 Introduction to multiplication of large numbersarith632 Multiplication with trailing zeros: Problem type 1arith638 Multiplication with trailing zeros: Problem type 2arith014 Multiplication of large numbersarith639 Using multiplication to find the number of squaresarith640 Using addition and multiplication to count the objects on a gridarith075 Simple divisionarith052 Division without carryarith005 Division with carryarith680 Division with trailing zeros: Problem type 1arith649 Division with trailing zeros: Problem type 2arith650 Division involving quotients with intermediate zerosarith644 Word problem on quotient and remainderarith023 Word problem using division


arith614 Basic word problem using multiplication or divisionarith651 Introduction to inequalitiesarith652 Comparing a simple numerical expression with a numberarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith101 Estimating a sumarith102 Estimating a differencearith677 Estimating a productarith678 Estimating a quotientarith103 Average of two numbersarith645 Introduction to parenthesesarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith646 Even and odd numbersarith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith240 Word problem with common multiplesarith655 Introduction to properties of additionarith656 Introduction to properties of multiplicationarith657 Introduction to the distributive propertyarith653 Fact families for addition and subtractionarith654 Fact families for multiplication and divisionarith658 Filling in missing operations to make an equationalge807 Finding the next terms of a simple sequence

Fractions and Proportions

arith623 Introduction to fractionsarith663 Introduction to ratiosarith665 Introduction to equivalent fractionsarith212 Equivalent fractionsarith666 Introduction to reduced fractionsarith067 Reduced fractionarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith044 Ordering fractions with same denominator


arith091 Ordering fractions with same numeratorarith092 Ordering fractionsarith667 Plotting fractions on a number linearith618 Addition or subtraction of fractions with the same denominatorarith664 Introduction to addition or subtraction of fractions with different denomina-torsarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith079 Product of a unit fraction and a whole numberarith009 Unit fraction multiplicationarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith095 Word problem with fractionsarith088 The reciprocal of a numberarith022 Fraction divisionarith662 Introduction to mixed numbers and improper fractionsarith215 Addition or subtraction of mixed numbers with same denominatorarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith085 Addition or subtraction of mixed numbers with different denominatorsarith020 Mixed number multiplication: Problem type 1arith076 Mixed number multiplication: Problem type 2arith068 Mixed number divisionarith228 Basic word problem on ratesalge272 Solving a proportion: Basicarith064 Simple word problem on proportionsarith610 Word problem on proportions: Problem type 1unit034 Conversion between metric and customary unit systems

Decimals and Percents

arith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimalsarith670 Introduction to writing a decimal as a fractionarith087 Converting a decimal to a fractionarith671 Introduction to converting a fraction to a decimalarith222 Converting a fraction to a terminating decimalarith089 Converting a fraction to a repeating decimalarith672 Introduction to writing a decimal as a mixed numberarith223 Converting a mixed number to a decimalarith624 Addition of aligned decimals


arith668 Addition with moneyarith625 Subtraction of aligned decimalsarith669 Subtraction with moneyarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith082 Multiplication of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith045 Word problem with powers of tenarith628 Word problem with multiple decimal operations: Problem type 1arith083 Division of a decimal by a power of tenarith081 Division of a decimal by a whole numberarith019 Decimal divisionarith629 Word problem with multiple decimal operations: Problem type 2arith674 Introduction to percentarith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith069 Writing a ratio as a percentagearith030 Percentage of a whole numberarith074 Word problem on percentage: Problem type 1arith232 Simple interest

Geometry and Measurement

geom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom154 Constructing the perpendicular bisector of a line segmentgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom801 Area of a trianglegeom001 Sum of the angle measures of a trianglegeom908 Solving a triangle: Problem type 1geom310 Classifying quadrilateralsgeom532 Classifying parallelogramsgeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom078 Sides of polygons having the same perimeter


geom353 Perimeter of a piecewise rectangular figuregeom019 Area of a square or a rectanglegeom217 Finding the side length of a rectangle given its perimeter or areageom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom347 Introduction to circle: diameter, radius, and chordgeom016 Circumference of a circlegeom802 Circumference and area of a circlegeom354 Volume of a solid made of unit cubesgeom311 Volume of a cube or a rectangular prismgeom090 Volume of a triangular prismgeom031 Surface area of a cube or a rectangular prismgeom345 Surface area of a solid made of unit cubesgeom091 Surface area of a triangular prismgeom219 Nets of solidsgeom348 Vertices, edges, and faces of a solidgeom359 Introduction to congruencegeom360 Introduction to similaritygeom037 Similar polygonsgeom355 Introduction to translationsgeom356 Introduction to reflectionsgeom357 Identifying transformationsgeom334 Drawing lines of symmetrymstat033 Measuring length to the nearest inchmstat034 Measuring length to the nearest quarter or half inchmstat035 Conversions involving measurements in feet and inchesmstat036 Adding customary units of lengthunit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversionunit007 Customary unit conversion with mixed number valuesunit008 Customary unit conversion with mixed number values, two-step conversionunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesunit003 Metric distance conversion with decimal valuesunit004 Metric conversion with decimal values, two-step conversiontime010 Telling timetime008 Reading a calendarunit012 Time unit conversion with whole number valuestime009 Introduction to adding timetime006 Adding timetime007 Subtracting time


Algebra and Graphs

mstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat024 Interpreting bar graphsmstat037 Line plotsmstat044 Double bar graphsmstat007 Interpreting line graphsstat804 Interpreting circle graphs or pie chartsmstat031 Interpreting a stem-and-leaf plotmstat003 Mode of a data setmstat028 Mean and median of a data setstat803 Finding the value for a new score that will yield a given meanmstat029 How changing a value affects the mean and medianmstat025 Finding if a question can be answered by the datamstat041 Tree diagramsmstat040 Introduction to the counting principlestat106 Outcomes and event probabilitymstat026 Introduction to probability of an eventmstat039 Understanding likelihoodmstat010 Probability of an eventmstat042 Venn diagrams with two setsmstat043 Venn diagrams with three setsmstat038 Reading the temperature from a thermometeralge286 Plotting integers on a number linearith605 Plotting rational numbers on a number linearith071 Absolute value of a numberarith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionalge284 Evaluating a simple algebraic expression: Problem type 1alge683 Evaluating a simple algebraic expression: Problem type 2alge285 Evaluating a simple algebraic expression: Problem type 3alge602 Writing a mathematical expressionalge016 Translating sentences into mathematical equationsalge009 Additive property of equality: Problem type 1alge010 Additive property of equality: Problem type 2alge800 Additive property of equality with decimalsalge801 Additive property of equality with fractionsalge813 Solving simple equations with multiplication or divisionalge008 Multiplicative property of equality: Problem type 1alge802 Multiplicative property of equality with fractions

B.4. MATHEMATICS - LV6 / ESSENTIAL MATHEMATICS 197

alge803 Using two steps to solve an equationalge281 Function tables with one-step rulesalge282 Function tables with two-step rulesfun005 Finding a function rule: Problem type 1alge278 Reading a point in quadrant 1alge064 Reading a point in the coordinate planealge279 Plotting a point in quadrant 1alge067 Plotting a point in the coordinate planealge283 Graphing whole number functionsalge066 Solutions to a linear equation in two variables: Problem type 1alge280 Graphing a line in quadrant 1arith233 Introduction to exponentsarith683 Powers of 10: Positive exponentarith036 Scientific notation with positive exponentarith016 Square root of a perfect square

B.4 Mathematics - LV6 / Essential Mathematics

Whole Numbers

arith066 Expanded formarith643 Expanded form with zerosarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith633 Single digit addition with carryarith634 Addition of 3 or 4 single-digit numbersarith635 Adding a 2-digit number and a 1-digit number with carryarith001 Addition without carryarith050 Addition with carryarith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith660 Finding the value of a collection of coinsarith661 Finding the value of a collection of bills and coinsarith636 Subtracting a 1-digit number from a 2-digit numberarith007 Subtraction without borrowingarith006 Subtraction with borrowingarith682 Subtraction with multiple regrouping stepsarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith008 One-digit multiplicationarith679 Multiplication by 10, 100, and 1000arith675 Understanding multiplication of a one-digit number with a larger number


arith003 Multiplication without carryarith004 Multiplication with carryarith615 Introduction to multiplication of large numbersarith632 Multiplication with trailing zeros: Problem type 1arith638 Multiplication with trailing zeros: Problem type 2arith014 Multiplication of large numbersarith639 Using multiplication to find the number of squaresarith640 Using addition and multiplication to count the objects on a gridarith641 Multiples: Problem type 1arith642 Multiples: Problem type 2arith075 Simple divisionarith052 Division without carryarith005 Division with carryarith680 Division with trailing zeros: Problem type 1arith649 Division with trailing zeros: Problem type 2arith650 Division involving quotients with intermediate zerosarith644 Word problem on quotient and remainderarith023 Word problem using divisionarith614 Basic word problem using multiplication or divisionarith651 Introduction to inequalitiesarith652 Comparing a simple numerical expression with a numberarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith101 Estimating a sumarith102 Estimating a differencearith677 Estimating a productarith678 Estimating a quotientarith103 Average of two numbersarith645 Introduction to parenthesesarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith658 Filling in missing operations to make an equationarith646 Even and odd numbersarith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith240 Word problem with common multiplesarith655 Introduction to properties of addition


arith656 Introduction to properties of multiplicationarith657 Introduction to the distributive propertyarith653 Fact families for addition and subtractionarith654 Fact families for multiplication and divisionalge807 Finding the next terms of a simple sequence

Fractions and Decimals

arith623 Introduction to fractionsarith665 Introduction to equivalent fractionsarith212 Equivalent fractionsarith666 Introduction to reduced fractionsarith067 Reduced fractionarith044 Ordering fractions with same denominatorarith091 Ordering fractions with same numeratorarith092 Ordering fractionsarith667 Plotting fractions on a number linearith618 Addition or subtraction of fractions with the same denominatorarith664 Introduction to addition or subtraction of fractions with different denomina-torsarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith215 Addition or subtraction of mixed numbers with same denominatorarith088 The reciprocal of a numberarith079 Product of a unit fraction and a whole numberarith009 Unit fraction multiplicationarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith095 Word problem with fractionsarith022 Fraction divisionarith662 Introduction to mixed numbers and improper fractionsarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith085 Addition or subtraction of mixed numbers with different denominatorsarith020 Mixed number multiplication: Problem type 1arith076 Mixed number multiplication: Problem type 2arith068 Mixed number divisionarith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimals


arith670 Introduction to writing a decimal as a fractionarith087 Converting a decimal to a fractionarith671 Introduction to converting a fraction to a decimalarith222 Converting a fraction to a terminating decimalarith089 Converting a fraction to a repeating decimalarith672 Introduction to writing a decimal as a mixed numberarith223 Converting a mixed number to a decimalarith624 Addition of aligned decimalsarith668 Addition with moneyarith625 Subtraction of aligned decimalsarith669 Subtraction with moneyarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith082 Multiplication of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith045 Word problem with powers of tenarith628 Word problem with multiple decimal operations: Problem type 1arith083 Division of a decimal by a power of tenarith081 Division of a decimal by a whole numberarith019 Decimal divisionarith629 Word problem with multiple decimal operations: Problem type 2

Geometry

geom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom305 Supplementary and vertical anglesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom154 Constructing the perpendicular bisector of a line segmentgeom525 Computing distances on the number linegeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom801 Area of a trianglegeom001 Sum of the angle measures of a trianglegeom908 Solving a triangle: Problem type 1geom044 Pythagorean Theorem


geom310 Classifying quadrilateralsgeom532 Classifying parallelogramsgeom078 Sides of polygons having the same perimetergeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom019 Area of a square or a rectanglegeom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom217 Finding the side length of a rectangle given its perimeter or areageom353 Perimeter of a piecewise rectangular figuregeom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom344 Area involving rectangles and trianglesgeom347 Introduction to circle: diameter, radius, and chordgeom016 Circumference of a circlegeom218 Finding the radius or the diameter of a circle given its circumferencegeom802 Circumference and area of a circlegeom301 Perimeter involving rectangles and circlesgeom036 Area between two concentric circlesgeom302 Area involving rectangles and circlesgeom214 Area involving inscribed figuresgeom311 Volume of a cube or a rectangular prismgeom354 Volume of a solid made of unit cubesgeom090 Volume of a triangular prismgeom033 Volume of a pyramidgeom035 Volume of a cylindergeom086 Volume of a conegeom348 Vertices, edges, and faces of a solidgeom031 Surface area of a cube or a rectangular prismgeom345 Surface area of a solid made of unit cubesgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom219 Nets of solidsgeom359 Introduction to congruencegeom360 Introduction to similaritygeom037 Similar polygonsgeom337 Indirect measurementgeom355 Introduction to translationsgeom330 Translation of a polygongeom356 Introduction to reflectionsgeom332 Reflection of a polygon over a vertical or horizontal linegeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origin


geom357 Identifying transformations

Measurement and Graphs

mstat033 Measuring length to the nearest inchmstat034 Measuring length to the nearest quarter or half inchunit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversionunit007 Customary unit conversion with mixed number valuesunit008 Customary unit conversion with mixed number values, two-step conversionmstat035 Conversions involving measurements in feet and inchesmstat036 Adding customary units of lengthunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesunit003 Metric distance conversion with decimal valuesunit004 Metric conversion with decimal values, two-step conversionunit034 Conversion between metric and customary unit systemstime010 Telling timeunit012 Time unit conversion with whole number valuestime008 Reading a calendartime009 Introduction to adding timetime006 Adding timetime007 Subtracting timearith063 Word problem with clocksmstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat037 Line plotsmstat024 Interpreting bar graphsmstat044 Double bar graphsmstat007 Interpreting line graphsstat804 Interpreting circle graphs or pie chartsmstat003 Mode of a data setmstat028 Mean and median of a data setmstat031 Interpreting a stem-and-leaf plotmstat027 Using back-to-back stem-and-leaf plots to compare data setsmstat006 Box-and-whisker plotsmstat014 Random samples and predictionmstat029 How changing a value affects the mean and medianstat803 Finding the value for a new score that will yield a given meanmstat025 Finding if a question can be answered by the data

Proportions, Percents, and Probability


arith663 Introduction to ratiosarith228 Basic word problem on ratesalge272 Solving a proportion: Basicarith064 Simple word problem on proportionsarith610 Word problem on proportions: Problem type 1arith674 Introduction to percentarith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith074 Word problem on percentage: Problem type 1arith225 Word problem on percentage: Problem type 3arith232 Simple interestmstat040 Introduction to the counting principlemstat015 Counting Principlemstat008 Permutationsmstat009 Combinationsstat106 Outcomes and event probabilitymstat026 Introduction to probability of an eventmstat039 Understanding likelihoodmstat010 Probability of an eventmstat012 Probability of independent eventsmstat013 Probability of dependent eventsmstat041 Tree diagramsmstat042 Venn diagrams with two setsmstat043 Venn diagrams with three sets

Algebra

mstat038 Reading the temperature from a thermometeralge286 Plotting integers on a number linearith605 Plotting rational numbers on a number linearith071 Absolute value of a numberarith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and divisionarith106 Signed fractions additionarith105 Signed fractions multiplicationarith234 Signed decimal additionalge001 Integers and rational numbersalge606 Distributive property, simple


alge607 Combining like terms, basicalge284 Evaluating a simple algebraic expression: Problem type 1alge683 Evaluating a simple algebraic expression: Problem type 2alge285 Evaluating a simple algebraic expression: Problem type 3alge602 Writing a mathematical expressionalge005 Evaluation of a linear expression in two variablesalge187 Properties of additionalge188 Properties of real numbersalge009 Additive property of equality: Problem type 1alge800 Additive property of equality with decimalsalge801 Additive property of equality with fractionsalge010 Additive property of equality: Problem type 2alge813 Solving simple equations with multiplication or divisionalge008 Multiplicative property of equality: Problem type 1alge802 Multiplicative property of equality with fractionsalge803 Using two steps to solve an equationalge006 Solving a linear equation: Problem type 1alge015 Writing an inequalityalge019 Solving a linear inequality: Problem type 1alge017 Graphing a linear inequality on the number linealge016 Translating sentences into mathematical equationsfun005 Finding a function rule: Problem type 1alge281 Function tables with one-step rulesalge282 Function tables with two-step rulesalge283 Graphing whole number functionsalge278 Reading a point in quadrant 1alge064 Reading a point in the coordinate planealge279 Plotting a point in quadrant 1alge067 Plotting a point in the coordinate planealge066 Solutions to a linear equation in two variables: Problem type 1alge280 Graphing a line in quadrant 1alge194 Graphing a line given its equation in slope-intercept formalge198 Graphing a vertical or horizontal linealge263 Interpreting the graphs of two functionsarith233 Introduction to exponentsarith683 Powers of 10: Positive exponentarith684 Powers of 10: Negative exponentarith036 Scientific notation with positive exponentarith037 Scientific notation with negative exponentarith047 Evaluating expressions with exponents: Problem type 1arith600 Exponents and order of operationsalge004 Evaluation of a polynomial in one variablearith029 Ordering numbers with positive exponentsarith016 Square root of a perfect square

B.5. MIDDLE SCHOOL MATH 1 205

arith602 Estimating a square root

B.5 Middle School Math 1

Whole Numbers

arith066 Expanded formarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith006 Subtraction with borrowingarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith004 Multiplication with carryarith615 Introduction to multiplication of large numbersarith014 Multiplication of large numbersarith005 Division with carryarith023 Word problem using divisionarith614 Basic word problem using multiplication or divisionarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith101 Estimating a sumarith102 Estimating a differencearith677 Estimating a productarith678 Estimating a quotientarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2alge285 Evaluating a simple algebraic expression: Problem type 3arith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith240 Word problem with common multiples



arith623 Introduction to fractionsarith665 Introduction to equivalent fractionsarith663 Introduction to ratiosarith212 Equivalent fractionsarith067 Reduced fractionarith667 Plotting fractions on a number linearith044 Ordering fractions with same denominatorarith091 Ordering fractions with same numeratorarith092 Ordering fractionsarith618 Addition or subtraction of fractions with the same denominatorarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith088 The reciprocal of a numberarith079 Product of a unit fraction and a whole numberarith009 Unit fraction multiplicationarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith095 Word problem with fractionsarith022 Fraction divisionarith662 Introduction to mixed numbers and improper fractionsarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith215 Addition or subtraction of mixed numbers with same denominatorarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith085 Addition or subtraction of mixed numbers with different denominatorsarith020 Mixed number multiplication: Problem type 1arith076 Mixed number multiplication: Problem type 2arith068 Mixed number divisionarith228 Basic word problem on ratesalge218 Word problem on ratesalge272 Solving a proportion: Basicarith064 Simple word problem on proportionsarith610 Word problem on proportions: Problem type 1


arith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimalsarith087 Converting a decimal to a fractionarith222 Converting a fraction to a terminating decimal


arith089 Converting a fraction to a repeating decimalarith223 Converting a mixed number to a decimalarith624 Addition of aligned decimalsarith625 Subtraction of aligned decimalsarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith082 Multiplication of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith045 Word problem with powers of tenarith628 Word problem with multiple decimal operations: Problem type 1arith083 Division of a decimal by a power of tenarith081 Division of a decimal by a whole numberarith019 Decimal divisionarith629 Word problem with multiple decimal operations: Problem type 2arith674 Introduction to percentarith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith074 Word problem on percentage: Problem type 1arith031 Word problem on percentage: Problem type 2arith225 Word problem on percentage: Problem type 3arith232 Simple intereststat801 Computations from circle graphsstat804 Interpreting circle graphs or pie chartsmstat014 Random samples and prediction

Measurement, Graphs, and Probability

mstat034 Measuring length to the nearest quarter or half inchunit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversionunit007 Customary unit conversion with mixed number valuesunit008 Customary unit conversion with mixed number values, two-step conversionmstat035 Conversions involving measurements in feet and inchesunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesunit003 Metric distance conversion with decimal valuesunit004 Metric conversion with decimal values, two-step conversionunit034 Conversion between metric and customary unit systemsunit012 Time unit conversion with whole number values


time006 Adding timetime007 Subtracting timemstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat024 Interpreting bar graphsmstat044 Double bar graphsmstat037 Line plotsmstat007 Interpreting line graphsmstat003 Mode of a data setmstat028 Mean and median of a data setstat803 Finding the value for a new score that will yield a given meanmstat029 How changing a value affects the mean and medianstat802 Rejecting unreasonable claims based on average statisticsmstat031 Interpreting a stem-and-leaf plotmstat027 Using back-to-back stem-and-leaf plots to compare data setsmstat006 Box-and-whisker plotsmstat025 Finding if a question can be answered by the datamstat030 Sketching the line of best fitmstat023 Scatterplots and correlationmstat043 Venn diagrams with three setsmstat041 Tree diagramsmstat040 Introduction to the counting principlemstat015 Counting Principlemstat008 Permutationsmstat009 Combinationsstat106 Outcomes and event probabilitymstat026 Introduction to probability of an eventmstat010 Probability of an eventmstat011 Area as probabilitymstat012 Probability of independent eventsmstat013 Probability of dependent events

Algebra

alge286 Plotting integers on a number linearith071 Absolute value of a numberarith104 Operations with absolute valuearith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and divisionarith234 Signed decimal additionarith047 Evaluating expressions with exponents: Problem type 1


alge001 Integers and rational numbersarith605 Plotting rational numbers on a number linegeom525 Computing distances on the number linearith657 Introduction to the distributive propertyalge606 Distributive property, simplealge607 Combining like terms, basicarith655 Introduction to properties of additionarith656 Introduction to properties of multiplicationalge187 Properties of additionalge005 Evaluation of a linear expression in two variablesalge602 Writing a mathematical expressionalge009 Additive property of equality: Problem type 1alge800 Additive property of equality with decimalsalge801 Additive property of equality with fractionsalge010 Additive property of equality: Problem type 2alge266 Additive property of equality: Problem type 3alge813 Solving simple equations with multiplication or divisionalge008 Multiplicative property of equality: Problem type 1alge802 Multiplicative property of equality with fractionsalge803 Using two steps to solve an equationalge006 Solving a linear equation: Problem type 1alge016 Translating sentences into mathematical equationsalge014 Solving a word problem using a linear equation: Problem type 1alge810 Introduction to algebraic symbol manipulationalge015 Writing an inequalityalge019 Solving a linear inequality: Problem type 1alge017 Graphing a linear inequality on the number linefun005 Finding a function rule: Problem type 1alge282 Function tables with two-step rulesfun001 Function tablesalge064 Reading a point in the coordinate planealge067 Plotting a point in the coordinate planefun002 Graphing integer functionsalge066 Solutions to a linear equation in two variables: Problem type 1alge194 Graphing a line given its equation in slope-intercept formalge198 Graphing a vertical or horizontal linealge263 Interpreting the graphs of two functionsalge807 Finding the next terms of a simple sequencearith233 Introduction to exponentsarith683 Powers of 10: Positive exponentarith036 Scientific notation with positive exponentarith016 Square root of a perfect squarearith602 Estimating a square root


Geometry

geom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom305 Supplementary and vertical anglesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom154 Constructing the perpendicular bisector of a line segmentgeom150 Constructing a pair of perpendicular linesgeom157 Constructing a pair of parallel linesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom801 Area of a trianglegeom001 Sum of the angle measures of a trianglegeom908 Solving a triangle: Problem type 1geom044 Pythagorean Theoremgeom310 Classifying quadrilateralsgeom532 Classifying parallelogramsgeom078 Sides of polygons having the same perimetergeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom019 Area of a square or a rectanglegeom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom217 Finding the side length of a rectangle given its perimeter or areageom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom344 Area involving rectangles and trianglesgeom347 Introduction to circle: diameter, radius, and chordgeom016 Circumference of a circlegeom218 Finding the radius or the diameter of a circle given its circumferencegeom802 Circumference and area of a circlegeom301 Perimeter involving rectangles and circlesgeom036 Area between two concentric circlesgeom302 Area involving rectangles and circlesgeom214 Area involving inscribed figuresgeom838 Circumference ratiosgeom354 Volume of a solid made of unit cubes


geom311 Volume of a cube or a rectangular prismgeom505 Volume of a piecewise rectangular prismgeom090 Volume of a triangular prismgeom035 Volume of a cylindergeom092 Rate of filling of a solidgeom348 Vertices, edges, and faces of a solidgeom031 Surface area of a cube or a rectangular prismgeom345 Surface area of a solid made of unit cubesgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom219 Nets of solidsgeom359 Introduction to congruencegeom360 Introduction to similaritygeom037 Similar polygonsgeom357 Identifying transformationsgeom330 Translation of a polygongeom332 Reflection of a polygon over a vertical or horizontal linegeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origin

B.6 Middle School Math 2

Whole Numbers and Integers

arith066 Expanded formarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith006 Subtraction with borrowingarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith004 Multiplication with carryarith615 Introduction to multiplication of large numbersarith014 Multiplication of large numbersarith005 Division with carryarith023 Word problem using divisionarith614 Basic word problem using multiplication or divisionarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith101 Estimating a sum


arith102 Estimating a differencearith677 Estimating a productarith678 Estimating a quotientarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith240 Word problem with common multiplesalge286 Plotting integers on a number linearith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and divisionarith071 Absolute value of a numberarith104 Operations with absolute value


arith623 Introduction to fractionsarith665 Introduction to equivalent fractionsarith663 Introduction to ratiosarith212 Equivalent fractionsarith067 Reduced fractionarith667 Plotting fractions on a number linearith044 Ordering fractions with same denominatorarith091 Ordering fractions with same numeratorarith092 Ordering fractionsarith618 Addition or subtraction of fractions with the same denominatorarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith088 The reciprocal of a numberarith079 Product of a unit fraction and a whole numberarith009 Unit fraction multiplicationarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith095 Word problem with fractionsarith022 Fraction division


arith662 Introduction to mixed numbers and improper fractionsarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith215 Addition or subtraction of mixed numbers with same denominatorarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith085 Addition or subtraction of mixed numbers with different denominatorsarith020 Mixed number multiplication: Problem type 1arith076 Mixed number multiplication: Problem type 2arith068 Mixed number divisionarith605 Plotting rational numbers on a number linearith106 Signed fractions additionarith105 Signed fractions multiplicationarith047 Evaluating expressions with exponents: Problem type 1arith600 Exponents and order of operationsarith228 Basic word problem on ratesalge218 Word problem on ratesalge272 Solving a proportion: Basicarith064 Simple word problem on proportionsarith610 Word problem on proportions: Problem type 1


arith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimalsgeom525 Computing distances on the number linearith087 Converting a decimal to a fractionarith222 Converting a fraction to a terminating decimalarith089 Converting a fraction to a repeating decimalarith223 Converting a mixed number to a decimalarith624 Addition of aligned decimalsarith625 Subtraction of aligned decimalsarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith234 Signed decimal additionarith082 Multiplication of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith045 Word problem with powers of tenarith628 Word problem with multiple decimal operations: Problem type 1arith083 Division of a decimal by a power of ten


arith081 Division of a decimal by a whole numberarith019 Decimal divisionarith629 Word problem with multiple decimal operations: Problem type 2arith674 Introduction to percentarith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith074 Word problem on percentage: Problem type 1arith031 Word problem on percentage: Problem type 2arith225 Word problem on percentage: Problem type 3arith232 Simple intereststat801 Computations from circle graphsstat804 Interpreting circle graphs or pie chartsmstat014 Random samples and prediction

Measurement, Graphs, and Probability

mstat034 Measuring length to the nearest quarter or half inchunit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversionunit007 Customary unit conversion with mixed number valuesunit008 Customary unit conversion with mixed number values, two-step conversionmstat035 Conversions involving measurements in feet and inchesunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesunit003 Metric distance conversion with decimal valuesunit004 Metric conversion with decimal values, two-step conversionunit034 Conversion between metric and customary unit systemsunit012 Time unit conversion with whole number valuestime006 Adding timetime007 Subtracting timemstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat024 Interpreting bar graphsmstat044 Double bar graphsmstat037 Line plotsmstat007 Interpreting line graphsmstat003 Mode of a data setmstat028 Mean and median of a data setstat803 Finding the value for a new score that will yield a given meanmstat029 How changing a value affects the mean and median


stat802 Rejecting unreasonable claims based on average statisticsmstat031 Interpreting a stem-and-leaf plotmstat027 Using back-to-back stem-and-leaf plots to compare data setsmstat006 Box-and-whisker plotsmstat025 Finding if a question can be answered by the datamstat030 Sketching the line of best fitmstat023 Scatterplots and correlationmstat043 Venn diagrams with three setsmstat041 Tree diagramsmstat040 Introduction to the counting principlemstat015 Counting Principlemstat008 Permutationsmstat009 Combinationsstat106 Outcomes and event probabilitymstat026 Introduction to probability of an eventmstat010 Probability of an eventmstat011 Area as probabilitymstat012 Probability of independent eventsmstat013 Probability of dependent eventsstat112 Die rolling

Algebra

alge001 Integers and rational numbersalge002 Integers, rational numbers, and irrational numbersarith657 Introduction to the distributive propertyalge606 Distributive property, simplealge607 Combining like terms, basicarith655 Introduction to properties of additionarith656 Introduction to properties of multiplicationalge187 Properties of additionalge188 Properties of real numbersalge285 Evaluating a simple algebraic expression: Problem type 3alge005 Evaluation of a linear expression in two variablesalge004 Evaluation of a polynomial in one variablealge602 Writing a mathematical expressionalge009 Additive property of equality: Problem type 1alge800 Additive property of equality with decimalsalge801 Additive property of equality with fractionsalge010 Additive property of equality: Problem type 2alge266 Additive property of equality: Problem type 3alge813 Solving simple equations with multiplication or divisionalge008 Multiplicative property of equality: Problem type 1


alge802 Multiplicative property of equality with fractionsalge012 Multiplicative property of equality: Problem type 2alge803 Using two steps to solve an equationalge006 Solving a linear equation: Problem type 1alge208 Solving a linear equation: Problem type 2alge017 Graphing a linear inequality on the number linealge016 Translating sentences into mathematical equationsalge014 Solving a word problem using a linear equation: Problem type 1alge173 Solving a word problem using a linear equation: Problem type 3alge810 Introduction to algebraic symbol manipulationalge015 Writing an inequalityalge019 Solving a linear inequality: Problem type 1alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3fun005 Finding a function rule: Problem type 1alge282 Function tables with two-step rulesfun001 Function tablesfun006 Finding a function rule: Problem type 2fun002 Graphing integer functionsalge807 Finding the next terms of a simple sequencealge064 Reading a point in the coordinate planealge067 Plotting a point in the coordinate planealge066 Solutions to a linear equation in two variables: Problem type 1alge216 Solutions to a linear equation in two variables: Problem type 2alge194 Graphing a line given its equation in slope-intercept formalge197 Graphing a line given the x- and y-interceptsalge195 Graphing a line given its equation in standard formalge198 Graphing a vertical or horizontal linealge196 Graphing a line through a given point with a given slopealge069 Y-intercept of a linealge637 Determining the slope of a line given its graphalge631 Finding the slope of a line given its equationalge070 Writing an equation of a line given the slope and the y-interceptalge263 Interpreting the graphs of two functionsalge252 Graphing a parabola: Problem type 1arith233 Introduction to exponentsarith683 Powers of 10: Positive exponentarith684 Powers of 10: Negative exponentarith036 Scientific notation with positive exponentarith037 Scientific notation with negative exponentarith016 Square root of a perfect squarearith602 Estimating a square root


Geometry

geom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom305 Supplementary and vertical anglesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom154 Constructing the perpendicular bisector of a line segmentgeom150 Constructing a pair of perpendicular linesgeom157 Constructing a pair of parallel linesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom520 Identifying and naming congruent trianglesgeom801 Area of a trianglegeom001 Sum of the angle measures of a trianglegeom908 Solving a triangle: Problem type 1geom309 Solving a triangle: Problem type 2geom044 Pythagorean Theoremgeom310 Classifying quadrilateralsgeom532 Classifying parallelogramsgeom078 Sides of polygons having the same perimetergeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom019 Area of a square or a rectanglegeom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom217 Finding the side length of a rectangle given its perimeter or areageom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom344 Area involving rectangles and trianglesgeom347 Introduction to circle: diameter, radius, and chordgeom016 Circumference of a circlegeom218 Finding the radius or the diameter of a circle given its circumferencegeom802 Circumference and area of a circlegeom301 Perimeter involving rectangles and circlesgeom036 Area between two concentric circlesgeom302 Area involving rectangles and circlesgeom214 Area involving inscribed figures


geom838 Circumference ratiosgeom354 Volume of a solid made of unit cubesgeom311 Volume of a cube or a rectangular prismgeom505 Volume of a piecewise rectangular prismgeom090 Volume of a triangular prismgeom035 Volume of a cylindergeom092 Rate of filling of a solidgeom348 Vertices, edges, and faces of a solidgeom031 Surface area of a cube or a rectangular prismgeom345 Surface area of a solid made of unit cubesgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom338 Surface area involving prisms or cylindersgeom219 Nets of solidsgeom359 Introduction to congruencegeom360 Introduction to similaritygeom037 Similar polygonsgeom038 Similar right trianglesgeom337 Indirect measurementgeom357 Identifying transformationsgeom330 Translation of a polygongeom331 Coordinates of translated pointsgeom332 Reflection of a polygon over a vertical or horizontal linegeom333 Coordinates of points reflected over an axisgeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origingeom336 Dilation

B.7 Middle School Math 3 / Foundations of High School Math


arith066 Expanded formarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith006 Subtraction with borrowingarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith004 Multiplication with carryarith615 Introduction to multiplication of large numbers

B.7. MIDDLE SCHOOL MATH 3 / FOUNDATIONS OF HIGH SCHOOL MATH 219

arith014 Multiplication of large numbersarith005 Division with carryarith023 Word problem using divisionarith614 Basic word problem using multiplication or divisionarith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith101 Estimating a sumarith102 Estimating a differencearith677 Estimating a productarith678 Estimating a quotientarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith240 Word problem with common multiplesalge286 Plotting integers on a number linearith605 Plotting rational numbers on a number linearith071 Absolute value of a numberarith104 Operations with absolute valuearith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and divisionpcalc038 Addition and subtraction of matrices

Rational Numbers

arith623 Introduction to fractionsarith663 Introduction to ratiosarith665 Introduction to equivalent fractionsarith212 Equivalent fractionsarith067 Reduced fractionarith667 Plotting fractions on a number linearith044 Ordering fractions with same denominatorarith091 Ordering fractions with same numeratorarith092 Ordering fractions


arith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimalsarith618 Addition or subtraction of fractions with the same denominatorarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith088 The reciprocal of a numberarith079 Product of a unit fraction and a whole numberarith009 Unit fraction multiplicationarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith095 Word problem with fractionsarith022 Fraction divisionarith662 Introduction to mixed numbers and improper fractionsarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith215 Addition or subtraction of mixed numbers with same denominatorarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith085 Addition or subtraction of mixed numbers with different denominatorsarith020 Mixed number multiplication: Problem type 1arith076 Mixed number multiplication: Problem type 2arith068 Mixed number divisionarith087 Converting a decimal to a fractionarith222 Converting a fraction to a terminating decimalarith089 Converting a fraction to a repeating decimalarith223 Converting a mixed number to a decimalarith624 Addition of aligned decimalsarith625 Subtraction of aligned decimalsarith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith082 Multiplication of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith045 Word problem with powers of tenarith628 Word problem with multiple decimal operations: Problem type 1arith083 Division of a decimal by a power of tenarith081 Division of a decimal by a whole numberarith019 Decimal divisionarith629 Word problem with multiple decimal operations: Problem type 2arith106 Signed fractions additionarith105 Signed fractions multiplicationarith234 Signed decimal addition


geom525 Computing distances on the number line

Measurement, Proportion, Percents, and Probability

mstat034 Measuring length to the nearest quarter or half inchunit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversionunit007 Customary unit conversion with mixed number valuesunit008 Customary unit conversion with mixed number values, two-step conversionmstat035 Conversions involving measurements in feet and inchesunit009 Customary area unit conversion with whole number valuesunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesunit003 Metric distance conversion with decimal valuesunit004 Metric conversion with decimal values, two-step conversionunit010 Metric area unit conversion with decimal number valuesunit034 Conversion between metric and customary unit systemsunit035 Conversion between compound units, basic problemunit036 Conversion between compound units, advanced problemunit012 Time unit conversion with whole number valuestime006 Adding timetime007 Subtracting timearith228 Basic word problem on ratesalge218 Word problem on ratesalge272 Solving a proportion: Basicarith064 Simple word problem on proportionsarith610 Word problem on proportions: Problem type 1arith674 Introduction to percentarith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith074 Word problem on percentage: Problem type 1arith031 Word problem on percentage: Problem type 2arith225 Word problem on percentage: Problem type 3arith232 Simple intereststat805 Making reasonable inferences based on proportion statisticsstat801 Computations from circle graphsstat804 Interpreting circle graphs or pie chartsmstat014 Random samples and predictionmstat041 Tree diagramsmstat040 Introduction to the counting principle


mstat015 Counting Principlemstat008 Permutationsmstat009 Combinationsstat106 Outcomes and event probabilitymstat026 Introduction to probability of an eventmstat010 Probability of an eventmstat011 Area as probabilitymstat012 Probability of independent eventsmstat013 Probability of dependent eventsstat112 Die rolling

Variable Expressions and Equations

alge001 Integers and rational numbersalge002 Integers, rational numbers, and irrational numbersarith655 Introduction to properties of additionarith656 Introduction to properties of multiplicationarith657 Introduction to the distributive propertyalge606 Distributive property, simplealge604 Distributive Property, advancedalge607 Combining like terms, basicalge663 Combining like terms, advancedalge187 Properties of additionalge188 Properties of real numbersalge285 Evaluating a simple algebraic expression: Problem type 3alge005 Evaluation of a linear expression in two variablesalge602 Writing a mathematical expressionalge009 Additive property of equality: Problem type 1alge800 Additive property of equality with decimalsalge801 Additive property of equality with fractionsalge010 Additive property of equality: Problem type 2alge266 Additive property of equality: Problem type 3alge813 Solving simple equations with multiplication or divisionalge008 Multiplicative property of equality: Problem type 1alge802 Multiplicative property of equality with fractionsalge012 Multiplicative property of equality: Problem type 2alge803 Using two steps to solve an equationalge006 Solving a linear equation: Problem type 1alge208 Solving a linear equation: Problem type 2alge011 Solving a linear equation with several occurrences of the variable: Problem type1alge013 Solving a linear equation with several occurrences of the variable: Problem type3


alge016 Translating sentences into mathematical equationsalge271 Solving a proportion: Advancedalge014 Solving a word problem using a linear equation: Problem type 1alge173 Solving a word problem using a linear equation: Problem type 3alge704 Solving a word problem using a linear equation: Problem type 4alge810 Introduction to algebraic symbol manipulationalge160 Algebraic symbol manipulationalge015 Writing an inequalityalge019 Solving a linear inequality: Problem type 1alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge017 Graphing a linear inequality on the number linealge166 Graphing a compound linear inequality on the number linearith233 Introduction to exponentsarith683 Powers of 10: Positive exponentarith684 Powers of 10: Negative exponentarith036 Scientific notation with positive exponentarith037 Scientific notation with negative exponentscinot002 Multiplying and dividing numbers written in scientific notationarith047 Evaluating expressions with exponents: Problem type 1arith049 Evaluating expressions with exponents: Problem type 2arith600 Exponents and order of operationsarith042 Writing a positive number without a negative exponentarith043 Writing a negative number without a negative exponentarith016 Square root of a perfect squarearith602 Estimating a square rootalge024 Product rule of exponentsarith029 Ordering numbers with positive exponentsalge030 Multiplying monomialsalge027 Power rule: Positive exponentsalge025 Power rule: Negative exponentsalge004 Evaluation of a polynomial in one variablealge029 Simplifying a polynomial expressionalge033 Multiplying two binomialsalge705 Factoring a quadratic with leading coefficient 1

Functions and Graphs

mstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat024 Interpreting bar graphsmstat044 Double bar graphsmstat037 Line plots


mstat007 Interpreting line graphsmstat003 Mode of a data setmstat028 Mean and median of a data setstat803 Finding the value for a new score that will yield a given meanmstat029 How changing a value affects the mean and medianstat802 Rejecting unreasonable claims based on average statisticsmstat031 Interpreting a stem-and-leaf plotmstat027 Using back-to-back stem-and-leaf plots to compare data setsmstat006 Box-and-whisker plotsmstat025 Finding if a question can be answered by the datamstat030 Sketching the line of best fitmstat023 Scatterplots and correlationmstat043 Venn diagrams with three setsfun005 Finding a function rule: Problem type 1alge282 Function tables with two-step rulesfun001 Function tablesfun006 Finding a function rule: Problem type 2alge064 Reading a point in the coordinate planealge067 Plotting a point in the coordinate planefun002 Graphing integer functionsalge807 Finding the next terms of a simple sequencepcalc085 Arithmetic sequencealge066 Solutions to a linear equation in two variables: Problem type 1alge216 Solutions to a linear equation in two variables: Problem type 2alge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge197 Graphing a line given the x- and y-interceptsalge196 Graphing a line through a given point with a given slopealge198 Graphing a vertical or horizontal linealge637 Determining the slope of a line given its graphalge631 Finding the slope of a line given its equationalge069 Y-intercept of a linealge210 X- and y-intercepts of a line given the equation in standard formalge070 Writing an equation of a line given the slope and the y-interceptalge071 Writing the equation of a line given the slope and a point on the linealge072 Writing the equation of the line through two given pointsalge701 Writing equations and drawing graphs to fit a narrativealge263 Interpreting the graphs of two functionsalge018 Graphing a linear inequality in the plane: Problem type 1alge132 Distance between two points in the planealge168 Graphing an equation involving absolute value in the planealge252 Graphing a parabola: Problem type 1


Geometry

geom349 Naming segments, rays, and linesgeom358 Introduction to parallel and perpendicular linesgeom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom305 Supplementary and vertical anglesgeom530 Solving equations involving vertical anglesgeom531 Solving equations involving angles and parallel linesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom154 Constructing the perpendicular bisector of a line segmentgeom150 Constructing a pair of perpendicular linesgeom157 Constructing a pair of parallel linesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom520 Identifying and naming congruent trianglesgeom801 Area of a trianglegeom001 Sum of the angle measures of a trianglegeom502 Solving triangles: Basicgeom908 Solving a triangle: Problem type 1geom309 Solving a triangle: Problem type 2geom044 Pythagorean Theorempcalc600 Sine, cosine, and tangent ratiospcalc601 Using a trigonometric ratio to find a side length in a right trianglegeom310 Classifying quadrilateralsgeom532 Classifying parallelogramsgeom078 Sides of polygons having the same perimetergeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom019 Area of a square or a rectanglegeom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom217 Finding the side length of a rectangle given its perimeter or areageom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom142 Area between two rectanglesgeom344 Area involving rectangles and trianglesgeom143 Area and perimeter of a rectanglegeom522 Interior angles of convex polygons


geom347 Introduction to circle: diameter, radius, and chordgeom016 Circumference of a circlegeom218 Finding the radius or the diameter of a circle given its circumferencegeom802 Circumference and area of a circlegeom301 Perimeter involving rectangles and circlesgeom036 Area between two concentric circlesgeom302 Area involving rectangles and circlesgeom214 Area involving inscribed figuresgeom133 Ratio of volumesgeom838 Circumference ratiosgeom354 Volume of a solid made of unit cubesgeom311 Volume of a cube or a rectangular prismgeom505 Volume of a piecewise rectangular prismgeom090 Volume of a triangular prismgeom033 Volume of a pyramidgeom035 Volume of a cylindergeom086 Volume of a conegeom092 Rate of filling of a solidgeom348 Vertices, edges, and faces of a solidgeom031 Surface area of a cube or a rectangular prismgeom345 Surface area of a solid made of unit cubesgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom338 Surface area involving prisms or cylindersgeom219 Nets of solidsgeom508 Length, area, and volume ratios of similar figuresgeom359 Introduction to congruencegeom360 Introduction to similaritygeom037 Similar polygonsgeom038 Similar right trianglesgeom337 Indirect measurementgeom357 Identifying transformationsgeom330 Translation of a polygongeom331 Coordinates of translated pointsgeom332 Reflection of a polygon over a vertical or horizontal linegeom333 Coordinates of points reflected over an axisgeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origingeom336 Dilation

B.8. MIDDLE SCHOOL GEOMETRY 227

B.8 Middle School Geometry

Angles and triangles

geom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom305 Supplementary and vertical anglesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom021 Area of a trianglegeom020 Area of an obtuse trianglegeom001 Sum of the angle measures of a trianglegeom308 Solving a triangle: Problem type 1geom309 Solving a triangle: Problem type 2geom044 Pythagorean Theoremgeom068 Computing an area using the Pythagorean Theorem

Polygons and quadrilaterals

geom310 Classifying quadrilateralsgeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom078 Sides of polygons having the same perimetergeom143 Area and perimeter of a rectanglegeom019 Area of a square or a rectanglegeom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom142 Area between two rectangles

Circles

geom016 Circumference of a circlegeom301 Perimeter involving rectangles and circlesgeom138 Circumference ratiosgeom026 Area of a circlegeom126 Area of a sector of a circlegeom036 Area between two concentric circlesgeom302 Area involving rectangles and circles


Volumes and surface areas

geom311 Volume of a cube or a rectangular prismgeom090 Volume of a triangular prismgeom033 Volume of a pyramidgeom035 Volume of a cylindergeom086 Volume of a conegeom092 Rate of filling of a solidgeom133 Ratio of volumesgeom031 Surface area of a cube or a rectangular prismgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom338 Surface area involving prisms or cylinders

Constructions

geom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom154 Constructing the perpendicular bisector of a line segmentgeom150 Constructing a pair of perpendicular linesgeom157 Constructing a pair of parallel lines

Similitudes and transformations

geom037 Similar polygonsgeom038 Similar right trianglesgeom337 Indirect measurementgeom330 Translation of a polygongeom331 Coordinates of translated pointsgeom332 Reflection of a polygon over a vertical or horizontal linegeom333 Coordinates of points reflected over an axisgeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origingeom336 Dilation

B.9 Pre-Algebra


B.9. PRE-ALGEBRA 229

arith630 Addition with carry to the hundreds placearith012 Addition of large numbersarith006 Subtraction with borrowingarith637 Subtraction and regrouping with zerosarith613 Word problem using addition or subtractionarith004 Multiplication with carryarith615 Introduction to multiplication of large numbersarith014 Multiplication of large numbersarith005 Division with carryarith023 Word problem using divisionarith614 Basic word problem using multiplication or divisionarith066 Expanded formarith028 Numeral translation: Problem type 1arith060 Numeral translation: Problem type 2arith077 Ordering large numbersarith078 Rounding: Problem type 1arith061 Rounding: Problem type 2arith101 Estimating a sumarith102 Estimating a differencearith677 Estimating a productarith678 Estimating a quotientarith103 Average of two numbersarith681 Introduction to order of operationsarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith240 Word problem with common multiplesarith647 Divisibility rules for 2, 5, and 10arith648 Divisibility rules for 3 and 9unit005 Customary unit conversion with whole number valuesunit006 Customary unit conversion with whole number values, two-step conversionunit009 Customary area unit conversion with whole number valuesunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesunit012 Time unit conversion with whole number valuesalge286 Plotting integers on a number linearith605 Plotting rational numbers on a number linearith071 Absolute value of a numberarith104 Operations with absolute valuearith200 Integer addition: Problem type 1


arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and division

Rational Numbers

arith623 Introduction to fractionsarith663 Introduction to ratiosarith665 Introduction to equivalent fractionsarith212 Equivalent fractionsarith067 Reduced fractionarith667 Plotting fractions on a number linearith044 Ordering fractions with same denominatorarith091 Ordering fractions with same numeratorarith092 Ordering fractionsarith618 Addition or subtraction of fractions with the same denominatorarith230 Addition or subtraction of fractions with different denominatorsarith100 Fractional part of a circlearith088 The reciprocal of a numberarith079 Product of a unit fraction and a whole numberarith009 Unit fraction multiplicationarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith095 Word problem with fractionsarith022 Fraction divisionarith106 Signed fractions additionarith105 Signed fractions multiplicationarith662 Introduction to mixed numbers and improper fractionsarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith215 Addition or subtraction of mixed numbers with same denominatorarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith085 Addition or subtraction of mixed numbers with different denominatorsarith020 Mixed number multiplication: Problem type 1arith076 Mixed number multiplication: Problem type 2arith068 Mixed number divisionarith220 Decimal place valuearith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimalsarith624 Addition of aligned decimalsarith625 Subtraction of aligned decimals


arith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith234 Signed decimal additionarith082 Multiplication of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith045 Word problem with powers of tenarith628 Word problem with multiple decimal operations: Problem type 1arith083 Division of a decimal by a power of tenarith081 Division of a decimal by a whole numberarith019 Decimal divisionarith629 Word problem with multiple decimal operations: Problem type 2arith087 Converting a decimal to a fractionarith222 Converting a fraction to a terminating decimalarith089 Converting a fraction to a repeating decimalarith223 Converting a mixed number to a decimalunit007 Customary unit conversion with mixed number valuesunit008 Customary unit conversion with mixed number values, two-step conversionunit003 Metric distance conversion with decimal valuesunit004 Metric conversion with decimal values, two-step conversionunit010 Metric area unit conversion with decimal number values

Proportion, Percent, Data and Probability

arith228 Basic word problem on ratesalge218 Word problem on ratesalge272 Solving a proportion: Basicalge271 Solving a proportion: Advancedarith064 Simple word problem on proportionsarith610 Word problem on proportions: Problem type 1arith611 Word problem on proportions: Problem type 2alge220 Word problem on inverse proportionsunit034 Conversion between metric and customary unit systemsunit035 Conversion between compound units, basic problemunit036 Conversion between compound units, advanced problemarith674 Introduction to percentarith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith074 Word problem on percentage: Problem type 1arith031 Word problem on percentage: Problem type 2


arith225 Word problem on percentage: Problem type 3arith232 Simple interestmstat014 Random samples and predictionmstat037 Line plotsmstat004 Histograms for numerical datamstat005 Bar graphs for non-numerical datamstat024 Interpreting bar graphsmstat044 Double bar graphsmstat007 Interpreting line graphsstat804 Interpreting circle graphs or pie chartsmstat003 Mode of a data setmstat028 Mean and median of a data setstat803 Finding the value for a new score that will yield a given meanmstat029 How changing a value affects the mean and medianstat802 Rejecting unreasonable claims based on average statisticsmstat031 Interpreting a stem-and-leaf plotmstat027 Using back-to-back stem-and-leaf plots to compare data setsmstat006 Box-and-whisker plotsmstat023 Scatterplots and correlationmstat030 Sketching the line of best fitmstat043 Venn diagrams with three setsmstat041 Tree diagramsmstat040 Introduction to the counting principlemstat015 Counting Principlemstat008 Permutationsmstat009 Combinationsstat106 Outcomes and event probabilitymstat026 Introduction to probability of an eventmstat010 Probability of an eventmstat012 Probability of independent eventsmstat013 Probability of dependent eventsstat112 Die rolling

Variable Expressions and Equations

arith655 Introduction to properties of additionarith656 Introduction to properties of multiplicationarith657 Introduction to the distributive propertyalge606 Distributive property, simplealge604 Distributive Property, advancedalge607 Combining like terms, basicalge663 Combining like terms, advancedalge001 Integers and rational numbers


alge002 Integers, rational numbers, and irrational numbersalge285 Evaluating a simple algebraic expression: Problem type 3alge005 Evaluation of a linear expression in two variablesalge004 Evaluation of a polynomial in one variablealge602 Writing a mathematical expressionalge009 Additive property of equality: Problem type 1alge800 Additive property of equality with decimalsalge801 Additive property of equality with fractionsalge010 Additive property of equality: Problem type 2alge266 Additive property of equality: Problem type 3alge008 Multiplicative property of equality: Problem type 1alge802 Multiplicative property of equality with fractionsalge012 Multiplicative property of equality: Problem type 2alge006 Solving a linear equation: Problem type 1alge208 Solving a linear equation: Problem type 2alge200 Solving a linear equation: Problem type 3alge011 Solving a linear equation with several occurrences of the variable: Problem type1alge061 Solving a linear equation with several occurrences of the variable: Problem type2alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge209 Solving a linear equation with several occurrences of the variable: Problem type4alge016 Translating sentences into mathematical equationsalge014 Solving a word problem using a linear equation: Problem type 1alge219 Solving a word problem using a linear equation: Problem type 2alge173 Solving a word problem using a linear equation: Problem type 3alge704 Solving a word problem using a linear equation: Problem type 4alge810 Introduction to algebraic symbol manipulationalge160 Algebraic symbol manipulationalge015 Writing an inequalityalge186 Writing a compound inequalityalge019 Solving a linear inequality: Problem type 1alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge207 Solving a linear inequality: Problem type 4alge017 Graphing a linear inequality on the number linealge166 Graphing a compound linear inequality on the number line

Functions and Graphs

alge282 Function tables with two-step rules


fun001 Function tablesfun005 Finding a function rule: Problem type 1fun006 Finding a function rule: Problem type 2alge064 Reading a point in the coordinate planealge067 Plotting a point in the coordinate planefun002 Graphing integer functionsfun010 Vertical line testalge263 Interpreting the graphs of two functionsalge807 Finding the next terms of a simple sequencepcalc085 Arithmetic sequencepcalc086 Geometric sequencealge197 Graphing a line given the x- and y-interceptsalge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge196 Graphing a line through a given point with a given slopealge198 Graphing a vertical or horizontal linealge191 Midpoint of a line segment in the planealge066 Solutions to a linear equation in two variables: Problem type 1alge216 Solutions to a linear equation in two variables: Problem type 2alge210 X- and y-intercepts of a line given the equation in standard formalge637 Determining the slope of a line given its graphalge631 Finding the slope of a line given its equationalge070 Writing an equation of a line given the slope and the y-interceptalge071 Writing the equation of a line given the slope and a point on the linealge072 Writing the equation of the line through two given pointsalge701 Writing equations and drawing graphs to fit a narrativealge018 Graphing a linear inequality in the plane: Problem type 1alge225 Graphing a linear inequality in the plane: Problem type 2alge252 Graphing a parabola: Problem type 1alge262 Graphing a simple cubic functionalge132 Distance between two points in the plane

Exponents and Polynomials

arith233 Introduction to exponentsarith047 Evaluating expressions with exponents: Problem type 1arith049 Evaluating expressions with exponents: Problem type 2arith600 Exponents and order of operationsarith042 Writing a positive number without a negative exponentarith043 Writing a negative number without a negative exponentarith029 Ordering numbers with positive exponentsarith024 Ordering numbers with negative exponentsarith036 Scientific notation with positive exponent


arith037 Scientific notation with negative exponentscinot002 Multiplying and dividing numbers written in scientific notationalge024 Product rule of exponentsalge027 Power rule: Positive exponentsalge025 Power rule: Negative exponentsarith016 Square root of a perfect squarearith601 Square root of a rational perfect squarearith602 Estimating a square rootarith093 Square root simplificationalge264 Square root of a perfect square monomialalge080 Simplifying a radical expression: Problem type 1arith094 Cube root of an integeralge029 Simplifying a polynomial expressionalge030 Multiplying monomialsalge033 Multiplying two binomialsalge032 Squaring a binomialalge180 Multiplying polynomialsalge037 Greatest common factor of two monomialsalge055 Least common multiple of two monomialsalge031 Degree of a multivariate polynomial

Geometry

geom349 Naming segments, rays, and linesgeom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom305 Supplementary and vertical anglesgeom530 Solving equations involving vertical anglesgeom531 Solving equations involving angles and parallel linesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom154 Constructing the perpendicular bisector of a line segmentgeom150 Constructing a pair of perpendicular linesgeom157 Constructing a pair of parallel linesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom801 Area of a trianglegeom001 Sum of the angle measures of a trianglegeom908 Solving a triangle: Problem type 1geom044 Pythagorean Theorem


pcalc600 Sine, cosine, and tangent ratiospcalc601 Using a trigonometric ratio to find a side length in a right trianglepcalc602 Using a trigonometric ratio to find an angle measure in a right trianglegeom310 Classifying quadrilateralsgeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom078 Sides of polygons having the same perimetergeom217 Finding the side length of a rectangle given its perimeter or areageom350 Distinguishing between area and perimetergeom351 Areas of rectangles with the same perimetergeom353 Perimeter of a piecewise rectangular figuregeom019 Area of a square or a rectanglegeom340 Area of a piecewise rectangular figuregeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom142 Area between two rectanglesgeom344 Area involving rectangles and trianglesgeom143 Area and perimeter of a rectanglegeom347 Introduction to circle: diameter, radius, and chordgeom016 Circumference of a circlegeom802 Circumference and area of a circlegeom218 Finding the radius or the diameter of a circle given its circumferencegeom838 Circumference ratiosgeom301 Perimeter involving rectangles and circlesgeom036 Area between two concentric circlesgeom302 Area involving rectangles and circlesgeom214 Area involving inscribed figuresgeom311 Volume of a cube or a rectangular prismgeom505 Volume of a piecewise rectangular prismgeom090 Volume of a triangular prismgeom033 Volume of a pyramidgeom035 Volume of a cylindergeom092 Rate of filling of a solidgeom086 Volume of a conegeom841 Volume of a spheregeom348 Vertices, edges, and faces of a solidgeom219 Nets of solidsgeom345 Surface area of a solid made of unit cubesgeom031 Surface area of a cube or a rectangular prismgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom338 Surface area involving prisms or cylindersgeom842 Surface area of a spheregeom037 Similar polygons

B.10. ALGEBRA 1 237

geom038 Similar right trianglesgeom337 Indirect measurementgeom330 Translation of a polygongeom331 Coordinates of translated pointsgeom332 Reflection of a polygon over a vertical or horizontal linegeom333 Coordinates of points reflected over an axisgeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origingeom336 Dilation

B.10 Algebra 1

Arithmetic readiness

arith101 Estimating a sumarith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith056 Factorsarith034 Prime numbersarith035 Prime number factorizationarith033 Greatest common factorarith070 Least common multiplearith064 Simple word problem on proportionsunit005 Customary unit conversion with whole number valuesunit001 Metric distance conversion with whole number valuesunit002 Metric mass or capacity conversion with whole number valuesarith212 Equivalent fractionsarith067 Reduced fractionarith092 Ordering fractionsarith618 Addition or subtraction of fractions with the same denominatorarith230 Addition or subtraction of fractions with different denominatorsarith088 The reciprocal of a numberarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith022 Fraction divisionarith015 Writing an improper fraction as a mixed numberarith619 Writing a mixed number as an improper fractionarith084 Addition of mixed numbers with same denominator and carryarith216 Subtraction of mixed numbers with same denominator and borrowingarith020 Mixed number multiplication: Problem type 1arith068 Mixed number divisionarith220 Decimal place value


arith221 Rounding decimalsarith608 Ordering decimalsarith609 Ordering fractions and decimalsarith087 Converting a decimal to a fractionarith222 Converting a fraction to a terminating decimalarith082 Multiplication of a decimal by a power of tenarith083 Division of a decimal by a power of tenarith017 Multiplication of a decimal by a whole numberarith081 Division of a decimal by a whole numberarith055 Decimal multiplication: Problem type 1arith626 Word problem with one decimal operation: Problem type 1arith627 Word problem with one decimal operation: Problem type 2arith628 Word problem with multiple decimal operations: Problem type 1arith629 Word problem with multiple decimal operations: Problem type 2arith226 Converting between percentages and decimalsarith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagearith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith074 Word problem on percentage: Problem type 1arith031 Word problem on percentage: Problem type 2arith225 Word problem on percentage: Problem type 3arith232 Simple interest

Real numbers and linear equations

arith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and divisionarith605 Plotting rational numbers on a number linearith106 Signed fractions additionarith105 Signed fractions multiplicationarith234 Signed decimal additionalge001 Integers and rational numbersalge002 Integers, rational numbers, and irrational numbersalge005 Evaluation of a linear expression in two variablesalge004 Evaluation of a polynomial in one variablealge606 Distributive property, simplealge604 Distributive Property, advancedalge607 Combining like terms, basicalge187 Properties of additionalge188 Properties of real numbers

B.10. ALGEBRA 1 239

pcalc709 Addition of matrices and multiplication of a matrix by a scalaralge009 Additive property of equality: Problem type 1alge010 Additive property of equality: Problem type 2alge266 Additive property of equality: Problem type 3alge800 Additive property of equality with decimalsalge008 Multiplicative property of equality: Problem type 1alge012 Multiplicative property of equality: Problem type 2alge802 Multiplicative property of equality with fractionsalge006 Solving a linear equation: Problem type 1alge208 Solving a linear equation: Problem type 2alge200 Solving a linear equation: Problem type 3alge011 Solving a linear equation with several occurrences of the variable: Problem type1alge061 Solving a linear equation with several occurrences of the variable: Problem type2alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge209 Solving a linear equation with several occurrences of the variable: Problem type4alge179 Solving a linear equation with several occurrences of the variable: Problem type5alge015 Writing an inequalityalge186 Writing a compound inequalityalge019 Solving a linear inequality: Problem type 1alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge207 Solving a linear inequality: Problem type 4alge017 Graphing a linear inequality on the number linealge166 Graphing a compound linear inequality on the number linealge602 Writing a mathematical expressionalge016 Translating sentences into mathematical equationsalge014 Solving a word problem using a linear equation: Problem type 1alge219 Solving a word problem using a linear equation: Problem type 2alge173 Solving a word problem using a linear equation: Problem type 3alge704 Solving a word problem using a linear equation: Problem type 4alge022 Word problem with linear inequalitiesarith071 Absolute value of a numberarith104 Operations with absolute valuealge270 Simple absolute value equationalge103 Solving an equation involving absolute value: Basicalge170 Solving an inequality involving absolute value: Basicalge169 Solving an inequality involving absolute value


Functions and systems of equations

fun001 Function tablesfun002 Graphing integer functionsfun005 Finding a function rule: Problem type 1fun006 Finding a function rule: Problem type 2fun016 Domain and range: Problem type 1alge213 Domain of a square root functionfun010 Vertical line testalge185 Vertical translation of the graph of a functionfun020 Vertical and horizontal translations of the graph of a functionalge807 Finding the next terms of a simple sequencepcalc085 Arithmetic sequencepcalc086 Geometric sequencepcalc713 Arithmetic and geometric sequences: Identifying and writing in standard formalge064 Reading a point in the coordinate planealge067 Plotting a point in the coordinate planealge197 Graphing a line given the x- and y-interceptsalge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge196 Graphing a line through a given point with a given slopealge198 Graphing a vertical or horizontal linealge018 Graphing a linear inequality in the plane: Problem type 1alge225 Graphing a linear inequality in the plane: Problem type 2alge701 Writing equations and drawing graphs to fit a narrativealge168 Graphing an equation involving absolute value in the planealge066 Solutions to a linear equation in two variables: Problem type 1alge216 Solutions to a linear equation in two variables: Problem type 2alge069 Y-intercept of a linealge210 X- and y-intercepts of a line given the equation in standard formalge631 Finding the slope of a line given its equationalge637 Determining the slope of a line given its graphalge070 Writing an equation of a line given the slope and the y-interceptalge071 Writing the equation of a line given the slope and a point on the linealge072 Writing the equation of the line through two given pointsalge073 Writing the equations of vertical and horizontal lines through a given pointgeom807 Slopes of parallel and perpendicular lines: Problem type 1geom808 Slopes of parallel and perpendicular lines: Problem type 2alge810 Introduction to algebraic symbol manipulationalge160 Algebraic symbol manipulationalge805 Application problem with a linear function: Problem type 1alge806 Application problem with a linear function: Problem type 2alge076 Solving a system of linear equationsalge075 Classifying a system of linear equations

B.10. ALGEBRA 1 241

alge078 Solving a word problem using a system of linear equations: Problem type 1alge184 Solving a word problem using a system of linear equations: Problem type 2alge224 Solving a word problem using a system of linear equations: Problem type 3alge192 Solving a word problem using a system of linear equations: Problem type 4alge172 Solving a word problem using a system of linear equations: Problem type 5alge079 Graphing a system of linear inequalitiespcalc093 Solving a word problem using a system of linear inequalities

Polynomials and quadratic equations

alge663 Combining like terms, advancedalge029 Simplifying a polynomial expressionalge030 Multiplying monomialsalge033 Multiplying two binomialsalge032 Squaring a binomialalge180 Multiplying polynomialsalge031 Degree of a multivariate polynomialalge708 Polynomial long division: Linear divisoralge039 Factoring a quadratic with leading coefficient 1alge040 Factoring a quadratic with leading coefficient greater than 1alge043 Factoring a perfect squarealge265 Factoring a quadratic polynomial in two variablesalge041 Factoring a product of a quadratic trinomial and a monomialalge624 Factoring a difference of squaresalge042 Factoring with repeated use of the difference of squares formulaalge037 Greatest common factor of two monomialsalge038 Factoring a multivariate polynomial by grouping: Problem type 1alge181 Factoring a multivariate polynomial by grouping: Problem type 2alge681 Solving equations written in factored formalge045 Finding the roots of a quadratic equation with leading coefficient 1alge048 Finding the roots of a quadratic equation with leading coefficient greater than1alge211 Solving a quadratic equation needing simplificationalge703 Solving a word problem using a quadratic equation with rational rootsalge094 Completing the squarealge095 Solving a quadratic equation using the quadratic formulaalge214 Discriminant of a quadratic equationalge524 Solving a word problem using a quadratic equation with irrational rootsFinding the x-intercept(s) and the vertex of a parabola (alge277) Browse: Question,Explanationalge252 Graphing a parabola: Problem type 1alge253 Graphing a parabola: Problem type 2alge254 Graphing a parabola: Problem type 3


alge255 Graphing a quadratic inequality

Rational expressions and proportions

alge053 Multiplying rational expressions: Problem type 1alge620 Multiplying rational expressions: Problem type 2alge054 Dividing rational expressionsalge058 Complex fraction: Problem type 1alge056 Adding rational expressions with common denominatoralge057 Adding rational expressionsalge055 Least common multiple of two monomialsalge226 Adding rational expressions with different denominatorsalge622 Adding and subtracting rational expressions: Problem type 1alge661 Adding and subtracting rational expressions: Problem type 2alge710 Simplifying a ratio of polynomials: Problem type 1alge682 Simplifying a ratio of polynomials: Problem type 2alge034 Ratio of multivariate polynomialsalge272 Solving a proportion: Basicalge271 Solving a proportion: Advancedalge049 Restriction on variable in a denominatoralge060 Solving a rational equation that simplifies to a linear equation: Problem type 1alge205 Solving a rational equation that simplifies to a linear equation: Problem type 2alge206 Solving a rational equation that simplifies to a linear equation: Problem type 3alge212 Solving a rational equation that simplifies to a quadratic equation: Problemtype 1alge062 Solving a rational equation that simplifies to a quadratic equation: Problemtype 2alge047 Solving a rational equation that simplifies to a quadratic equation: Problemtype 3arith228 Basic word problem on ratesalge218 Word problem on ratesarith610 Word problem on proportions: Problem type 1arith611 Word problem on proportions: Problem type 2arith612 Word problem involving multiple ratesalge220 Word problem on inverse proportionsalge175 Word problem on direct variationalge176 Word problem on inverse variationunit034 Conversion between metric and customary unit systemsunit035 Conversion between compound units, basic problemunit036 Conversion between compound units, advanced problempcalc108 Sketching the graph of a rational function: Problem type 1

Exponents and square roots

B.10. ALGEBRA 1 243

arith233 Introduction to exponentsarith047 Evaluating expressions with exponents: Problem type 1arith049 Evaluating expressions with exponents: Problem type 2arith600 Exponents and order of operationsalge024 Product rule of exponentsalge027 Power rule: Positive exponentsarith042 Writing a positive number without a negative exponentarith043 Writing a negative number without a negative exponentalge025 Power rule: Negative exponentsalge028 Product rule of exponents in a multivariate monomialarith029 Ordering numbers with positive exponentsarith024 Ordering numbers with negative exponentsarith036 Scientific notation with positive exponentarith037 Scientific notation with negative exponentscinot002 Multiplying and dividing numbers written in scientific notationalge177 Solving a word problem using an exponential equation: Problem type 1arith016 Square root of a perfect squarearith601 Square root of a rational perfect squarearith602 Estimating a square rootarith093 Square root simplificationalge264 Square root of a perfect square monomialalge080 Simplifying a radical expression: Problem type 1alge275 Simplifying a radical expression: Problem type 2arith032 Square root additionarith039 Square root multiplicationalge276 Simplifying a product of radical expressions using the distributive propertyalge086 Rationalizing the denominator of a radical expressionalge088 Rationalizing the denominator of a radical expression using conjugatesalge089 Solving an equation with radicals: Problem type 1alge090 Solving an equation with radicals: Problem type 2alge091 Solving an equation with radicals: Problem type 3

Geometry and trigonometry

alge191 Midpoint of a line segment in the planealge132 Distance between two points in the planegeom500 Vertical angles and linear pairsgeom001 Sum of the angle measures of a trianglegeom044 Pythagorean Theorempcalc600 Sine, cosine, and tangent ratiospcalc601 Using a trigonometric ratio to find a side length in a right trianglepcalc602 Using a trigonometric ratio to find an angle measure in a right trianglegeom300 Perimeter of a square or a rectangle


geom339 Perimeter of a polygongeom019 Area of a square or a rectanglegeom801 Area of a trianglegeom217 Finding the side length of a rectangle given its perimeter or areageom143 Area and perimeter of a rectanglegeom340 Area of a piecewise rectangular figuregeom142 Area between two rectanglesgeom802 Circumference and area of a circlegeom036 Area between two concentric circlesgeom311 Volume of a cube or a rectangular prismgeom035 Volume of a cylindergeom092 Rate of filling of a solidgeom031 Surface area of a cube or a rectangular prismgeom034 Surface area of a cylindergeom037 Similar polygonsgeom337 Indirect measurement

Data analysis and probability

mstat004 Histograms for numerical datamstat024 Interpreting bar graphsmstat007 Interpreting line graphsalge263 Interpreting the graphs of two functionsstat801 Computations from circle graphsstat804 Interpreting circle graphs or pie chartsmstat023 Scatterplots and correlationmstat030 Sketching the line of best fitmstat031 Interpreting a stem-and-leaf plotmstat027 Using back-to-back stem-and-leaf plots to compare data setsmstat006 Box-and-whisker plotsmstat003 Mode of a data setmstat028 Mean and median of a data setmstat029 How changing a value affects the mean and medianstat803 Finding the value for a new score that will yield a given meanmstat014 Random samples and predictionmstat025 Finding if a question can be answered by the datastat802 Rejecting unreasonable claims based on average statisticsstat805 Making reasonable inferences based on proportion statisticsmstat015 Counting Principlemstat008 Permutationsmstat009 Combinationsstat790 Permutations, combinations, and the multiplication principle for countingmstat026 Introduction to probability of an event

B.11. HIGH SCHOOL GEOMETRY 245

mstat010 Probability of an eventstat106 Outcomes and event probabilitystat112 Die rollingmstat011 Area as probabilitymstat012 Probability of independent eventsmstat013 Probability of dependent eventsmstat032 Probability of the union of two events

B.11 High School Geometry

Arithmetic and algebra readiness

arith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith056 Factorsarith070 Least common multiplearith212 Equivalent fractionsarith067 Reduced fractionarith230 Addition or subtraction of fractions with different denominatorsarith086 Product of a fraction and a whole numberarith053 Fraction multiplicationarith022 Fraction divisionarith015 Writing an improper fraction as a mixed numberarith220 Decimal place valuearith221 Rounding decimalsarith030 Percentage of a whole numberarith071 Absolute value of a numberarith200 Integer addition: Problem type 1arith108 Integer addition: Problem type 2arith107 Integer subtractionarith231 Integer multiplication and divisionalge005 Evaluation of a linear expression in two variablesalge004 Evaluation of a polynomial in one variablealge016 Translating sentences into mathematical equationsalge606 Distributive property, simplealge607 Combining like terms, basicalge007 Additive property of equality: Problem type 3alge012 Multiplicative property of equality: Problem type 2alge006 Solving a linear equation: Problem type 1alge208 Solving a linear equation: Problem type 2alge011 Solving a linear equation with several occurrences of the variable: Problem type1


alge019 Solving a linear inequality: Problem type 1alge017 Graphing a linear inequality on the number linealge166 Graphing a compound linear inequality on the number linealge060 Solving a rational equation that simplifies to a linear equation: Problem type 1alge205 Solving a rational equation that simplifies to a linear equation: Problem type 2arith047 Evaluating expressions with exponents: Problem type 1arith016 Square root of a perfect squarearith093 Square root simplificationalge086 Rationalizing the denominator of a radical expression

Plane geometry

glogic001 Conditional statements and negationsglogic005 The converse, inverse, and contrapositive of a conditional statementglogic008 Conditional statements and deductive reasoninggeom151 Measuring an angle with the protractorgeom152 Drawing an angle with the protractorgeom303 Acute, obtuse, and right anglesgeom039 Supplementary and complementary anglesgeom304 Corresponding and alternate anglesgeom800 Identifying linear pairs and vertical anglesgeom500 Vertical angles and linear pairsgeom503 Angles and parallel linesgeom159 Constructing congruent anglesgeom158 Constructing an angle bisectorgeom516 Angle addition and angle bisectorsgeom154 Constructing the perpendicular bisector of a line segmentgeom150 Constructing a pair of perpendicular linesgeom157 Constructing a pair of parallel linesgeom616 Introduction to proofs: Justifying statementsgeom614 Proofs involving segment congruencegeom611 Congruent anglesgeom610 Angles and parallel linesgeom306 Acute, obtuse, and right trianglesgeom307 Scalene, isosceles, and equilateral trianglesgeom001 Sum of the angle measures of a trianglegeom809 Relationship between angle measures and side lengths of a trianglegeom504 Triangle inequalitygeom507 Right triangles and geometric meangeom520 Identifying and naming congruent trianglesgeom502 Solving triangles: Basicgeom908 Solving a triangle: Problem type 1geom309 Solving a triangle: Problem type 2

B.11. HIGH SCHOOL GEOMETRY 247

geom044 Pythagorean Theoremgeom068 Computing an area using the Pythagorean Theoremgeom617 Congruent triangles: Problem type 1geom612 Congruent triangles: Problem type 2geom613 Congruent triangles: Problem type 3proof by contradiction Indirect proofgeom310 Classifying quadrilateralsgeom523 Classifying quadrilaterals: Advanced problemgeom524 Hierarchy of quadrilateral figuresgeom528 Properties of parallelograms: Problem type 1geom527 Properties of parallelograms: Problem type 2geom522 Interior angles of convex polygonsgeom343 Identifying central angles, inscribed angles, arcs, chords, and tangents of acirclegeom514 Inscribed angles of a circlegeom515 Tangents of a circlegeom512 Central angles and inscribed angles of a circlegeom511 Lengths of chords, secants, and tangentsgeom513 Angles of intersecting secants and tangentsgeom037 Similar polygonsgeom510 Triangles and parallel linesgeom038 Similar right trianglesgeom337 Indirect measurementgeom508 Length, area, and volume ratios of similar figures

Lengths, areas, and volumes

geom525 Computing distances on the number linegeom526 Midpoint of a number line segmentgeom521 Segment addition and midpointsgeom300 Perimeter of a square or a rectanglegeom339 Perimeter of a polygongeom078 Sides of polygons having the same perimetergeom019 Area of a square or a rectanglegeom143 Area and perimeter of a rectanglegeom340 Area of a piecewise rectangular figuregeom801 Area of a trianglegeom022 Area of a parallelogramgeom023 Area of a trapezoidgeom142 Area between two rectanglesgeom213 Area of a regular polygongeom802 Circumference and area of a circlegeom301 Perimeter involving rectangles and circles


geom838 Circumference ratiosgeom805 Arc length and area of a sector of a circlegeom036 Area between two concentric circlesgeom302 Area involving rectangles and circlesgeom211 Area involving rectangles and circles: Advanced problemmstat011 Area as probabilitygeom311 Volume of a cube or a rectangular prismgeom505 Volume of a piecewise rectangular prismgeom090 Volume of a triangular prismgeom033 Volume of a pyramidgeom035 Volume of a cylindergeom086 Volume of a conegeom092 Rate of filling of a solidgeom133 Ratio of volumesgeom841 Volume of a spheregeom031 Surface area of a cube or a rectangular prismgeom091 Surface area of a triangular prismgeom034 Surface area of a cylindergeom338 Surface area involving prisms or cylindersgeom842 Surface area of a sphere

Analytic geometry

alge067 Plotting a point in the coordinate planealge191 Midpoint of a line segment in the planealge132 Distance between two points in the planealge197 Graphing a line given the x- and y-interceptsalge194 Graphing a line given its equation in slope-intercept formalge210 X- and y-intercepts of a line given the equation in standard formalge195 Graphing a line given its equation in standard formalge196 Graphing a line through a given point with a given slopealge637 Determining the slope of a line given its graphalge631 Finding the slope of a line given its equationgeom807 Slopes of parallel and perpendicular lines: Problem type 1geom808 Slopes of parallel and perpendicular lines: Problem type 2alge070 Writing an equation of a line given the slope and the y-interceptalge071 Writing the equation of a line given the slope and a point on the linealge072 Writing the equation of the line through two given pointspcalc605 Graphing a circle given its equation in standard formpcalc065 Writing an equation of a circle given its center and a point on the circlepcalc066 Writing an equation of a circle given the endpoints of a diameter

Transformations, trigonometry, and vectors

B.12. ALGEBRA 2 249

geom330 Translation of a polygongeom331 Coordinates of translated pointsgeom332 Reflection of a polygon over a vertical or horizontal linegeom333 Coordinates of points reflected over an axisgeom334 Drawing lines of symmetrygeom335 Rotation of a figure about the origingeom336 Dilationgeom506 Special right trianglespcalc600 Sine, cosine, and tangent ratiospcalc601 Using a trigonometric ratio to find a side length in a right trianglepcalc602 Using a trigonometric ratio to find an angle measure in a right trianglegeom212 Circles inscribed in and circumscribed around regular polygonspcalc739 Multiplication of a vector by a scalarpcalc725 Linear combination of vectors: Algebraic approachpcalc726 Linear combination of vectors: Geometric approachpcalc060 Magnitude of a vectorvector002 Calculating the magnitude and direction of a vectorvector005 Finding the components of a vectorpcalc063 Translation of a vector

B.12 Algebra 2

Real numbers and linear equations

arith605 Plotting rational numbers on a number linearith071 Absolute value of a numberarith104 Operations with absolute valuearith106 Signed fractions additionarith105 Signed fractions multiplicationarith234 Signed decimal additionarith047 Evaluating expressions with exponents: Problem type 1arith049 Evaluating expressions with exponents: Problem type 2alge005 Evaluation of a linear expression in two variablesalge004 Evaluation of a polynomial in one variablearith600 Exponents and order of operationsarith016 Square root of a perfect squarealge001 Integers and rational numbersalge002 Integers, rational numbers, and irrational numbersalge602 Writing a mathematical expressionalge016 Translating sentences into mathematical equationsalge015 Writing an inequalityalge186 Writing a compound inequality


alge606 Distributive property, simplealge604 Distributive Property, advancedalge607 Combining like terms, basicalge663 Combining like terms, advancedalge187 Properties of additionalge188 Properties of real numbersalge010 Additive property of equality: Problem type 2alge266 Additive property of equality: Problem type 3alge802 Multiplicative property of equality with fractionsalge008 Multiplicative property of equality: Problem type 1alge012 Multiplicative property of equality: Problem type 2alge006 Solving a linear equation: Problem type 1alge208 Solving a linear equation: Problem type 2alge200 Solving a linear equation: Problem type 3alge011 Solving a linear equation with several occurrences of the variable: Problem type1alge061 Solving a linear equation with several occurrences of the variable: Problem type2alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge209 Solving a linear equation with several occurrences of the variable: Problem type4alge179 Solving a linear equation with several occurrences of the variable: Problem type5alge810 Introduction to algebraic symbol manipulationalge160 Algebraic symbol manipulationalge019 Solving a linear inequality: Problem type 1alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge207 Solving a linear inequality: Problem type 4alge017 Graphing a linear inequality on the number linealge166 Graphing a compound linear inequality on the number linealge014 Solving a word problem using a linear equation: Problem type 1alge219 Solving a word problem using a linear equation: Problem type 2alge173 Solving a word problem using a linear equation: Problem type 3alge704 Solving a word problem using a linear equation: Problem type 4alge022 Word problem with linear inequalitiesmstat014 Random samples and predictionarith232 Simple intereststat801 Computations from circle graphsarith074 Word problem on percentage: Problem type 1arith031 Word problem on percentage: Problem type 2arith225 Word problem on percentage: Problem type 3stat803 Finding the value for a new score that will yield a given mean

B.12. ALGEBRA 2 251

geom300 Perimeter of a square or a rectanglegeom078 Sides of polygons having the same perimetergeom019 Area of a square or a rectanglegeom217 Finding the side length of a rectangle given its perimeter or areageom143 Area and perimeter of a rectanglegeom311 Volume of a cube or a rectangular prismgeom802 Circumference and area of a circlegeom036 Area between two concentric circlesgeom031 Surface area of a cube or a rectangular prismgeom034 Surface area of a cylindergeom035 Volume of a cylindergeom092 Rate of filling of a solidgeom500 Vertical angles and linear pairsgeom502 Solving triangles: Basicalge270 Simple absolute value equationalge103 Solving an equation involving absolute value: Basicalge167 Solving an equation involving absolute value: Advancedalge169 Solving an inequality involving absolute valuealge170 Solving an inequality involving absolute value: Basic

Graphs and linear functions

alge064 Reading a point in the coordinate planealge067 Plotting a point in the coordinate planealge066 Solutions to a linear equation in two variables: Problem type 1alge216 Solutions to a linear equation in two variables: Problem type 2alge197 Graphing a line given the x- and y-interceptsalge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge196 Graphing a line through a given point with a given slopealge637 Determining the slope of a line given its graphalge198 Graphing a vertical or horizontal linealge210 X- and y-intercepts of a line given the equation in standard formalge631 Finding the slope of a line given its equationalge070 Writing an equation of a line given the slope and the y-interceptalge071 Writing the equation of a line given the slope and a point on the linealge072 Writing the equation of the line through two given pointsalge073 Writing the equations of vertical and horizontal lines through a given pointalge701 Writing equations and drawing graphs to fit a narrativealge805 Application problem with a linear function: Problem type 1alge806 Application problem with a linear function: Problem type 2geom807 Slopes of parallel and perpendicular lines: Problem type 1geom808 Slopes of parallel and perpendicular lines: Problem type 2


alge018 Graphing a linear inequality in the plane: Problem type 1alge225 Graphing a linear inequality in the plane: Problem type 2set001 Set builder notationset002 Union and intersection of finite setsset004 Set builder and interval notationset005 Union and intersection of intervalsfun001 Function tablesfun002 Graphing integer functionsfun016 Domain and range: Problem type 1fun004 Domain and range: Problem type 2fun010 Vertical line test

Systems of linear equations

alge075 Classifying a system of linear equationsalge076 Solving a system of linear equationsalge077 Creating an inconsistent system of linear equationsalge263 Interpreting the graphs of two functionsalge079 Graphing a system of linear inequalitiespcalc095 Linear programmingpcalc094 Solving a word problem using linear programmingalge078 Solving a word problem using a system of linear equations: Problem type 1alge184 Solving a word problem using a system of linear equations: Problem type 2alge224 Solving a word problem using a system of linear equations: Problem type 3alge192 Solving a word problem using a system of linear equations: Problem type 4alge172 Solving a word problem using a system of linear equations: Problem type 5pcalc093 Solving a word problem using a system of linear inequalitiespcalc709 Addition of matrices and multiplication of a matrix by a scalarpcalc042 Finding the determinant of a 2x2 matrixpcalc043 Finding the determinant of a 3x3 matrixpcalc045 Cramer’s rule: Problem type 1pcalc047 Cramer’s rule: Problem type 2pcalc712 Gauss-Jordan elimination with a 2x2 matrixpcalc046 Augmented matrix and solution set of a system of linear equations

Exponents and polynomials

alge024 Product rule of exponentsalge030 Multiplying monomialsalge027 Power rule: Positive exponentsarith042 Writing a positive number without a negative exponentarith043 Writing a negative number without a negative exponent

B.12. ALGEBRA 2 253

alge025 Power rule: Negative exponentsalge028 Product rule of exponents in a multivariate monomialarith029 Ordering numbers with positive exponentsarith024 Ordering numbers with negative exponentsarith036 Scientific notation with positive exponentarith037 Scientific notation with negative exponentscinot002 Multiplying and dividing numbers written in scientific notationalge031 Degree of a multivariate polynomialalge029 Simplifying a polynomial expressionalge033 Multiplying two binomialsalge032 Squaring a binomialalge180 Multiplying polynomialsalge708 Polynomial long division: Linear divisoralge709 Polynomial long division: Quadratic divisorpcalc117 Synthetic divisionalge039 Factoring a quadratic with leading coefficient 1alge040 Factoring a quadratic with leading coefficient greater than 1alge265 Factoring a quadratic polynomial in two variablesalge043 Factoring a perfect squarealge041 Factoring a product of a quadratic trinomial and a monomialalge045 Finding the roots of a quadratic equation with leading coefficient 1alge048 Finding the roots of a quadratic equation with leading coefficient greater than1alge211 Solving a quadratic equation needing simplificationalge681 Solving equations written in factored formalge046 Roots of a product of polynomialsalge703 Solving a word problem using a quadratic equation with rational rootsalge163 Writing a quadratic equation given the roots and the leading coefficientalge624 Factoring a difference of squaresalge042 Factoring with repeated use of the difference of squares formulaalge044 Factoring a sum or difference of two cubesalge037 Greatest common factor of two monomialsalge055 Least common multiple of two monomialsalge038 Factoring a multivariate polynomial by grouping: Problem type 1alge181 Factoring a multivariate polynomial by grouping: Problem type 2

Rational expressions and functions

alge053 Multiplying rational expressions: Problem type 1alge620 Multiplying rational expressions: Problem type 2alge054 Dividing rational expressionsalge058 Complex fraction: Problem type 1alge162 Complex Fraction: Problem type 2


alge056 Adding rational expressions with common denominatoralge057 Adding rational expressionsalge226 Adding rational expressions with different denominatorsalge622 Adding and subtracting rational expressions: Problem type 1alge661 Adding and subtracting rational expressions: Problem type 2alge034 Ratio of multivariate polynomialsalge710 Simplifying a ratio of polynomials: Problem type 1alge682 Simplifying a ratio of polynomials: Problem type 2alge049 Restriction on variable in a denominatoralge060 Solving a rational equation that simplifies to a linear equation: Problem type 1alge205 Solving a rational equation that simplifies to a linear equation: Problem type 2alge206 Solving a rational equation that simplifies to a linear equation: Problem type 3alge212 Solving a rational equation that simplifies to a quadratic equation: Problemtype 1alge062 Solving a rational equation that simplifies to a quadratic equation: Problemtype 2alge047 Solving a rational equation that simplifies to a quadratic equation: Problemtype 3pcalc108 Sketching the graph of a rational function: Problem type 1alge218 Word problem on ratesarith228 Basic word problem on ratesalge271 Solving a proportion: Advancedarith610 Word problem on proportions: Problem type 1arith611 Word problem on proportions: Problem type 2arith612 Word problem involving multiple ratesalge059 Ordering fractions with variablesalge220 Word problem on inverse proportionsgeom037 Similar polygonsalge175 Word problem on direct variationalge176 Word problem on inverse variationgeom133 Ratio of volumesgeom138 Circumference ratios

Radicals and quadratic equations

arith601 Square root of a rational perfect squarearith093 Square root simplificationalge264 Square root of a perfect square monomialalge080 Simplifying a radical expression: Problem type 1alge275 Simplifying a radical expression: Problem type 2arith032 Square root additionalge084 Simplifying a sum of radical expressionsarith039 Square root multiplication

B.12. ALGEBRA 2 255

alge640 Simplifying a product of radical expressionsalge082 Simplifying a product of radical expressions: Problem type 3alge276 Simplifying a product of radical expressions using the distributive propertyalge086 Rationalizing the denominator of a radical expressionalge088 Rationalizing the denominator of a radical expression using conjugatesgeom044 Pythagorean Theoremalge089 Solving an equation with radicals: Problem type 1alge090 Solving an equation with radicals: Problem type 2alge091 Solving an equation with radicals: Problem type 3alge182 Solving an equation with radicals: Problem type 4arith094 Cube root of an integeralge273 Simplifying a higher radical: Problem type 1alge811 Simplifying a higher radical: Problem type 2alge092 Even root propertyalge093 Odd root propertyalge227 Solving an equation with exponent using the even-root propertyalge228 Solving an equation with exponent using the odd-root propertyalge250 Rational exponents: Basicalge251 Rational exponents: Negative exponents and fractional basesalge249 Rational exponents: Powers of powersalge812 Converting between radical form and exponent formalge230 Solving an equation with positive rational exponentalge231 Solving an equation with negative rational exponentpcalc048 Adding and subtracting complex numberspcalc049 Multiplying complex numberspcalc050 Dividing complex numberspcalc053 Simplifying a power of ialge094 Completing the squarealge095 Solving a quadratic equation using the quadratic formulapcalc051 Solving a quadratic equation with imaginary rootsalge214 Discriminant of a quadratic equationalge193 Discriminant of a quadratic equation with parameteralge524 Solving a word problem using a quadratic equation with irrational rootsalge771 Solving a quadratic inequalityalge252 Graphing a parabola: Problem type 1alge253 Graphing a parabola: Problem type 2alge254 Graphing a parabola: Problem type 3Finding the x-intercept(s) and the vertex of a parabola (alge277) Browse: Question,Explanationalge255 Graphing a quadratic inequality

Functions and logarithms


fun019 Sum, difference, and product of two functionsalge213 Domain of a square root functionalge185 Vertical translation of the graph of a functionfun020 Vertical and horizontal translations of the graph of a functionfun011 Horizontal line testfun012 Inverse functions: Basicalge130 Inverse functions: Advancedfun021 Composition of two functions: Domain and rangefun022 Composition of two functions: Basicalge129 Composition of two functions: Advancedfun023 Piecewise-defined functionsalge108 Exponential and logarithmic equationsalge232 Evaluating a logarithmic expressionpcalc708 Basic properties of logarithmsalge107 Change of base for logarithmsalge233 Solving a logarithmic equation: Problem type 1alge113 Solving a logarithmic equation: Problem type 2alge111 Solving an exponential equation: Problem type 1alge112 Solving an exponential equation: Problem type 2alge177 Solving a word problem using an exponential equation: Problem type 1alge178 Solving a word problem using an exponential equation: Problem type 2pcalc737 Solving a word problem using an exponential equation: Problem type 3alge262 Graphing a simple cubic functionalge168 Graphing an equation involving absolute value in the planealge712 Sketching the graph of an exponential function: Basicpcalc103 Sketching the graph of an exponential function: Advancedpcalc104 Sketching the graph of a logarithmic functionpcalc102 Translating the graph of a logarithmic or exponential function

Conic sections and sequences

alge191 Midpoint of a line segment in the planealge132 Distance between two points in the planepcalc067 Graphing a parabola with a horizontal or a vertical axispcalc068 Writing an equation of a parabola given the vertex and the focuspcalc069 Finding the focus of a parabolapcalc605 Graphing a circle given its equation in standard formpcalc064 Graphing a circle given its equation in general formpcalc065 Writing an equation of a circle given its center and a point on the circlepcalc066 Writing an equation of a circle given the endpoints of a diameterpcalc070 Graph of an ellipse centered at the originpcalc734 Graphing an ellipse given its equation in standard formpcalc071 Graphing an ellipse given its equation in general form

B.13. TRIGONOMETRY 257

pcalc075 Graph of a hyperbola centered at the originpcalc735 Graphing a hyperbola given its equation in standard formpcalc076 Graphing a hyperbola given its equation in general formpcalc098 Solving a system of nonlinear equationspcalc096 Graphing a system of nonlinear inequalities: Problem type 1pcalc097 Graphing a system of nonlinear inequalities: Problem type 2pcalc736 Classifying conics given their equationspcalc080 Finding the first terms of a sequencepcalc715 Arithmetic sequencespcalc717 Geometric sequencespcalc718 Sum of the first n terms of an arithmetic sequencepcalc719 Sum of the first n terms of a geometric sequencepcalc720 Sum of a geometric seriespcalc082 Factorial expressionspcalc087 Binomial formula

B.13 Trigonometry

Algebra review

alge061 Solving a linear equation with several occurrences of the variable: Problem type2alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge209 Solving a linear equation with several occurrences of the variable: Problem type4alge179 Solving a linear equation with several occurrences of the variable: Problem type5alge173 Solving a word problem using a linear equation: Problem type 3alge014 Solving a word problem using a linear equation: Problem type 1alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge076 Solving a system of linear equationsalge060 Solving a rational equation that simplifies to a linear equation: Problem type 1alge205 Solving a rational equation that simplifies to a linear equation: Problem type 2alge206 Solving a rational equation that simplifies to a linear equation: Problem type 3alge029 Simplifying a polynomial expressionalge030 Multiplying monomialsalge180 Multiplying polynomialsalge705 Factoring a quadratic with leading coefficient 1alge040 Factoring a quadratic with leading coefficient greater than 1alge624 Factoring a difference of squares


alge024 Product rule of exponentsalge027 Power rule: Positive exponentsalge080 Simplifying a radical expression: Problem type 1alge086 Rationalizing the denominator of a radical expressionalge250 Rational exponents: Basicpcalc048 Adding and subtracting complex numberspcalc049 Multiplying complex numbersset004 Set builder and interval notationset005 Union and intersection of intervalsfun018 Introduction to functions: Notation and graphsfun016 Domain and range: Problem type 1fun010 Vertical line testfun019 Sum, difference, and product of two functionsalge185 Vertical translation of the graph of a functionfun020 Vertical and horizontal translations of the graph of a functionfun022 Composition of two functions: Basicfun012 Inverse functions: Basicalge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge071 Writing the equation of a line given the slope and a point on the linealge196 Graphing a line through a given point with a given slopealge631 Finding the slope of a line given its equationalge637 Determining the slope of a line given its graphalge072 Writing the equation of the line through two given pointsalge073 Writing the equations of vertical and horizontal lines through a given pointalge198 Graphing a vertical or horizontal linealge045 Finding the roots of a quadratic equation with leading coefficient 1alge048 Finding the roots of a quadratic equation with leading coefficient greater than1alge094 Completing the squarealge095 Solving a quadratic equation using the quadratic formulaalge252 Graphing a parabola: Problem type 1alge253 Graphing a parabola: Problem type 2alge710 Simplifying a ratio of polynomials: Problem type 1alge681 Solving equations written in factored formpcalc053 Simplifying a power of i

Right triangle trigonometry and trigonometric values

pcalc001 Converting between a decimal degree and degrees-minutes-secondspcalc002 Converting between degree and radian measurepcalc003 Coterminal anglespcalc005 Arc length and central angle measure

B.13. TRIGONOMETRY 259

pcalc006 Sketching an angle in standard positiongeom506 Special right trianglespcalc600 Sine, cosine, and tangent ratiospcalc601 Using a trigonometric ratio to find a side length in a right trianglepcalc602 Using a trigonometric ratio to find an angle measure in a right trianglepcalc007 Common angles and trigonometric functionspcalc008 Finding trigonometric ratios given a right trianglepcalc011 Finding values of trigonometric functions given information about an angle:Problem type 1pcalc012 Finding values of trigonometric functions given information about an angle:Problem type 2pcalc013 Finding values of trigonometric functions given information about an angle:Problem type 3

Trigonometric functions

pcalc107 Sketching the graph of a sine or cosine function: Problem type 1pcalc106 Sketching the graph of a sine or cosine function: Problem type 2pcalc014 Sketching the graph of a sine or cosine function: Problem type 3pcalc017 Sketching the graph of a secant or cosecant functionpcalc105 Sketching the graph of a tangent or cotangent function: Problem type 1pcalc015 Sketching the graph of a tangent or cotangent function: Problem type 2pcalc016 Values of inverse trigonometric functionspcalc018 Composition of a trigonometric function and an inverse trigonometric func-tion: Problem type 1pcalc019 Composition of a trigonometric function and an inverse trigonometric func-tion: Problem type 2pcalc036 Composition of a trigonometric function and an inverse trigonometric func-tion: Problem type 3

Trigonometric identities and equations

pcalc126 Cofunction identitiespcalc029 Sum and difference identitiespcalc124 Product-to-sum and sum-to-product identitiespcalc030 Double-angle identitiespcalc110 Verifying a trigonometric identitypcalc034 Proving a trigonometric identity: Problem type 1pcalc435 Proving trigonometric identities: Problem type 2pcalc400 Proving trigonometric identities: Problem type 3pcalc401 Proving trigonometric identities: Problem type 4pcalc020 Solving a basic trigonometric equation involving sine or cosine


pcalc021 Solving a basic trigonometric equation involving tangent, cotangent, secant,or cosecantpcalc022 Solving a trigonometric equation involving a squared functionpcalc024 Solving a trigonometric equation involving more than one functionpcalc025 Solving a trigonometric equation involving an angle multiplied by a constantpcalc026 Solving a trigonometric equation using sum and difference identitiespcalc027 Solving a trigonometric equation using double-angle identitiespcalc028 Solving a trigonometric equation using half-angle identitiespcalc127 Solving a trigonometric inequality

Applications of trigonometry

pcalc031 Solving a triangle with the law of sines: Problem type 1pcalc032 Solving a triangle with the law of sines: Problem type 2pcalc033 Solving a triangle with the law of cosinespcalc060 Magnitude of a vectorpcalc729 Unit vectorspcalc739 Multiplication of a vector by a scalarpcalc063 Translation of a vectorpcalc725 Linear combination of vectors: Algebraic approachpcalc726 Linear combination of vectors: Geometric approachvector002 Calculating the magnitude and direction of a vectorvector005 Finding the components of a vectorpcalc727 Solving a word problem using vectorspcalc728 Dot productpcalc730 Finding the angle between two vectorsvector006 Finding the component of a vector along another vectorpcalc055 Plotting a point in polar coordinatespcalc056 Converting rectangular coordinates to polar coordinatespcalc057 Converting polar coordinates to rectangular coordinatespcalc058 Converting an equation written in rectangular coordinates to one written inpolar formpcalc059 Converting an equation written in polar form to one written in rectangularcoordinatespcalc052 Writing a complex number in trigonometric formpcalc054 De Moivre’s theorempcalc724 Finding the nth roots of a number

B.14 PreCalculus without Trigonometry / College Algebra

Algebra review

B.14. PRECALCULUS WITHOUT TRIGONOMETRY / COLLEGE ALGEBRA 261

alge061 Solving a linear equation with several occurrences of the variable: Problem type2alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge209 Solving a linear equation with several occurrences of the variable: Problem type4alge179 Solving a linear equation with several occurrences of the variable: Problem type5alge173 Solving a word problem using a linear equation: Problem type 3alge014 Solving a word problem using a linear equation: Problem type 1alge219 Solving a word problem using a linear equation: Problem type 2alge704 Solving a word problem using a linear equation: Problem type 4alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge207 Solving a linear inequality: Problem type 4alge103 Solving an equation involving absolute value: Basicalge167 Solving an equation involving absolute value: Advancedalge170 Solving an inequality involving absolute value: Basicalge169 Solving an inequality involving absolute valuealge060 Solving a rational equation that simplifies to a linear equation: Problem type 1alge205 Solving a rational equation that simplifies to a linear equation: Problem type 2alge206 Solving a rational equation that simplifies to a linear equation: Problem type 3alge029 Simplifying a polynomial expressionalge030 Multiplying monomialsalge180 Multiplying polynomialsalge705 Factoring a quadratic with leading coefficient 1alge040 Factoring a quadratic with leading coefficient greater than 1alge041 Factoring a product of a quadratic trinomial and a monomialalge624 Factoring a difference of squaresalge042 Factoring with repeated use of the difference of squares formulaalge044 Factoring a sum or difference of two cubesalge038 Factoring a multivariate polynomial by grouping: Problem type 1alge024 Product rule of exponentsalge027 Power rule: Positive exponentsalge025 Power rule: Negative exponentsalge028 Product rule of exponents in a multivariate monomialscinot001 Converting between decimal numbers and numbers written in scientific nota-tionscinot002 Multiplying and dividing numbers written in scientific notationalge080 Simplifying a radical expression: Problem type 1alge084 Simplifying a sum of radical expressionsalge640 Simplifying a product of radical expressionsalge086 Rationalizing the denominator of a radical expressionalge088 Rationalizing the denominator of a radical expression using conjugates


alge089 Solving an equation with radicals: Problem type 1alge091 Solving an equation with radicals: Problem type 3alge182 Solving an equation with radicals: Problem type 4alge250 Rational exponents: Basicalge251 Rational exponents: Negative exponents and fractional basesalge249 Rational exponents: Powers of powers

Functions and graphs

set004 Set builder and interval notationset005 Union and intersection of intervalsfun018 Introduction to functions: Notation and graphsfun016 Domain and range: Problem type 1fun004 Domain and range: Problem type 2fun010 Vertical line testpcalc114 Even and odd functionsfun019 Sum, difference, and product of two functionsalge185 Vertical translation of the graph of a functionfun020 Vertical and horizontal translations of the graph of a functionfun023 Piecewise-defined functionsalge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge071 Writing the equation of a line given the slope and a point on the linealge196 Graphing a line through a given point with a given slopealge631 Finding the slope of a line given its equationalge637 Determining the slope of a line given its graphalge072 Writing the equation of the line through two given pointsalge073 Writing the equations of vertical and horizontal lines through a given pointalge198 Graphing a vertical or horizontal linegeom807 Slopes of parallel and perpendicular lines: Problem type 1geom808 Slopes of parallel and perpendicular lines: Problem type 2alge701 Writing equations and drawing graphs to fit a narrativealge018 Graphing a linear inequality in the plane: Problem type 1alge225 Graphing a linear inequality in the plane: Problem type 2alge168 Graphing an equation involving absolute value in the planefun021 Composition of two functions: Domain and rangefun022 Composition of two functions: Basicalge129 Composition of two functions: Advancedfun011 Horizontal line testfun012 Inverse functions: Basicalge130 Inverse functions: Advanced

Polynomial and rational functions


alge045 Finding the roots of a quadratic equation with leading coefficient 1alge048 Finding the roots of a quadratic equation with leading coefficient greater than1alge094 Completing the squarealge095 Solving a quadratic equation using the quadratic formulaalge707 Finding the discriminant of a quadratic equationalge703 Solving a word problem using a quadratic equation with rational rootsalge524 Solving a word problem using a quadratic equation with irrational rootsalge771 Solving a quadratic inequalityalge252 Graphing a parabola: Problem type 1alge253 Graphing a parabola: Problem type 2alge254 Graphing a parabola: Problem type 3alge255 Graphing a quadratic inequalityalge708 Polynomial long division: Linear divisoralge709 Polynomial long division: Quadratic divisorpcalc117 Synthetic divisionpcalc118 Remainder theoremalge710 Simplifying a ratio of polynomials: Problem type 1pcalc092 Partial fraction decompositionalge681 Solving equations written in factored formalge211 Solving a quadratic equation needing simplificationpcalc700 Finding a polynomial of a given degree with given zerospcalc123 Using a given zero to write a polynomial as a product of linear factorspcalc701 Finding all potential zeros of a polynomial given by the rational zeros theorempcalc702 Using the rational zeros theorem to find zeros of a polynomialpcalc704 Solving a word problem involving a polynomial of degree 3pcalc048 Adding and subtracting complex numberspcalc049 Multiplying complex numberspcalc050 Dividing complex numberspcalc053 Simplifying a power of ipcalc051 Solving a quadratic equation with imaginary rootspcalc705 N zeros theorem and conjugate zeros theorempcalc703 Using the conjugate zeros theorem to find all zeros of a polynomialpcalc115 Solving a word problem by finding a local extremum of a polynomial functionpcalc738 Inferring properties of a polynomial function from its graphpcalc108 Sketching the graph of a rational function: Problem type 1pcalc109 Sketching the graph of a rational function: Problem type 2pcalc706 Choosing the form of a rational function given its graph

Exponential and logarithmic functions

alge108 Exponential and logarithmic equationsalge232 Evaluating a logarithmic expression


pcalc708 Basic properties of logarithmsalge107 Change of base for logarithmsalge233 Solving a logarithmic equation: Problem type 1alge113 Solving a logarithmic equation: Problem type 2alge111 Solving an exponential equation: Problem type 1alge112 Solving an exponential equation: Problem type 2alge177 Solving a word problem using an exponential equation: Problem type 1alge178 Solving a word problem using an exponential equation: Problem type 2pcalc737 Solving a word problem using an exponential equation: Problem type 3alge712 Sketching the graph of an exponential function: Basicpcalc103 Sketching the graph of an exponential function: Advancedpcalc104 Sketching the graph of a logarithmic functionpcalc102 Translating the graph of a logarithmic or exponential function

Systems of linear equations and matrices

alge075 Classifying a system of linear equationsalge076 Solving a system of linear equationsalge077 Creating an inconsistent system of linear equationspcalc099 Consistency and independence of a system of linear equationsalge078 Solving a word problem using a system of linear equations: Problem type 1alge184 Solving a word problem using a system of linear equations: Problem type 2alge224 Solving a word problem using a system of linear equations: Problem type 3alge192 Solving a word problem using a system of linear equations: Problem type 4alge172 Solving a word problem using a system of linear equations: Problem type 5alge079 Graphing a system of linear inequalitiespcalc093 Solving a word problem using a system of linear inequalitiespcalc095 Linear programmingpcalc094 Solving a word problem using linear programmingpcalc709 Addition of matrices and multiplication of a matrix by a scalarpcalc039 Multiplication of matrices: Basicpcalc710 Multiplication of matrices: Advancedpcalc042 Finding the determinant of a 2x2 matrixpcalc043 Finding the determinant of a 3x3 matrixpcalc040 Finding the inverse of a 2x2 matrixpcalc041 Finding the inverse of a 3x3 matrixpcalc045 Cramer’s rule: Problem type 1pcalc047 Cramer’s rule: Problem type 2pcalc711 Using the inverse of a matrix to solve a system of linear equationspcalc712 Gauss-Jordan elimination with a 2x2 matrixpcalc046 Augmented matrix and solution set of a system of linear equations

Sequences, series, and probability


pcalc080 Finding the first terms of a sequencepcalc713 Arithmetic and geometric sequences: Identifying and writing in standard formpcalc715 Arithmetic sequencespcalc717 Geometric sequencespcalc718 Sum of the first n terms of an arithmetic sequencepcalc719 Sum of the first n terms of a geometric sequencepcalc720 Sum of a geometric seriespcalc082 Factorial expressionspcalc088 Permutations and combinations: Problem type 1pcalc089 Permutations and combinations: Problem type 2pcalc090 Permutations and combinations: Problem type 3pcalc087 Binomial formulastat117 Probabilities of draws with replacementstat118 Probabilities of draws without replacementstat119 Venn diagrams: Two eventsstat101 Venn diagrams: Word problemsstat106 Outcomes and event probabilitystat112 Die rollingstat114 Probability of intersection or union: Word problemsstat115 Independent events: Basicstat120 Probability of union: Basicstat109 Intersection and conditional probability

Conic sections

pcalc067 Graphing a parabola with a horizontal or a vertical axispcalc068 Writing an equation of a parabola given the vertex and the focuspcalc069 Finding the focus of a parabolapcalc605 Graphing a circle given its equation in standard formpcalc064 Graphing a circle given its equation in general formpcalc065 Writing an equation of a circle given its center and a point on the circlepcalc066 Writing an equation of a circle given the endpoints of a diameterpcalc734 Graphing an ellipse given its equation in standard formpcalc071 Graphing an ellipse given its equation in general formpcalc072 Finding the foci of an ellipsepcalc073 Writing an equation of an ellipse given the foci and the major axis lengthpcalc074 Writing an equation of an ellipse given the center, an endpoint of an axis, andthe length of the other axispcalc735 Graphing a hyperbola given its equation in standard formpcalc076 Graphing a hyperbola given its equation in general formpcalc077 Finding the foci of a hyperbolapcalc078 Writing an equation of a hyperbola given the foci and the verticespcalc079 Writing an equation of a hyperbola given the foci and the asymptotes


alge191 Midpoint of a line segment in the planealge132 Distance between two points in the planepcalc736 Classifying conics given their equationspcalc098 Solving a system of nonlinear equationspcalc096 Graphing a system of nonlinear inequalities: Problem type 1

B.15 PreCalculus

Algebra review

alge061 Solving a linear equation with several occurrences of the variable: Problem type2alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge209 Solving a linear equation with several occurrences of the variable: Problem type4alge179 Solving a linear equation with several occurrences of the variable: Problem type5alge173 Solving a word problem using a linear equation: Problem type 3alge014 Solving a word problem using a linear equation: Problem type 1alge219 Solving a word problem using a linear equation: Problem type 2alge704 Solving a word problem using a linear equation: Problem type 4alge020 Solving a linear inequality: Problem type 2alge021 Solving a linear inequality: Problem type 3alge207 Solving a linear inequality: Problem type 4alge103 Solving an equation involving absolute value: Basicalge167 Solving an equation involving absolute value: Advancedalge170 Solving an inequality involving absolute value: Basicalge169 Solving an inequality involving absolute valuealge060 Solving a rational equation that simplifies to a linear equation: Problem type 1alge205 Solving a rational equation that simplifies to a linear equation: Problem type 2alge206 Solving a rational equation that simplifies to a linear equation: Problem type 3alge029 Simplifying a polynomial expressionalge030 Multiplying monomialsalge180 Multiplying polynomialsalge705 Factoring a quadratic with leading coefficient 1alge040 Factoring a quadratic with leading coefficient greater than 1alge041 Factoring a product of a quadratic trinomial and a monomialalge624 Factoring a difference of squaresalge042 Factoring with repeated use of the difference of squares formulaalge044 Factoring a sum or difference of two cubesalge038 Factoring a multivariate polynomial by grouping: Problem type 1

B.15. PRECALCULUS 267

alge024 Product rule of exponentsalge027 Power rule: Positive exponentsalge025 Power rule: Negative exponentsalge028 Product rule of exponents in a multivariate monomialscinot001 Converting between decimal numbers and numbers written in scientific nota-tionscinot002 Multiplying and dividing numbers written in scientific notationalge080 Simplifying a radical expression: Problem type 1alge084 Simplifying a sum of radical expressionsalge640 Simplifying a product of radical expressionsalge086 Rationalizing the denominator of a radical expressionalge088 Rationalizing the denominator of a radical expression using conjugatesalge089 Solving an equation with radicals: Problem type 1alge091 Solving an equation with radicals: Problem type 3alge182 Solving an equation with radicals: Problem type 4alge250 Rational exponents: Basicalge251 Rational exponents: Negative exponents and fractional basesalge249 Rational exponents: Powers of powers

Functions and graphs

set004 Set builder and interval notationset005 Union and intersection of intervalsfun018 Introduction to functions: Notation and graphsfun016 Domain and range: Problem type 1fun004 Domain and range: Problem type 2fun010 Vertical line testpcalc114 Even and odd functionsfun019 Sum, difference, and product of two functionsalge185 Vertical translation of the graph of a functionfun020 Vertical and horizontal translations of the graph of a functionfun023 Piecewise-defined functionsalge194 Graphing a line given its equation in slope-intercept formalge195 Graphing a line given its equation in standard formalge071 Writing the equation of a line given the slope and a point on the linealge196 Graphing a line through a given point with a given slopealge631 Finding the slope of a line given its equationalge637 Determining the slope of a line given its graphalge072 Writing the equation of the line through two given pointsalge073 Writing the equations of vertical and horizontal lines through a given pointalge198 Graphing a vertical or horizontal linegeom807 Slopes of parallel and perpendicular lines: Problem type 1geom808 Slopes of parallel and perpendicular lines: Problem type 2


alge701 Writing equations and drawing graphs to fit a narrativealge018 Graphing a linear inequality in the plane: Problem type 1alge225 Graphing a linear inequality in the plane: Problem type 2alge168 Graphing an equation involving absolute value in the planefun021 Composition of two functions: Domain and rangefun022 Composition of two functions: Basicalge129 Composition of two functions: Advancedfun011 Horizontal line testfun012 Inverse functions: Basicalge130 Inverse functions: Advanced

Polynomial and rational functions

alge045 Finding the roots of a quadratic equation with leading coefficient 1alge048 Finding the roots of a quadratic equation with leading coefficient greater than1alge094 Completing the squarealge095 Solving a quadratic equation using the quadratic formulaalge707 Finding the discriminant of a quadratic equationalge703 Solving a word problem using a quadratic equation with rational rootsalge524 Solving a word problem using a quadratic equation with irrational rootsalge771 Solving a quadratic inequalityalge252 Graphing a parabola: Problem type 1alge253 Graphing a parabola: Problem type 2alge254 Graphing a parabola: Problem type 3alge255 Graphing a quadratic inequalityalge708 Polynomial long division: Linear divisoralge709 Polynomial long division: Quadratic divisorpcalc117 Synthetic divisionpcalc118 Remainder theoremalge710 Simplifying a ratio of polynomials: Problem type 1pcalc092 Partial fraction decompositionalge681 Solving equations written in factored formalge211 Solving a quadratic equation needing simplificationpcalc700 Finding a polynomial of a given degree with given zerospcalc123 Using a given zero to write a polynomial as a product of linear factorspcalc701 Finding all potential zeros of a polynomial given by the rational zeros theorempcalc702 Using the rational zeros theorem to find zeros of a polynomialpcalc704 Solving a word problem involving a polynomial of degree 3pcalc048 Adding and subtracting complex numberspcalc049 Multiplying complex numberspcalc050 Dividing complex numberspcalc053 Simplifying a power of i


pcalc051 Solving a quadratic equation with imaginary rootspcalc705 N zeros theorem and conjugate zeros theorempcalc703 Using the conjugate zeros theorem to find all zeros of a polynomialpcalc115 Solving a word problem by finding a local extremum of a polynomial functionpcalc738 Inferring properties of a polynomial function from its graphpcalc108 Sketching the graph of a rational function: Problem type 1pcalc109 Sketching the graph of a rational function: Problem type 2pcalc706 Choosing the form of a rational function given its graph

Exponential and logarithmic functions

alge108 Exponential and logarithmic equationsalge232 Evaluating a logarithmic expressionpcalc708 Basic properties of logarithmsalge107 Change of base for logarithmsalge233 Solving a logarithmic equation: Problem type 1alge113 Solving a logarithmic equation: Problem type 2alge111 Solving an exponential equation: Problem type 1alge112 Solving an exponential equation: Problem type 2alge177 Solving a word problem using an exponential equation: Problem type 1alge178 Solving a word problem using an exponential equation: Problem type 2pcalc737 Solving a word problem using an exponential equation: Problem type 3alge712 Sketching the graph of an exponential function: Basicpcalc103 Sketching the graph of an exponential function: Advancedpcalc104 Sketching the graph of a logarithmic functionpcalc102 Translating the graph of a logarithmic or exponential function

Trigonometry

pcalc001 Converting between a decimal degree and degrees-minutes-secondspcalc002 Converting between degree and radian measurepcalc003 Coterminal anglespcalc005 Arc length and central angle measurepcalc006 Sketching an angle in standard positiongeom506 Special right trianglespcalc600 Sine, cosine, and tangent ratiospcalc601 Using a trigonometric ratio to find a side length in a right trianglepcalc602 Using a trigonometric ratio to find an angle measure in a right trianglepcalc007 Common angles and trigonometric functionspcalc008 Finding trigonometric ratios given a right trianglepcalc011 Finding values of trigonometric functions given information about an angle:Problem type 1


pcalc012 Finding values of trigonometric functions given information about an angle:Problem type 2pcalc013 Finding values of trigonometric functions given information about an angle:Problem type 3pcalc107 Sketching the graph of a sine or cosine function: Problem type 1pcalc106 Sketching the graph of a sine or cosine function: Problem type 2pcalc014 Sketching the graph of a sine or cosine function: Problem type 3pcalc017 Sketching the graph of a secant or cosecant functionpcalc105 Sketching the graph of a tangent or cotangent function: Problem type 1pcalc015 Sketching the graph of a tangent or cotangent function: Problem type 2pcalc016 Values of inverse trigonometric functionspcalc018 Composition of a trigonometric function and an inverse trigonometric func-tion: Problem type 1pcalc019 Composition of a trigonometric function and an inverse trigonometric func-tion: Problem type 2pcalc036 Composition of a trigonometric function and an inverse trigonometric func-tion: Problem type 3pcalc126 Cofunction identitiespcalc029 Sum and difference identitiespcalc124 Product-to-sum and sum-to-product identitiespcalc030 Double-angle identitiespcalc110 Verifying a trigonometric identitypcalc034 Proving a trigonometric identity: Problem type 1pcalc435 Proving trigonometric identities: Problem type 2pcalc400 Proving trigonometric identities: Problem type 3pcalc401 Proving trigonometric identities: Problem type 4pcalc020 Solving a basic trigonometric equation involving sine or cosinepcalc021 Solving a basic trigonometric equation involving tangent, cotangent, secant,or cosecantpcalc022 Solving a trigonometric equation involving a squared functionpcalc024 Solving a trigonometric equation involving more than one functionpcalc025 Solving a trigonometric equation involving an angle multiplied by a constantpcalc026 Solving a trigonometric equation using sum and difference identitiespcalc027 Solving a trigonometric equation using double-angle identitiespcalc028 Solving a trigonometric equation using half-angle identitiespcalc127 Solving a trigonometric inequalitypcalc031 Solving a triangle with the law of sines: Problem type 1pcalc032 Solving a triangle with the law of sines: Problem type 2pcalc033 Solving a triangle with the law of cosinespcalc060 Magnitude of a vectorpcalc729 Unit vectorspcalc739 Multiplication of a vector by a scalarpcalc063 Translation of a vectorpcalc725 Linear combination of vectors: Algebraic approach


pcalc726 Linear combination of vectors: Geometric approachvector002 Calculating the magnitude and direction of a vectorvector005 Finding the components of a vectorpcalc727 Solving a word problem using vectorspcalc728 Dot productpcalc730 Finding the angle between two vectorsvector006 Finding the component of a vector along another vectorpcalc055 Plotting a point in polar coordinatespcalc056 Converting rectangular coordinates to polar coordinatespcalc057 Converting polar coordinates to rectangular coordinatespcalc058 Converting an equation written in rectangular coordinates to one written inpolar formpcalc059 Converting an equation written in polar form to one written in rectangularcoordinatespcalc052 Writing a complex number in trigonometric formpcalc054 De Moivre’s theorempcalc724 Finding the nth roots of a number

Systems of linear equations and matrices

alge075 Classifying a system of linear equationsalge076 Solving a system of linear equationsalge077 Creating an inconsistent system of linear equationspcalc099 Consistency and independence of a system of linear equationsalge078 Solving a word problem using a system of linear equations: Problem type 1alge184 Solving a word problem using a system of linear equations: Problem type 2alge224 Solving a word problem using a system of linear equations: Problem type 3alge192 Solving a word problem using a system of linear equations: Problem type 4alge172 Solving a word problem using a system of linear equations: Problem type 5alge079 Graphing a system of linear inequalitiespcalc093 Solving a word problem using a system of linear inequalitiespcalc095 Linear programmingpcalc094 Solving a word problem using linear programmingpcalc709 Addition of matrices and multiplication of a matrix by a scalarpcalc039 Multiplication of matrices: Basicpcalc710 Multiplication of matrices: Advancedpcalc042 Finding the determinant of a 2x2 matrixpcalc043 Finding the determinant of a 3x3 matrixpcalc040 Finding the inverse of a 2x2 matrixpcalc041 Finding the inverse of a 3x3 matrixpcalc045 Cramer’s rule: Problem type 1pcalc047 Cramer’s rule: Problem type 2pcalc711 Using the inverse of a matrix to solve a system of linear equations


pcalc712 Gauss-Jordan elimination with a 2x2 matrixpcalc046 Augmented matrix and solution set of a system of linear equations

Sequences, series, and probability

pcalc080 Finding the first terms of a sequencepcalc713 Arithmetic and geometric sequences: Identifying and writing in standard formpcalc715 Arithmetic sequencespcalc717 Geometric sequencespcalc718 Sum of the first n terms of an arithmetic sequencepcalc719 Sum of the first n terms of a geometric sequencepcalc720 Sum of a geometric seriespcalc082 Factorial expressionspcalc088 Permutations and combinations: Problem type 1pcalc089 Permutations and combinations: Problem type 2pcalc090 Permutations and combinations: Problem type 3pcalc087 Binomial formulastat117 Probabilities of draws with replacementstat118 Probabilities of draws without replacementstat119 Venn diagrams: Two eventsstat101 Venn diagrams: Word problemsstat106 Outcomes and event probabilitystat112 Die rollingstat114 Probability of intersection or union: Word problemsstat115 Independent events: Basicstat120 Probability of union: Basicstat109 Intersection and conditional probability

Conic sections

pcalc067 Graphing a parabola with a horizontal or a vertical axispcalc068 Writing an equation of a parabola given the vertex and the focuspcalc069 Finding the focus of a parabolapcalc605 Graphing a circle given its equation in standard formpcalc064 Graphing a circle given its equation in general formpcalc065 Writing an equation of a circle given its center and a point on the circlepcalc066 Writing an equation of a circle given the endpoints of a diameterpcalc734 Graphing an ellipse given its equation in standard formpcalc071 Graphing an ellipse given its equation in general formpcalc072 Finding the foci of an ellipsepcalc073 Writing an equation of an ellipse given the foci and the major axis lengthpcalc074 Writing an equation of an ellipse given the center, an endpoint of an axis, and

B.16. AP STATISTICS (QUANTITATIVE) 273

the length of the other axispcalc735 Graphing a hyperbola given its equation in standard formpcalc076 Graphing a hyperbola given its equation in general formpcalc077 Finding the foci of a hyperbolapcalc078 Writing an equation of a hyperbola given the foci and the verticespcalc079 Writing an equation of a hyperbola given the foci and the asymptotesalge191 Midpoint of a line segment in the planealge132 Distance between two points in the planepcalc736 Classifying conics given their equationspcalc098 Solving a system of nonlinear equationspcalc096 Graphing a system of nonlinear inequalities: Problem type 1

B.16 AP Statistics (Quantitative)

Mathematical Readiness

arith048 Order of operations: Problem type 1arith051 Order of operations: Problem type 2arith220 Decimal place valuearith221 Rounding decimalsarith226 Converting between percentages and decimalsarith030 Percentage of a whole numberarith069 Writing a ratio as a percentagearith090 Converting a percentage to a fractionarith002 Converting a fraction to a percentagestat022 Summation of indexed dataalge006 Solving a linear equation: Problem type 1alge011 Solving a linear equation with several occurrences of the variable: Problem type1alge013 Solving a linear equation with several occurrences of the variable: Problem type3alge256 Y-intercept of a linealge257 X- and y-intercepts of a line given the equation in standard formalge070 Writing an equation of a line given the slope and the y-interceptalge197 Graphing a line given the x- and y-interceptsalge194 Graphing a line given its equation in slope-intercept formalge196 Graphing a line through a given point with a given slope

Descriptive Statistics

stat904 Interpreting pie charts


stat901 Computations from pie chartsstat844 Double bar chartsstat702 Histograms for grouped datastat703 Frequency polygons for grouped datastat717 Interpreting relative frequency histogramsstat718 Cumulative distributions and ogivesstat164 Comparing means without calculationstat165 Comparing standard deviations without calculationstat023 Box-and-whisker plotsstat831 Interpreting a stem-and-leaf displaystat827 Using back-to-back stem-and-leaf displays to compare data setsstat706 Mean, median, and mode: Computationsstat902 Rejecting unreasonable claims based on average statisticsstat007 Weighted mean: Tabular datastat719 Estimating the mean of grouped datastat009 Percentilesstat021 Population standard deviationstat011 Sample standard deviationstat729 Estimating the standard deviation of grouped datastat730 Chebyshev’s theorem and the empirical rulestat798 Mean, median, and mode: Comparisonsstat025 Transforming the mean and standard deviation of data setsstat905 Making reasonable inferences based on proportion statistics

Probability

stat782 Factorial expressionsstat788 Combinationsstat789 Permutationsstat790 Permutations, combinations, and the multiplication principle for countingstat117 Probabilities of draws with replacementstat118 Probabilities of draws without replacementstat119 Venn diagrams: Two eventsstat100 Venn diagrams: Three eventsstat101 Venn diagrams: Word problemsstat106 Outcomes and event probabilitystat226 Die rollingstat114 Probability of intersection or union: Word problemsstat115 Independent events: Basicstat120 Probability of union: Basicstat104 Mutually exclusive events: Two eventsstat102 Mutually exclusive events: Three eventsstat850 Probability of independent events

B.16. AP STATISTICS (QUANTITATIVE) 275

stat105 Independent events: Two eventsstat103 Independent events: Three eventsstat113 The curious diestat020 Calculating relative frequencies in a contingency tablestat116 Conditional probability: Basicstat851 Probability of dependent eventsstat109 Intersection and conditional probabilitystat107 Conditional probability: Mutually exclusive eventsstat108 Conditional probability: Independent eventsstat756 Tree diagrams for conditional probabilitiesstat110 Law of total probabilitiesstat111 Bayes’ theorem

Random Variables

stat777 Classification of variables and levels of measurementstat142 Discrete versus continuous variablesstat151 Discrete probability distribution: Basicstat143 Discrete probability distribution: Word problemsstat149 Cumulative distribution functionstat150 Expectation and variance of a random variablestat153 Rules for expectation and variance of random variablesstat145 Marginal distributions of two discrete random variablesstat146 Joint distributions of dependent or independent random variablesstat147 Probabilities of two random variables given their joint distributionstat148 Conditional probabilities of two random variables given their joint distribution

Distributions

stat156 Binomial problems: Mean and standard deviationstat174 Binomial problems: Basicstat155 Binomial problems: Advancedstat157 Standard normal probabilitiesstat760 Standard normal values: Basicstat160 Standard normal values: Advancedstat159 Normal versus standard normal density curvesstat161 Normal distribution raw scoresstat162 Mean and deviation of a normal distributionstat163 Normal distribution: Word problemsstat173 t distributionstat170 Chi-square distributionstat187 Normal approximation to binomial


stat185 Central limit theorem: Sample meanstat186 Central limit theorem: Sample sumstat188 Central limit theorem: Sample proportion

Inferential Statistics

stat200 Selecting a distribution for inferences on the population meanstat201 Confidence interval for the population mean: Use of the standard normalstat755 Choosing an appropriate sample sizestat202 Confidence interval for the population mean: Use of the t distributionstat203 Confidence interval for a population proportionstat205 Confidence interval for the difference of population means: Use of the standardnormalstat206 Confidence interval for the difference of population means: Use of the t distri-butionstat207 Confidence interval for the difference of population proportionsstat300 Determining null and alternative hypothesesstat190 Type I and Type II errorsstat192 Type I and Type II errors and powerstat194 Effect size, sample size, and powerstat301 Hypothesis test for the population mean: Z teststat302 Hypothesis test for the population mean: t teststat303 Hypothesis test for a population proportionstat305 Hypothesis test for the difference of population means: Z teststat309 Hypothesis test for the difference of population means: Paired comparisonsstat306 Hypothesis test for the difference of population means: t teststat307 Hypothesis test for the difference of population proportionsstat319 Contingency tables: Expected frequenciesstat320 Chi-square goodness-of-fit teststat321 Chi-square test of independence

Regression and Correlation

stat339 Sketching the least-squares regression linestat333 Linear relationship and the sample correlation coefficientstat340 Predictions from the least-squares regression linestat930 Computing the sample correlation coefficient and the coefficients for the least-squares regression linestat931 Explained and unexplained variation and the least-squares regression linestat325 Confidence intervals and prediction intervals from simple linear regressionstat947 Hypothesis tests for the correlation coefficient and the slope of the least-squaresregression line

Index

(UG) = User’s Guide (Appendix A)

——————————

absolute values, entering 24

Access Code 8

access, restricting 99

Advanced options, class account 100

Advanced options, Teacher account 98

Advanced Teacher Module 72

ALEKS account, extending (UG) 180

ALEKS account, renewing (UG) 180

ALEKS educational paradigm 127

ALEKS, what is 1

America Online requirements (UG) 166

Answer Editor, graphing 26

Answer Editor, help with (UG) 171

Answer Editor, histograms 28

Answer Editor, manipulators for mathematicalexpressions 19

Answer Editor, mathematical expressions in20

Answer Editor, number line 25

Answer Editor, purpose of (UG) 168

Answer Editor, what is 18

arithmetic facts 119

Ask a Friend 99

Ask a Friend button 44

assessment, first 13

assessment, in Knowledge Space Theory 145

Assessment Mode 15

Assessment options, class account 100

Assessment Report, format 29

Assessment Report, interpreting 29

Assessment Report, progress bars in 31

Assessment Report, viewing (UG) 171

Assessment Report, what is 29

assessments, automatic 17

assessments, automatic (UG) 169

assessments, canceling 70, 88, 89

assessments, changing of 70

assessments, completion 17

assessments, final 181

assessments, initial 16

assessments, initial, continued 14, 16

assessments, lengthy 181

assessments, login time 17

assessments, progress 17

assessments, purpose of 15

assessments, purpose of (UG) 169

assessments, requested 17

assessments, requested, on selected slices 17

assessments, requesting 67, 88, 89

assessments, restricting 99

assessments, results of (UG) 169

assessments, rules for 16

assessments, rules for (UG) 173

assessments, scheduled 84

assessments, scheduling of 16, 67, 70, 88, 89

assessments, when to order 136

asymptotes, graphing with 27

authorization of registration 9

authorizing a student account 105, 72

automatic assessments, blocking, Advanced TeacherModule 91

automatic assessments, blocking, Teacher Module69

availability of quizzes, Teacher Module 71, 93

Average, Class Report 61, 87

Average Report, display options for 61

basic interface, Teacher Module 45

blocking automatic assessments, Advanced TeacherModule 91

blocking automatic assessments, Teacher Module

277

278 INDEX

69

bulletin board for teachers 78

buttons, Assessment Mode 18

buttons, Learning Mode 34

Calculator button 35

calculator, disabling 99

calculator, use of with ALEKS (UG) 173

Cancel Assessment button 88

class account, creating 48, 99

class account, editing 101, 49

class account, moving from one instructor toanother 101

class account, moving from one teacher to an-other 52

Class Admin, in Teacher Module 48

class assessment, canceling, Advanced TeacherModule 89

class assessment, scheduling, Advanced TeacherModule 89

Class Code 8

Class Code, how to obtain 101, 3, 48, 49,99

Class Code (UG) 166

class, deleting 101, 50

Class Program button 101

class program, selecting 101

Class Progress 53

Class Progress, display options for, AdvancedTeacher Module 83

Class Progress, display options for, recommended83

Class Progress, Full progress over last 3 months84

Class Progress, Full progress over last 6 months58, 84

Class Progress, Full progress over last month84

Class Progress, Most recent progress 83

Class Progress, Most recent progress only 84

Class Progress, Progress in learning mode 57,83

Class Progress, Progress over last 3 months83

Class Progress, Progress over last 6 months

83

Class Progress, Progress over last month 83

Class Progress, report style for, Advanced TeacherModule 83

Class Progress, sorting in 54, 84

Class Progress, statistical information in 54,84

Class Progress, Total progress 59, 83

Class Progress, viewing, Advanced Teacher Module82

Class Report, Average 61, 87

Class Report, display options for, AdvancedTeacher Module 86

Class Report, Ready to learn 62, 87

Class Report, Scheduled assessment 60

Class Report, viewing, Advanced Teacher Module86

Class Report, What students can do 62, 87

class results for quiz 63

classroom integration of ALEKS 134

classroom teaching with ALEKS 128

Cleanup Tools 98, 99

Clear button, Answer Editor 20

Clear Records 98

Clear Stats 98

Compose Message button 95

computer lab, checking 8

conic sections, graphing 27

Content Editor 108

coordinates, non-integer, graphing with 27

course content, modifying 108

courses, planning and structuring 129

crashing, how to fix 181

Dictionary, access to 41

Dictionary button 35

Dictionary, searching (UG) 171

display options for Average Report 61

display options for Class Progress, AdvancedTeacher Module 83

display options for Class Report, AdvancedTeacher Module 86

distance learning with ALEKS 134, 136

domain address 100, 89, 91

domain, in Knowledge Space Theory 141

INDEX 279

downloading in Excel format 80, 85, 94

downloading in spreadsheet format 80, 85, 94

Edit button 101, 104, 98

educational paradigm in ALEKS 127

English menu 34

Enroll in Class button 103

enrolling students in a class 103, 50

enrollment, restricting 99

eraser tool 27

Exit button 34

exiting ALEKS 34

expiration date of student account 104

explanation page in Learning Mode 39

exponents, entering 24

extending an ALEKS account (UG) 180

Extra pie chart 30

facts, arithmetic 119

facts, math 119

FAQ 153

FAQ (UG) 175

features in ALEKS (UG) 171

feedback in Learning Mode 42

focusing instruction with ALEKS 87

fractions, entering 22

freezing, how to fix 181

frequently asked questions 153

frequently asked questions (UG) 175

Full progress over last 3 months, Class Progress84

Full progress over last 6 months, Class Progress58, 84

Full progress over last month, Class Progress84

grading with quizzes, Teacher Module 71, 93

grading with scheduled assessments, AdvancedTeacher Module 90

grading with scheduled assessments, TeacherModule 69

graphing, Answer Editor for 26

graphing conic sections 27

graphing points with non-integer coordinates27

graphing with asymptotes 27

graph P tool 27

graph x tool 27

graph y tool 27

grouping students 85, 87, 91, 95

guidelines for ALEKS use (UG) 173

Help button, Advanced Teacher Module 78

Help button 37

help, context-sensitive 37

help, in Advanced Teacher Module 78

help, online (UG) 171

histogram, adding and subtracting bars in 28

histograms, Answer Editor for 28

histogram, setting bars to any value in 28

How do I, in Teacher Module 46

independent study with ALEKS 136

individual results for quiz 67

inner fringes, in Knowledge Space Theory 144

installation of ALEKS plugin 6

installation of ALEKS plugin (UG) 172

instances, in Knowledge Space Theory 141

instruction, planning and focusing 131

integrating a textbook 101

Intermediate Objectives 105

Internet access 5

Internet access (UG) 166

introduction 1

item page in Learning Mode 38

items in Algebra 1 237

items in Algebra 2 249

items in AP Statistics (Quantitative) 273

items in High School Geometry 245

items, in Knowledge Space Theory 141

items in Mathematics - LV3 183



items in Mathematics - LV6 / Essential Math-ematics 197

items in Middle School Geometry 227

items in Middle School Math 1 205

items in Middle School Math 2 211

items in Middle School Math 3 / Foundationsof High School Math 218

items in Pre-Algebra 228

items in PreCalculus 266

items in PreCalculus without Trigonometry /

280 INDEX

College Algebra 260

items in Trigonometry 257

items, programs, standards 112

items, what are 112

keyboard shortcuts, Answer Editor 19

Knowledge Spaces, bibliography 146

Knowledge Spaces, history 141

knowledge spaces, in Knowledge Space Theory143

Knowledge Spaces, Theory 141

Knowledge Spaces, what are 141

knowledge states, in Knowledge Space Theory142

knowledge structures, in Knowledge Space Theory143

language menu 34

Learning log, viewing, Advanced Teacher Module82

Learning log, viewing, Teacher Module 66

Learning Mode, access to (UG) 170

Learning Mode, beginning 14

Learning Mode, collaborative help in 44

Learning Mode, explanation page 39

Learning Mode, feedback in 42

Learning Mode, interface 38

Learning Mode, item page 38

Learning Mode, practice page 39

Learning Mode, progress in (UG) 170

Learning Mode, review in 42

Learning Mode, rules for (UG) 173

Learning Mode, what is 33

Learning Mode, wrong answer page 41

Learning options, class account 100

learning rates, assigning 109

learning rates in ALEKS 138

limiting scheduled assessments, Advanced TeacherModule 91

limiting scheduled assessments, Teacher Module69

lists, entering 23

logging on to ALEKS (UG) 171

Login Name (UG) 167

login, unsuccessful 180

Macintosh requirements 5

Macintosh requirements (UG) 166

mailing list for teachers 78

Mail options, Teacher account 98

makeup quizzes 94

manual, structure and use of 1

Mastery pie chart 30

materials, supplementary (UG) 173

mathematical expressions, advanced 24

mathematical expressions, Answer Editor for20

mathematical expressions, types of 22

mathematical expressions, using in MessageCenter 95

mathematical signs, in Answer Editor 21

math facts 119

math lab, in structured course 134

math lab, supervised 134

matrices, entering 24

Message button 36

Message button, Teacher Module 96

Message Center 95, 96

Message Center, use of mathematical expres-sions in 95

messages, checking, Teacher Module 96

message, sending to student or class 95

messages, how students receive (UG) 171

message with scheduled assessments, AdvancedTeacher Module 90

mixed numbers, entering 23

mixed numbers, problems with 181

monitoring class progress 135

monitoring individual progress 135

monitoring student use of ALEKS 135

Most recent assessment only, Class Progress84

Most recent progress, Class Progress 83

moving a student to a new class 136

moving students from one class to another 103,50

MyPie button 37

MyPie (UG) 171

New Class button 99

New Teacher button 97

number line, Answer Editor for 25

INDEX 281

objectives, intermediate 105

Options button 34

orientation for students 8

outer fringes, in Knowledge Space Theory 144

parentheses, in Answer Editor 21

Password, changing (UG) 171

Password, obtaining (UG) 167

PC requirements 5

PC requirements (UG) 166

pencil tool 26

percentages, entering 22

pie chart, interpretation of (UG) 169

pie chart, reduced 181

pie charts, multiple 30

plugin, downloading and installing 6

plugin, downloading and installing (UG) 172

practice page in Learning Mode 39

preparation for teachers 5

Print button 35

printing, problems 182

printing, procedure for 35

Program Editor, buttons 116

Program Editor, fields 116

Program Editor, using 116

Program Editor, what is 114

programs in ALEKS 183

programs, modifying 138

programs, what are 112

Progress button 79, 82

Progress in learning mode, Class Progress 57,83

Progress over last 3 months, Class Progress83

Progress over last 6 months, Class Progress83

Progress over last month, Class Progress 83

progress reporting in QuickTables 124

quick start 3

QuickTables, additional features 125

QuickTables, advanced options in 125

QuickTables 119

QuickTables, reporting in 124

QuickTables, setting up 119

QuickTables, student use 121

QuickTables (UG) 173

QuickTables, worksheets in 125

Quiz button, Advanced Teacher Module 91

Quiz button 36

quiz, class results 63

quiz, creating 70, 92

quiz, creating makeup 70, 92

quiz, deleting 71, 94

quiz, editing 71, 94

quiz, individual results 67

quiz (UG) 171

quizzes, availability of, Teacher Module 71,93

quizzes, grading with, Teacher Module 71, 93

quizzes, makeup 94

quizzes, viewing 91

Readiness pie chart 30

Ready to learn, Class Report 62, 87

ready to learn items, significance of 31

region tool 26

registration, authorization of 9

registration in ALEKS 8

registration in ALEKS (UG) 166

regularity of ALEKS use (UG) 173

renewing an ALEKS account (UG) 180

repeating decimals, entering 23

Report button, Advanced Teacher Module 81,86

Report button 35

reporting in QuickTables 124

Reporting, in Teacher Module 53

report style for Class Progress, Advanced TeacherModule 83

Report Tutorial 13

Request Assessment button 88

Results & Progress, Advanced Teacher Module75

review 42

Review button 36

review, extensive 42

reviewing past material (UG) 171

Schedule Assessment button 89

Scheduled assessment, Class Report 60

scheduled assessment menu 84

282 INDEX

scheduled assessments, grading with, AdvancedTeacher Module 90

scheduled assessments, grading with, TeacherModule 69

scheduled assessments, limiting, Advanced TeacherModule 91

scheduled assessments, limiting, Teacher Module69

scheduled assessments, message with, AdvancedTeacher Module 90

scheduled assessments, slices with, AdvancedTeacher Module 67, 90

School Admin, in Teacher Module 51

Selector (Advanced Teacher Module) 77

self-paced learning with ALEKS 134

Server Stats button 96

server usage 96

session control 34

set notation, entering 24

setting up QuickTables 119

setup guide for teachers 5

slices with scheduled assessments, AdvancedTeacher Module 67, 90

slowness, how to fix 181

small-group instruction with ALEKS 134

sorting in Class Progress 54, 84

Spanish translation 34

special keys, Answer Editor 20

square roots, entering 23

square roots with multiplier, entering 24

Standards & Programs, Advanced Teacher Module111

standards, what are 113

State standards report for an individual stu-dent 64, 82

State standards report for class 55, 86

State standards report (student account) 30

statistical information in Class Progress 54,84

Status options, class account 99

structure 137

student account, authorizing 105, 72

student account, editing 104, 49

student account, expiration date of 104

student assessment, canceling, Advanced TeacherModule 88

student assessment, canceling, Teacher Module70

student assessment, changing, Teacher Module70

student assessment, scheduling, Advanced TeacherModule 88

student assessment, scheduling, Teacher Module67, 70

student password, changing 104, 49

student progress, viewing, Advanced TeacherModule 79

student progress, viewing, Teacher Module 65

student reports, dating of 81

student report, viewing, Advanced Teacher Module81

student report, viewing, Teacher Module 66

students, grouping 85, 87, 91, 95

students, how to register 4

students, preparing for ALEKS 130

student, unenrolling 50

Student User Guide 165

support and consultation 163

system requirements 5

system requirements (UG) 166

Taking Actions, in Teacher Module 67

teacher account, creating 51, 97

teacher account, deleting 52, 98

teacher account, editing 49, 52, 98

Teacher Module, Advanced, access to 77

Teacher Module, Advanced 72

Teacher Module, Advanced, buttons in 114

Teacher Module, Advanced, editing programs114

Teacher Module, Advanced, entering 73

Teacher Module, Advanced, levels of privilege77

Teacher Module, Advanced, navigation anduse of 113

Teacher Module, Advanced, online help 78

Teacher Module, Advanced, Results & Progress75

Teacher Module, Advanced, Standards & Pro-

INDEX 283

grams 111Teacher Module, Advanced, tutorial for 72Teacher Module, Advanced, what is 75Teacher Module, basic interface 45Teacher Module 7Teacher Module, suggestions for use 127teacher password, changing 51teaching with ALEKS, suggestions for 127technical requirements 5technical requirements (UG) 166technical support 163textbook integration 101time to completion, current objective 54, 84topics mastered, complete list of 66, 82Total progress, Class Progress 59, 83troubleshooting 180Tutorial, Advanced Teacher Module 72, 75Tutorial, Advanced Teacher Module, return to

77Tutorial, purpose of 13Tutorial, purpose of (UG) 168typing input, problems 181Undo button, Answer Editor 20unenrolling a student 50unenrolling students from a class 103, 50units, answers with 23What students can do, Class Report 62, 87worksheet 43Worksheet button 36worksheets, answers to 43worksheets, creating for student 72worksheets in QuickTables 125worksheets, records of 43worksheets, viewing for student 72worksheet (UG) 171wrong answer page in Learning Mode 41

ALEKS - Manual for Educators K12 - August 2008

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Transcript of ALEKS - Manual for Educators K12 - August 2008