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Elementary Mathematics: Alaska Curriculum Guide.First Edition.Alaska State Dept. of Education, Juneau.Aug 85177p.; Support of the Model Curriculum Project wasprovided through a special grant from ECIA Chapter II(Block Grant).Cuides - Classroom Use - Guides (For Teachers) (052)

EDRS PRICE MF01/PC08 Pins Postage.DESCRIPTORS *Behavioral Objectives; Elementary Education;

*Elementary School Mathematics; *MathematicalConcepts; Mathematics Education; *MathematicsInstruction; *Mathematics Skills; State CurriculumGuides

IDENTIFIERS *Alaska

ABSTRACTThis curriculum guide lists mathematics topics and

concepts, learning outcomes, and sample learning objectives (in threecolumns) for grades 1 to 8. Topics/concepts, in the first column,describe the major parts of the subject under consideration. Theydefine broadly the content to be included in the study of eachsubject area. Learning outcomes, in the second column, describe, ingeneral terms, the behaviors students are expected to demonstrate asa result of their learning experiences. These outcomes are the goalstoward which student learning is directed. Sample learningobjectives, shown in the third column, are indicators of studentprogress toward the stated goals. At least one sample learningobjective is stated for each learning outcome. Included in anappendix is a table showing the grade-level placement for these topicareas (which are listed under the topics/concepts column): sets;whole numbers (counting and numeration); whole numbers (operations);fractions and decimals; fraction operations; measurement andestimation; geometry; math sentences; probability and statistics;graphs and scale drawings; problem-solving; calculators andcomputers; integers; and ratio, percent, and proportion. (JN)

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Reproducti*

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ons supplied by EDRS are the best that can be madefrom the original document.

t

ELEMENTARY MATHEMATICS

ALASKA CURRICULUM GUIDE

First Edition

Support of the Model Curriculum Project was provided througha special grant from ECIA Chapter II (Block Grant)

Alaska Department of Education

August 1985

1 3

ELEMENTARY MATHEMATICS

TABLE OF CONTENTS

Preface to the Series

PrefaceAcknowledgements

i

iv

vi

Grade 1 1

Grade 2 9

Grade 3 19

Grade 4 34

Grade 5 46

Grade 6 59

Grade 7 68

Grade 8 74

Appendix A

1

"Some measure of genius is the rightful inheritanceof every person '

Alfred North Whitehead

PREFACF TO THE SERIES

Among the many decisions that schools must make, none is more

important than the choice of curriculum. Curriculum defines the intent

behind instruction and the expectations for student performance. This

first field edition curriculum guide is one of a series intended to serve

as a model to aid school districts as they develop and review their own

curriculum documents. It is not intended that any of these field edition

guides be used directly by teachers for instructional purposes.

Districts are expected to develop their own locally suitable curriculum

based on these guides. Districts have or are developing their own

locally suitable curriculum using these guides as a base and point of

departure. In the future as schools use this material to plan and

implement programs, its value will be measured by the increased abilities

of students to learn, think, and perform as informed and productive

citizens.

In their present form these guides represent a synthesis of input

from many sources, both Alaskan and national. They were originally

prepared by staff at the Department of Education with the help of

professional content associations, Alaskan teachers and administrators.

An extensive review and revision process was conducted in 1984-85.

School districts, subject matter associations, other professional

associations, and interested individuals provided input to a revision

process that was contracted to the Northwest Regional Educational

Laboratory. A panel of nationally recognized curriculum specialists

assisted in the review of each content area. contributors to specific

guides are listed in the acknowledgements sections of those guides. In

i

5

one sense, these guides will never be finished. It is the intention of

the Department of Education that they be dynamic documents subject to

revision every few years as part of the six year curriculum review cycle

that was recently initiated by new curriculum regulations. Guides exist

in the areas of:

Kindergarten Fine ArtsLanguage Arts Social StudiesScience Computer EducationForeign Languages (Secondary) HealthMathematics Physical Education

The format of the guides is straightforward but not oversimplified.

Each guide lists topics/concepts, learning outcomes, and sample ledrninq

objectives in three columns. (In the case of Secondary Foreign Language,

the first column is headed topics/skills.)

Topics/concepts, in the first column, describe the major parts of the

subject under consideration. They define broadly the content to be

included in the study of each subject area.

Learning outcomes, in the second column, describe, in general terms,

the behaviors students are expected to demonstrate as a result of their

learning experiences. Learning outcomes are the goals toward which

student learning is directed.

Sample learning objectives, shown in the third column, are indicators

of student progress toward the stated goals, i.e., the learning

outcomes. At least one sample learning objective is stated for each

learning outcome. It is intended that the sample learning objectives are

just that: samples only. They do not constitute a learning Rrogram.

School districts generate their own locally applicable learning

objectives within the framework of their district topics/concepts and

learning outcomes.

6ii

1

The guides are grouped by grade level groupings (except Mathematics)

-- grades 1-3, 4-6, 7-8 for the elementary level, and 9-12 for the

secondary level. Mathematics is presented sequentially grade by grade.

Recognizing the unique characteristics of the five year old learner,

Kindergarten was prepared as a separate guide. In the development,

grades 7-8 were generally seen as the end of the elementary years, but

with some beginnings for the secondary level. On the secondary level the

guides generally contain discrete courses that would be offered; these

aa.e nut always tied to a particular grade level as the local district

must determine the most effective sequence for those courses.

The Alaska State Board of Education stated, "The Model Curriculum

G,:ides are intended to serve as a model, not a mandate." They

underscored the fact that a partnership between state and local school

districts is crucial. We seek to promote individual variation while

stressing the collective responsibility for educating all students in

Alaska. It is in this spirit that the Department of Education welcomes

the opportunity for continuous collaboration with those interested in the

further development and refinement of this entire series of guides.

iii 7

PREFACE TO

ELEMENTARY MATHEMATICS CURRICULUM GUIDE

The major goal of the Alaska Mathematics Curriculum Guide for

elementary students in grades 1-8 is to provide a set of related and

specific goals, instructional objectives and choice of essential subject

matter. This is done through an exemplary model that incorporates the

clearest and most viable ideas about mathematics and the teaching of

mathematics.

Specific goals of the Alaska Elementary Mathematics Curriculum Guide

have been developed to help young people do the following:

1. Use the language and symbolism of sets, set operations and their

properties.

2. Use the principles of inductive and deductive logic.

3. Measure things using specific units of measure.

4. Use the symbols, elements, operations and functions of whole

numbers, integers, rational numbers, real numbers and when

appropriate, complex numbers and finite and infinite systems.

5. Solve open sentences.

6. Solve problems using graphs, tables and mathematical statements.

7. Use problem identification, analysis, organization, evaluation,

application and generalization to solve real and everyday

problems.

8. Value the development of mathematical skills and knowledge.

9. Solve practical problems using mathematical sentences or models

and interpret the solution in the context of the problem.

iv

10. Use geometric definitions, postulates and theorems to solve

problems.

11. Compute using numbers and algebraic expressions.

12. Describe the importance of counting, measuring, mathematical

symbols and systems to historical and cultural development.

13. Use probability and statistics to solve problems.

14. Use calculators, computers, slide rules and other support

technology to solve problems.

The curriculum guide offers examples of how these skills can be

demonstrated within the learning environment: it is expected that local

districts will consider the outcomes and objectives in light of their own

curricular goals and educational program.

ACKNOWLEDGEMENTS

In preparing the Model Curriculum Guides, the Department of Education

requested and received copies of curriculum materials from school

districts in Alaska, the state's own Centralized Correspondence Study and

other state departments of education. The department thanks the

following school districts and state departments for submitting materials:

Alaska School Districts

Adak Galena . NenanaAnchorage Haines Nome

Annette Island Iditarod North SlopeBristol Bay Kenai Peninsula Northwest ArcticCopper River Ketchikan PelicanCordova Klawock RailbeltCraig Lower Kuekokwim- ValdezDelta/Greely Lower Yukon YakutatFairbanks Matanuska-Susitne

State Departments of Education

Alabama Maine South CarolinaArizona Minnesota South DakotaArkansas Maryland TennesseeCalifornia Nebraska TexasConnecticut Nevada UtahDelaware new Mexico VermontFlorida New York VirginiaIdaho North Carolina West VirginiaIlinois Oregon Virgin IslandsIndiana Rhode Island Guam

vi 10

The department appreciates the efforts of its staff who reviewed and

synthesized specific content area materials which resulted in this draft

Model Curriculum Guide. Contributors in elementary mathematics included:

Raymond Coxe

Margaret MacKinnonBrian Rae

The department also appreciates the efforts of members of the Alaska

Council of Teachers of Mathematics who reviewed and critiqued an earlier

draft of this Model Curriculum. Working within very tight timelines,

they provided useful and helpful suggestions for how the document could

be improved. People who were involved included:

Doris Ayres, Eagle RiverDwayne Craig, KenaiCheryl Girradot, PalmerFlo Larson, Kenai

Daryl Mannausa, SoldotnaAlicia Newman, AnchorageDennis Ostrander, SoldotnaLouise Petermann, AnchorageJames Seitz, AnchorageJames Simeroth, KenaiHolly Stephans, PalmerCaroline Valentine, AnchorageVirginia Walters, KenaiDorothy Zarelli, Eagle River

In addition, several persons contributed their time to reviewing the

1984 Elementary Mathematics Guide. Their comments and suggestions were

used to preparing the 1985 Model Mathematics Curriculum Guide. These

people ihclude:

Lyn Maslow, Bering Strait

Jerry S]olander, Alaska Pacific UniversityCarol H. Jerue, Iditarod Area S.D.Doris Ayers, A.C.T.M.Jim Seitz, A.C.T.M.Cheryl Girardon, A.C.T.M.Phyllis Marchese, C.C.S.

Margaret MacKinnon, C.C.S.

vii

11

The Northwest Laboratory's chief writer for this Elementary

Mathematics Guide was Leslie Crohn. Dr. Shirley A. Hill, University of

Mi:.isouri, Kansas City, was chief consultant to this NWREL team. Dr. Dana

Davidson was consultant on matters of child development. Project design

and management was by Dr. William G. Savard of NWREL's Assessment and

Evaluation Program. Dr. Gary Estes provided overall direction.

Special thanks are due to Gloria Lerma and Andrea Levy for their

cheerful and seemingly endless typing and management of details.

viii 12

A

ELEMENTARY MATH

GRADE 1

TOPIC/CONCEPT LEARNING OUTCOME

The Learner will:

SETS Understand set attributes, equivalencyand number.

WHOLE NUMBERS COUNTINGUnderstand concepts related to counting,

reading and writing numbers 0-99.

13

SAMPLE LEARNING OBJECTIVE

The Learner will:

Tell which taings are members of a setand which things are not, given a pictureof a set.

Demonstrate a one-to-one matching betweenmembers of t.4,o equivalent sets.

Identify sets as equivalent ornonequivalent; tell which set has fewerand which set has more members.

Describe a set with no members, such as aset of elephants in the classroom.

Identify a subset of a given set.

Count and name the numbers of a given set.

Identify 0 as the number associated withthe set with no members (empty set).

Identify the numbers which immediatelyprecede and follow a given number.

Arrange ten nonequivalent sets in orderof cardinal size.

1 14


The Learner will:

WHOLE NUMBERS - COUNTING (Cont.)

15

ELEMENTARY MATHGRADE 1

Know the ordinal numbers first throughtenth.

Know place value of two-digit numerals.

Understand the concept of odd and evennumbers.

2

SAMPLE LEARNING JBJECTIVE

The Learner will:

Recite the first 100 counting numbers inproper order.

Identify and read numerals for wholenumbers 0-99.

Read and write number words one throughten.

Order numbers such as 47 and 95 bysaying, "47 is less than 95".

Identify the position of objects orevents using first through tenthpositions.

Identify the numerals in the ones placeand numerals in the tens place, given alist of two-digit numerals.

Identify and name odd and even numbers.


TOPIC/CONCEPT LEARNING OUTCOME SAMPLE LEARNING OBJECTIVE

The Learner will: The Learner will:

WHOLE NUMBERS - OPERATIONSUnderstand addition and subtractionfacts with sums through 18.

17

Understand column addition andsubtraction with no regrouping.

Understand the commutative propertyof addition (the sum of two numbers isnot affected by reversing their order).

3

Construct sets, combine and removesubsets to determine sums and differences.

Demonstrate addition and subtraction byusing sets or a number line.

Name the sum or difference of an additionor subtraction fact through sums of 18.

Find the sums and differences forproblems with two-digit numerals that donot require regrouping.

Use sets or a number line to demonstratethe commutative property of addition.

18


The Learner will:

WHOLE NUMBERS - OPERATIONS (Cont.)

FRACTIONS

V-


Understand the associative property ofaddition (the sum of three numbers isindependent of the way in which the numbersare grouped or paired for adding).

Understand the identity element foraddition (the number which does not changethe value when the operation of addition isperformed; for addition, this number is 0).

Know how to solve simple word problems.

Understand the fractions 1/2, 1/3,and 1/4.

4


The Learner will:

Use sets or a number line to demonstratethe associative property of addition.

Use sets or a number line to demonstratethe identity element for addition.

Solve simple oral or written one-stepword problems involving addition andsubtraction of one-digit numbers.

Identify and name the fractions 1/2, 1/3and 1/4, given models.

Construct models for 1/2, 1/3, and 1/4.



The Learner will:

MEASUREMENT AND ESTIMATION

Understand appropriate uses basic

units of measure.

Know how to tell time and count money.

21


The Learner will:

Measure an object by counting the numberof units needed to match the length ofthe object, using counters such as sticks

or tongue depressors.

Compare the lengths of various objects inthe roam by estimation, and then bymatching to measure which is longer, andwhich is shorter.

Weigh a set of objects and identify theheaviest and lightest, using a scale.

Measure distances and heights usingnonstandard units of measure.

Answer questions such as the following:"How can you tell if it is warmer insideor outride the classroom?".

Tell tine on the hour.

Name the months of the year.

Name the days of the week.

22

ti




MEASUREMENT ANDESTIMATION (Cont.)

GEOMETRY

2 3

Understand relative positioli, size andnames of basic geometric shapes.

6

Identify and name pennies, nickels anddimes and tell the value of each coin incents.

Select coins needed to solve simple wordproblems related to money.

Identify objects as in front of, behind,below, on or above other objects.

Identify objects that are inside,outside, or are a boundary of otherobjects.

Identify objects as larger, smaller orabout the same size as other objects.

Distinguish among basic geometric figures.

Name basic geometric figures.

Classify models or figures with roundedand straight sides into two groups.

Identify and name edges, corners andfaces of objects.


TOPIC/CONCEPT LEARNIVG OUTCOME SAMPLE LEARNING OBJECTIVE


GEOMETRY (Cont.)

PROBABILAY AND STATISTICS

Understand data gathering and simplegraphs.

Understand chance and probability.

PROBLEM SOLVINGUnderstand simple patterns.

257

Draw basic geometric figures.

Collect, organize and graph a variety ofdata related to personal experiences, andpreferences.

Tally information in games and classroomactivities.

Use blocks and pictographs to recordinformation.

Discuss situations which involve the

likelihood of events happening.

Predict and record the outccmes of coin

tossing.

Recognize a pattern; describe and extend

it.

26

DOPIC/CCNCEPT LEARNING OUTCOME

The Learner will:

PROBLEM SOLVING (Cunt.)

CALCULATORS ANDCOMPUTERS

2'7


Use a computer as a learning tool.(See also Computer Education CurriculumGuide.)

8


The Learner will:

Estimate or guess a solution to a givenproblem and test the solution foraccuracy.

Play computer mathematics games.

0


TOPIC/CONCEPT LEARNING OUTCOME SAMPLB LEARNING OBJECTIVE


SETSUnderstand one-to-one correspondence,set equivalency, empty set, subsets

and set union.

WHOLE NUMBERS - COUNTINGUnderstand concepts related to counting.reading and writing numbers 0-99.

29

Demonstrate one-to-one matching between

members of two equivalent sets in more

than one way.

Identify two sets as equivalent ornonequivalent; tell which set has more

and which set has fewer members; write

number sentences to describe the sets.

Describe and generate a set which has no

members.

Identify a subset of a set.

Remove a subset from a given set ofelements and get a remaining subset.

Associate a numeral with a set that namesthe number of elements in the set.

Identify the numbers which immediatelyfollow and precede a given number.

9 30

31



The Learner will:


Know cardinal numbers 0-100.

Know the ordinal numbers first throughtwentieth.

Understand place value.

10


The Learner will:

Count by 2s and 58 to 100.

Count by 100s to 1,000.

Identify, read and write numerals forwhole numbers 0-99.

Group the members of a given set by ones,twos, fives, and tens by counting howmany members are in the set.

Identify, name, read and write numerals0-999.

Read and write number words throughtwenty.

Compare two whole numbers, each less than1,000, by telling which is greater orless than the other.

Write whole numbers in order from leastto greatest and from greatest to least.

Identify the position of objects orevents using first through twentiethpositions.



The Learner will:


Understand the concept of odd and even

numbers.

WHOLE NUMBERS - OPERATIONSKnow how to add and subtract wholenumbers.

33

11


The Learner will:

Identify the numerals in the ones, tensand hundreds places, given a list ofthree-digit numerals.

Write the expanded version of a given

numeral, 0-1000.

Identify and name odd and even numbers,

0-1000.

Solve an addition or subtraction problemusing sets on a number line and name thesum or difference of the numbers.

Write two addition and two subtractionfacts to describe a set.

Name, using immediate recall, the sum ordifference of an addition or subtractionfact through sums of 18.

Name, using immediate recall, sums anddifferences in problems written in bothhorizontal and vertical notation.

34


The Learner will:

WHOLE NUMBERS OPERATIONS (Cont.)

35



The Learner will:

Understand column addition andsubtraction of three-digit numerals.

Name the sums and differences forproblems with three-digit numerals.

Know how to use regrouping to solveproblems.

Name the sums and differences forproblems with too-digits using regrouping.

Understand the commutative propertyof addition (the sum of two numbers is notaffected by reversing their order).

Write addition equations to describe thecommutative property.

Understand the associative propertyof addition (the sum of three numbers isindependent of the way in which the numbersare grouped or paired for addition).

Write and solve an addition equationusing the associative property.

12

w r r

ELEMENTARY MATH

GRADE 2


The Learner will:

WHOLE NUMBERS OPERATIONS (Cont.)

Understand the identity element foraddition (the number which does not changethe value when the operation of additionis performed; for addition, this number is 0).

FRACTIONS AND DECIMALSKnow how to read and write the fractionalnumeral.

MEASUREMENT AND ESTIMATIONUnderstand appropriate uses for basicunits of measure. (See also ScienceCurriculum Guide.)

37

13


The Learner will:

Solve equations using the identityelement.

Identify, name, read and write a numeralfor the fraction that is represented by aphysical model.

Identify and represent halves, thirds,fourths and tenths by parts of sets andon a number line.

Measure an object, using a suitable unitof length, by counting the number ofunits needed to r tch the length of theobject.

Use appropriate terms of measurement.

38



The Learner will:

MEASUREMENT AND ESTIMATION (Cont.)

Know how to estimate.

Know how to tell time and count money.

14


The Learner will:

Measure a line segment to the nearestwhole unit

Measure and compare the capacity of acontainer to the nearest whole unit.

Determine which of two objects isheavier, using a simple balance.

Give the weight of an object using asimple scale.

Record temperatures inside and outsidethe classroom.

Determine if the temperature is warmer orcooler than the previous day.

Estimate length within reasonable limits.

Tell time on the hour and half hour.

Tell time in terms of days, weeks andmonths.

Interpret a calendar.


The Learner will:


GEOMETRY

41

ELEMENTARY MATH

GRADE 2

Understand basic geometric shapes.

15


The Learner will:

Tell the value of a set of coins in centnotation.

Tell if a set of coins (values to $1.00)is enough to purchase a given object.

Name pennies, nickels, dimes and quartersand state the value of each coin in cents.

Solve simple addition or subtractionmoney problems for amounts up to $1.00.

Determine what foods to buy for a mealand how much the foods cost given agrocery advertisement and play money.

Identify and name circles, triangles,line segments and number lines.

Identify and name cylinders and cones.

Group a set of objects containing balls,boxes and cylindrical-shaped objectsaccording to shapes and tell whichattributes were used.

Describe a line segment or curve as a setof points.

Describe a atraighc line as a set ofpoints with no beginning and no end.




GEOMETRY (Cont.)

MATH SENTENCES

43

Understand math sentences.

(See also Language Arts Curriculum Guide.)

16

Describe a simple curve as one that doesnot cross itIself.

Identify and name closed and open simplecurves.

Identify the inside and outside of simpleclosed figures.

Select figures which are congruent.

Draw models of line segments which arecongruent to the original model.

Draw a square, rectangle and triangleusing a straightedge.

Draw a number line and label whole numberpoints, using a ruler.

Draw a line segment of given length usinga ruler.

Write an open sentence which models astory problem and find the solution setfor it.


The Learner will:

PROBABILITY AND STATISTICS

GRAPHS AND SCALE

DRAWINGS

45


Understand data gathering and simple

graphs.

Know how to read a map.

(See also Elementary Social StudiesCurriculum Guide.)

17


The Learner will:

Arrange collected data in tables and

illustrate the data with bar graphs.

Interpret a simple bar graph or

pictograph.

Explain how to tally information in gamesand other classroce situations.

Play probability games and describe theresults.

Make a simple map with miles indicatedbetween towns or villages.

Make up word problems to find theshortest route, how far from one place toanother, etc.

46



PROBLEM &AXING

The Learner will:

Know how to solve problems.

Know how to make math sentences todescribe problem solving situations.(See also Language Arts Curriculum Guide.)

Know how to use estimation for solvingproblems.

CALCULATORS ANDCOMPUTERS Use a computer to solve problems.

(See also Computer Education Curriculum Guide.)

4718


The Learner will:

Complete a pattern of shapes in a drawing.

Group objects based on common ay.tributes.

Complete a simple number pattern.

Solve a number sentence for a one-stepstory problem.

Choose the appropriate operation(addition or subtraction) to solve anumber sentence which describes anillustration.

Use estimation or "guess and check'

techniques to solve measurement problems.

Use a computer to solve problemsinvolving sets.

48




SETSUnderstand set concepts and basicprinciples of sets.

WHOLE NUMBERS - COUNTINGAND NUMERATION

49

Understand concepts related to counting,reading, writing and recognizing numbers.

19

Explain how to use clearly definedattributes to distinguish between membersof a set and things which are not members.

Demonstrate the equivalency of two setsby comparing the cardinal numbers of each.

Tell how many more or how many fewermembers in nonequivalent sets.

Identify subsets of sets.

Remove a subset of elements fran a givenset and get another subset.

Identify the numbers which precede andfollow a given number, 0-10,000.

Read and write number words through ninehundred and ninety-nine.

50




WHOLE NUMBERS - COUNTINGAND NUMERATION (Cont.)

Understand the order relationshipsbetween large numbers.

51

Understand ordinal numbers beyond

twentieth.

Understand place value up to four digits.

20

Write a set of whole numbers in orderfrom least to greatest and from greatestto least.

Write the symbols, 'Pi<to express the relationship between twogiven numbers.

Identify the position of a particularobject or event, using more than 20objects or events.

Identify and name the numerals in ones,tens, hundreds and thousands places,given a list of four-digit numerals.

Write the expanded version of afour-digit numeral.




WHOLE NUMBERS - COUNTING

AND NUMERATION (Cont.)

Know Roman numerals through XV.

Understand the concept of odd and even

numbers.

WHOLE NUMBERS - OPERATIONS

53

Know how to add and subtract wholenumbers using standard algorithmsin both regrouping and nonregroupingsituations.

21

Write the Roman numerals for numbers less

than 15.

Write the Arabic numbers for Ramannumerals less than XV.

Identify and name cdd and even numbers to

10,000.

Write the two related subtractionequations of an addition equation.

Check subtraction problems using addition.

54





(Cont.)

55

Understand the commutative property ofaddition the sum of two numbers is notaffected by reversing their order).

Understand the associative propertyof addition (the sum of three numbers isindependent of the way in which the numbersare grouped or paired for addition).

22

Name the sums and differences forproblems (four-digit numerals) without:

regrouping.

Identify and name suns, differences,missing addends and missing operationalsigns in problems written in bothhorizontal and vertical notation.

Use mental arithmetic to compute sums anddifferences less than 100.

Solve equations with sums to 10,000 usingthe commutative property.

Indicate the grouping of addends whichwill make the addition easiest for agiven problem.

ELEMENTARY MATHGI ADE 3



WHOLE NUMBERS - OPERATIONS(Cont.)

57

Understand the identity element foraddition (the number which does not change thevalue when the operation of addition isperformed; for addition, this number is 0).

Understand multiplication and divisionof whole numbers and their relatedproperties.

23


Use pictures or objects to show thecombination of sets; determine and nametne product of the numbers.

Divide a set of objects into equivalentsubsets; name how many subsets can beformed.

Design a simple experiment involving setpartition to determine and name thequotient of a division problem.

Demonstrate inverse relation ofmultiplication to division.

Identify and name products and quotientsin problems written in both horizontaland vertical notation.

58




WHOLE NUMBERS - OPERATIONS(Cont.)

Understand the identity element formultiplication (the number which does notchange the value when the operation ofmultiplication is performed; for

multiplication, this number is 1).

Understand the multiplication propertyof zero.

Understand the distributive property ofmultiplication over addition (the number tobe multiplied can be renamed and the operationcan then be performed in two steps:

for example, 2x32=2x(30+2)2,(2x30)+(2x2)).

Know how to solve word problems.

59

Solve equations using the associativeproperty of multiplication to simplifycomputations.

Solve equations using the identityelement for multiplication.

Solve equations using the property of

zero.

Demonstrate the distributive property byusing sets.

25 60


TOPIC /CONCEPT LEARNING OUTCOME SAMPLE LEARNING OBJECTIVE



(Cont.)

FRACTIONS AND DECIMALS

Know how to read and write fractionalnumbers and equivalent fractions.

Understand fraction operations.

6126

Solve one-step word problems involvingmultiplication of a one- or two-digitnumber by a one-digit number.

Identify, name, read and write a numeralassociated with the model of a fractionwith a denominator lees Lhan 12.

Construct and identify models forfractions with denominators 2-12.

Determine whether two fractions areequivalent by using sets or pictures.

Identify fractions that are equivalent toone, using concrete objects or models.

Write the symbols se, , 7 , to

express the relationship between twofractions having the same denominators.

Add and subtract fractions with likedenominators.

Determine and name the sum of twofractions with the same denominators(less than 12).

62

TOP IC /CONCEPT LEARNING OUTCOME

The Learner will:


63


Know how to measure using units of

length, time, money, capacity,temperature, perimeter, area and

weight.

27


The Learner will:

Select a suitable unit and count tomeasure the length of the object.

Tell time to the nearest minute.

Measure time in terms of days, weeks,months and years.

Name and state the value of all U.S.

coins and bills.

Determine the total value in decimalnotation of pictures of coins and billsof different denominations.

Measure the length of an object to thenearest half unit (inch, foot, yard,centimeter, meter).

Find the perimeter of a figure bymeasuring the length of its sides.

Determine the area of a given region bycounting the number of square unitsneeded to cover the region.

64



The Learner will:


Know how to express relationshipsbetween units of measure.

28


The Learner will:

Determine the volume of a givenrectangular space by counting the numberof cubic units needed to fill the space.

Measure the surface of a rectangle.

Measure and compare capacity (volume).

Determine which of two objects isheavier, using a balance.

Determine the weight of a given objectusing a scale.

Record inside and outside temperaturesusing a thermometer; identify freezingpoint and boiling point. (See also

Science Curriculum Guide.)

Use terms, abbreviations and symbols forunits of measurement.

Estimate length and weight using standardunits, within reasonable margins of error.

Rename a measure in other units withinthe same system.




GEOMETRYKnow how to identify simple planegeometric and space figures.

Understand congruency.

Understand symmetry.

Understand similarity.

MATH SENTENCESKnow how to write and solve math

sentences.

517

29

Identify and name two-dimensionalgeometric figures.

Identify and name cubes, spheres,cylinders and cones.

Find examples of lines that appear to beparallel, such as railroad tracks,telephone lines, or lines on a paper.

Match angles to determine which arecongruent.

Choose figures which possess linesymmetry.

itligLIfi squares and triangles thatpossess similarity.

68



The Learner will:

MATH SENTbNCES (Cont.)


Understand data gathering and simplegraphs.

Understand simple probability.

Understand simple permutations.

30


The Learner will:

Solve open sentences using the additionfacts for whole numbers with sums lessthan or equal to 999.

Use < ,,P,sentences.

to make true number

Classify types of sentences as open, trueor false; correct or answer the false andopen sentences.

Construct a bar graph.

Interpret a bar, circle and picture graphand identify which quantities in each,rapt are larger or smaller.

Predict the outcomes of experiments,perform the experiments and compareresults with predictions.

Count the number of possible arrangementswithin a set, using concrete objects;record the arrangtaients.


LEARNING OUTCOME SAMPLE LEARNING OBJECTIVE


TOPIC/CONCEPT

GRAPHS AND SCALE

DRAWINGS Know how to read and make graphs and charts.

Know how to make and read maps.(See also Social Studies Curriculum Guide.)

PROBLEM SOLVING

Know how to use patterns and sequencesto solve problems.

71

31

Make a chart to keep a record 3f daily

weather.

Make a chart or graph to keep a record of

achievement in some area.

Use introductory computer graphicsprograms such as Deer, Drawing, MECCpictures and LOGO. (See also Computer

Education Curriculum Guide.)

Draw a map of an imaginary town,including a scale; measure the distancebetween various locations,

Continue a pattern of numbers,subtrActive or additive, in increments of

five or less.

72



The Learner will:

PROBLEM SOLVING (Cont.)


The Learner will:

Know how to use diagrams as an aid toproblem solving.

Interpret and find solutions for word andpicture problems.

Know how to use estimation and "guessand check" methods for solving problems.

Know how to restate a problem.

Estimate answers in problem solving andcomputation problems.

Estimate or guess a solution to a problemand test that solution.

Restate a problem in his or her own words.

Make up a word problem using everydaysituations. (See also Language ArtsCurriculum Guide.)

Know how to formulate math statementsto describe problem situations.

Find an answer to a problem bysimplifying an expression or formulatinga math statement.

32





Know how to use simple calculating devices.(See also Computer Education CurriculumGuide. )

Know how to use the computer to solve problems.

Use a hand calculator to add or subtract.

Use programming readiness programs suchas Face Maker, Creature Creator andMuggles.

75 76






`77

Understand concepts related to counting,reading, writing and recognizing numbersand their order.

Understand place value to six digits.

34

Join two or more sets and get a third set.

Remove a subset from a given set ofelements and get a remaining subset;write the number sentence that describesthis process.

Identify, name, read and write five ormore different names for the same number.

Identify, name, read and write numeralsfor whole numbers, 0-100,000.

Order a set of whole numbers from largestto smallest or from smallest to largest.

Identify a number as cardinal or ordinal.

Identify and name the values of digitsthat are in ones, hundreds, thousands,ten-thousands and hundred-thousandsplaces given a list of six-digit numerals.



The Learner will:

WHOLE NUMBERS - COUNTING AND

NUMERATION (Cont.)

Understand nondecimal numeration.

Understand the concept of odd and

even numbers.


Know how to add and subtract whole

numbers using standard algorithms.

Understand the commutative andassociative properties of addition (asdefined in previous grades).

79

35


The Learner will:

Write the expanded numeral of a base ten

numeral (decimal), 0-1,000,000.

Write the Roman numeral for an Arabicnumeral, 0-500.

Write the Arabic numeral for a Romannumeral up to D.

Find sums and differences for problemsusing odd and even numbers.

Check subtraction problems by writingrelated forms of the problems in addition.

Use mental arithmetic to compute sums and

differences less than 100.

80


mhe Learner will


t; 81


Understand multiplication and divisionof whole numbers.

36


The Learner will:

Find the sum of an addition problem withthree to six addends by renaming andrearranging the addends using thecommutative and associative properties.

Use sets or a number line t' findproducts or quotients.

Show how to find products and quotientsthrough repeated addition or subtraction.

Write two multiplication and two divisionequations to describe a physicalsituation.

Name, using immediate recall, products orquotients through 81; use a number lineas proof.

Name the products for problems up tothree digits.


The Learner wIll:


83


Understand the commutative property ofmultiplication using one-digit numerals(as defined ia previous grades).

Understand the associative property ofmultiplication using one-digit numerals(as defined in previous grades).

Undeirtan.: the identity clement for

multiplicatiop lsing one-digitnumerals (as le_ined in previous grade-).

Understand the multiplicative propertof n.

Understand the distributive property ofmultiplication over addition (as defined ingrade 3).

37


The Learner will:

Solve equations usin; the commutative

property of multiplication and one-digitnumerals.

Solve equations using the associativeproperty of multiplication and one-digitnumerals.

Solve equations using the identityelement for multiplication and one-digitn. (erals.

Solve equations using the property of 0.

84

TOPIr/CONCEPT LEARNING OUTCOME

The Learner will:'


FRACTIONS ANDDECIMALS

85


Understand fractional numbers, equivalentfractions, :improper and mixed fractions.

Understand decimal fractions tohundredths.

Understand place value of fractions.

38


The Learner will:

Demonstrate the distributive propertyusing sets.

Identify, name, read and write thefraction and/or the mixed numeral for thenumber associated with a given fraction.

Write a set of fractions which areequivalent.

Rename a given fraction in simplest form.

Name two fractions with like denominatorsand write the symbols 7,/c,=:,to express the relationship between them.

Identify, name, read and write a decimalfraction for a given model.

Identify, name, read and write givendecimal fractions with common fractionshaving denominators of 10 or 100.


The Learner will:

FRACTIONS AND

DECIMALS (Cont.)

Know how to order fractions.

FRACTION OPERATIONS


Know how to add and subtract fractionsor decimals.


87

Understand the following units ofmeasurement: length, area, capacity,tine, money, weight, temperature.

39


The Learner will:

Name the place value for each digit in adecimal fraction to the hundredths place.

Order decimal fractiors up to tenthsplace.

Name the suss or differences of twofractions or decimal fractions.

Add and subtract decimal fractions to thehundredths place, including expressionsof money.

Select a suitable unit and/or measuringdevice and measure physical property.

Tell and write time to the nearestminute, showing e 2. and p.m.

88



The Learner will:



The Learner will:

Count money and make change up to $25.00.

Use various m-asuring devices to measurelength in whole and fractional parts ofunits.

Find the perimeter of a polygon by addingthe measures of the sides.

Measure the capacity of a containerwithout using a formula.

Give the weight of an object to thenearest pound (kg.), using simple scales.

Give the temperature in Fahrenheit andCelsius to the nearest degree usingthermometers. (See also ScienceCurriculum Guide.)

Use appropriate terms, abbreviations andsymbols for the units of measurement inboth English and metric systems.


TOPIC /CONCEPT LEARNING OUTCOME

The Learner will:

MEASUREMENT AND ESTIM\TION (Cont.)

Know how to estimate measures.

GEOMETRY

91

Understand the relationship betweenunits of measure.

Know how to identify simple planegeometric and space figures.

41


The Learner will:

Estimate length, weight and capacityusing standard units of measure.

Convert units of measure into other unitsof the same system.

Distinguish among isosceles, equilateraland right triangles.

Identify the diagonal of a square or

rectangle.

Define Due and plane.

Identify simple closed curves andinterior and exterior regions of planefigures.

Fill the interior space of a simple solidfigure with unit cubes to determinevolume.

92

TOP IC, CONCEPT

GEOMETRY (Cont.)

93


LEARNING OUTCOME SAMPLE LEARNING OBJECTIVE


Know how to construct basicgeometric figures.

Know how to graph on a number lineor coordinate plane.

42

Draw and label lines, line segments,rays, angles, polygons and quadrilateralsusing a straightedge and compass.

Construct a right angle and righttriangle using a straightedge and foldedpaper.

Construct a circle, given the radius.

Draw intersecting and perpendicular lines.

Explain and demonstrate that points in aplane (the first quadrant) can berepresented by ordered pairs of numbers(coordinates).

Plot ordered pairs on a coordinate plane(first quadrant).

Graph a set of num,rs on a number line.

94




GEOMETRY (Cont.)

MATH SENTENCES

Know how to measure geometric figures.

Elow how to write and solve mathsentences.

PROBABILITY AND STATISTICSKnow how to gather data, make simple

graphs and average.

Understand simple permutations.

95

43

Find the perimeter of a polygon by addingthe measures of the sides.

Translate an English sentence into amathematical sentence and solve.

Use information from charts and tables tosolve problems.

Construct simple bar, line, picture and

circle graphs.

Solve problems that involve a systematicidentification of ordered arrangementsusing models, picturer, lists or diagramsto orertnize data.

96



PROBLEM SOLVING

The Learner will:

Understand patterns and sequencesin problem solving.

Know how to identify relevant andnonrelevant information in problemsol 'ng.

Understand the role of estimation inproblem solving.

Know how to restate a problem.

41


The Learner will:

Continue a pattern of numbers involvingmultiplication or division and with fiveor fewer factors.

Solve problems involving the four basicmathematical operations, using data fromcharts, tables, graphs and maps.

Create word problems from a socialstudies or science text that can besolved with a mathematical operation.

Tell when information is insufficient tosolve a problem.

Explain how to use estimation as a toolfor solving a problem.

Restate a problem in his or her own wordsand select the data and operationsnecessary for solving the problem. (See

also Language Arts Curriculum Guide.)


The Learner will:

PROBLEM SOLVING (Cont.)


99


Know how to operate a hand calculator.(See also Computer Education Curriculum

Guide.)

Know how to use software and hardware tosolve problems.

45


The Learner will:

Express a solution in a form compatiblewith a problem context.

Demonstrate how to add, subtract,multiply and divide on a hand calculator.

Use a computer to perform calculations.

100






101

Understand concepts related to counting,reading, writing and recognizingnumbers and their order.

Understand place value to ten digits.

46

Identify the set that is the union and

the set that is the intersection of twogiven sets.

Define finite, infinite and empty sets.

Construct a Venn diagram that illustratesthe relationships between two or three

given sets.

Identify, name, read and write numerals

for whole numbers 0-1,000,000.

Used, 7, i to express therelationship between numbers up to

1,000,000.






103


Know how to round and estimate whole

numbers.

47

Identify and name place value for each

digit in a base ten (decimal) numeral.

Write the expanded numeral usingmultiples of 10 for numerals up to

1,000,000.

Write the Roman numeral for numbers up to

1,000.

Write the Arabic number for a Raman

numeral up to M.

Round a whole number to any place, up to

1,000,000.

Estimate the sum, difference, product, orquotient of whole numbers.

104






Understand factors and multiples.

Understand primes and composites.

WHOLE NUMBERS - OPERATIONSKnow how to add and subtract wholenanbers using standard algorithms.

1L3

48

List all factors of any whole number less

than 100.

Name the leas._ common multiplier (LCM) of

two whole numbers less than 20.

Classify whole numbers greater than 1 andless than 100 as prime or composite.

Name the sums and differences forproblems with numerals up to 1,000,000.

Use mental arithmetic to computereasonable sums and differences less than

1000.

1'.

TOPIC/COWEPT LEARNING OUTCOME

The Learner will:


107


Know how to use the commutative andassociative properties of addition andmultiplication (as defined in previous .

grades).

Know how to multiply and divide wholenumbers using standard algorithms.

49


The Learner will:

Find the sum and product of a problemwith three or more addends or factors inthe easiest way by using the commutative

and associative properties.

Write the two related division equations

of a multiplication equation.

Name the products for problems usingfour-digit factors by three-digit factors.

Name the quotients and remainders forproblems with five-digit dividends andtwo-digit divisors with and without

remainders.

108



The Learner will:



Understand fractional numerals,equivalent, improper and mixedfractions.


1u9

50


The Learner will:

Use the short algorithm (short divisionform) to find quotients and remaindersfor problems with four-digit aividendsand one-digit divisors with and withoutremainders.

Use the distributive property formultiplying two digits times one digitproblems.

Identify, name, read and write fractionsthat are pictured or modeled.

Name the numerators and denominators of agiven list of fractions.

Rename an improper fraction as a mixednumber and vice versa.

Write a set of fractions that areequivalent to a given fraction.

Order up to five fractions from least togreatest or from greatest to least. 110



The Learner will:

FRACTIONS AND DECIMALS (Cont.)

Understand decimal fractions to

thousandths.

FRACTION OPERATIONSKnow how to add and subtract fractionsusing standard algorithms.

111


The Learner will:

Identify, name, read and write decimalfractions having denceinatora of 10, 100,

or 1000.

Name the place value for each digit in a

list of decimal fractions up to thethousandth place.

Round decimal fractions to the nearestwhole number, tenth or hundredth.

Find the sum or difference of fractionsusing a model.

Check subtraction of fraction problemsthrough addition.

Estimate the sum or difference of twofractions'to the nearest whole number.

Use the commutative and associativeproperties to add and subtract fractions.

11251

113



The Learner will:

FRACTION OPERATIONS (Cont.)

Know how to multiply fractions usingstandard algorithms.


Understand the process of measurement.

52


The Learner will:


Multiply fractions and find the productsusing a multiplication model.

Solve equations giving the products inlowest terms and written as whole numbersand fractions.

Check division problems throughmultiplication.

Use the nommutative and as:;f:ciativeproperties to simplify computations.

Determine local time for cities in theU.S.: explain the concept of time zones.

Measure time in seconds, minutes, hours,days, weeks, months, years, &Jades andcent4ries.

Compute math problems that involve money.

114


The Learner will:


115


Understand the relationships betweenunits of measure.

S3


The Learner will:

Measure length in whole and fractionalunits using various measuring devices.

Compute the perimeter of a polygon.

Give the temperature to the nearestdegree in Celsius and Fahrenheit.

Give the freezing and boiling points ofwater in English and metric units.

Use the appropriate terms, abbreviationsand symbols for unite of measurement.

Estimate length, weight, capacity, time,temperature and money.

Rename a measure in other units.

Compute a measurement problem, and renamethe result if necessary.

116

ELEMENTARY. MATH

GRADE 5



GEOMETRY

Know how to identify and measuresimple plane figures.

Know how to identify simple spacefigures.

Understand symmetry.

Understand. congruency.

Understand intersecting andperpendicular lines.

54

Define plane geometric figures.

Read and write standard notation forplane figures.

Define and measure an angle using aprotractor.

Distinguish among models of commonpolyhedra.

Define symmetry as it relates to pointand line.

Identify pairs of line segment3, angles,triangles or other polygons as congruentor not congruent.

Sketch, describe and give examples ofintersecting and perpendicular lines.


GEOMETRY (Cont.)

MATH SENTENCES

119




Know how to construct and bisectplane figures.

Know how to measure gecmetric figures.

Understand math sentences of greatercomplexity.

55

Construct and label models of lines, linesegments, rays, angles, and polygonsusing a straightedge.

Bisect a given line segment and angleusing a straightedge and compass.

Construct a circle with a given centerand radius or diameter, using a compass.

Measure the circumference and diameter of

cutout circles; explain the relationshipbetween circumference and diameter.

Use 7 ,4;, i to make true number

sentences.

Classify types of sentences as true or

false.

Translate an English sentence into amathematical sentence and solve.




PROBABILITY ANDSTATISTICS

Understand data gathering and

organization.

Understand probability.

Compare bar, line and picture graphswhich represent the same information;exrimin the advantages and disadvantagesof each form.

Analyze collected data according to range

and mean.

Make predictions based on simple data andverify the predictions with furtherexperiments or additional research.

Conduct probability experiments, using anincreasing number of trials to obtainmore reliable results.

Identify events that are impossible andrelate them to a probability of zero.

Identify events that are certain andrelate them to a probability of one.

Conduct an experiment using random and

unbiased samples.



GRAPHS AND SCALE

.DRAWING

PROBLEM SOLVING

The Learner wv

Know how to construct picture, barand line graphs.



The Learner will:

Coltruct picture, bar and line graphsgiven suitable data.

Use the number linl to represent positiveand negative integers.

Construct a double bar graph.

Record statistical data on tables orgraphs, indicating change.

Use data from charts, tables, graphs,tree diagrams and maps to solve problems.

Tell when information is insufficient tosolve a problem and irrelevant to theproblem.

Use rounding to estimate results for wordproblems.




PROBLEM SOLVING(Cont.)

CALCULATORS AND

COMPUTERS

125

Know how to write computer programs tosolve problems. (See also Computer EducationCurriculum Guide.)

Know how to use calculating devices.

Se

Choose items from a catabn and calculatetheir cost including postage, handlingand other expensee.

Calculate the balance in a checkingaccount using bank statements, bankdeposit slips and bank checks.

Program and use the computer to creategraphics.

Program and use the computer to performarithmetic operations.

U60 a calculator to add, subtract,multiply and divide whole numbers and

decimals.

ELEMENTARY KATE(

GRADE 6

TOPIC/CONCEPr LEARNING OUTCOME SAMPLE LEARNING OBJECTIVE



AND NUMERATIONUnderstand concepts related tocounting, reading, writing andrecognizing numbers and theirorder.

Understand place value.


127

59

Write the number words and Arabicnumerals for numbers up to 15 digits.

Write a subset of whole numbers in orderfray least to greatest.

Name the wriod value for each group ofthree digits and place value for eachdigit of a base ten numeral.

Write a six-digit numeral in expandednotation.

Describe the difference between Roman and

Arabic nmerals, including place value.

Describe the cardinal number of a set ofelements (0-100) in a base other than 10.

Write a decimal numeral in a different

base.

128






Know how to round and estimate wholenumbers.

129


Understand prime numbers and composites.

60

Round a seven-digit numeral.

Estimate sums, differences, products andquotients of whole numbers.

List all factors of any whole number lessthan 100.

Name the greatest common factor of thenumbers less than 25.

Name the least common multiple of thenumbers less than 20.

Classify a set of whole numbers as prime,composite or units.

Define composite number.

List all prima numbers less than 100.

4

4






Understand exponential notation.

Understand scientific notation.

WHOLE NUMBERS - OPERATIONSKnow how to add, subtract, multiplyand divide whole numbers usingstandard algorithms.

131

61

Identify and rename a product inexponential form.

Find the value of a number expressed inexponential form.

Rename a given numeral using scientificnotation.

Find the sum of an addition ormultiplication problem with three or moreaddends or products using the associativeand commutative properties.

Check division problems without remainderby multiplication: check divisionproblems with remainder by multiplicationand addition.

Use the short algorithm to name thequotient and remainder for any reasonabledivision problem with a single-digitdivisor.

132





133

Understand fractional numerals,equivalent, improper and mixedfractions.


Understand decimal fractions.

4

62

Explain the function of numerators anddenominators.

Name the missing numerator or denominatorfor a mathematical sentence.

Order more than five fractions from leastto greatest.

Identify, name, read and write decimalfractions having denominators of 10, 100,1000 or 10,000.

Write a fraction in decimal form or adecimal fraction as a fraction insimplest form.

Distinguish between repeating andterminating decimal fractions.

Sound decimals to any place.

Estimate the sum, difference, product orquotient of the decimals.

134


RATIO, PERCENT

AND PROPORTION

FRACTION OPERATIONS




Understand ratio, percent and proportion.

Understand multiplication inverses.

Know how to multiply and dividefractions.

135

63

Write a ratio using a rational numberfora and express the ratio in words.

Name the equivalent form of a ratio witha denominator of 100.

Rename percents as fractions or decimals.

Name the multiplication inverses of a setof rational numbers (reciprocals) anddemonstrate that the product of anyrational number and its reciprocal is one.

Multiply two decimals to the hundredthsplace.

Divide a decimal by a whole number or bya decimal to the hundredths place.

136




INTEGERS

GEOMETRY

137

Understand concepts related to integers.

Know how to identify simple planeand space figures.

Understand similarity and congruency.

Know how to construct and bisectplane figures.

64

Represent a ph /sisal situation such as a

gain or loss :n temperature with apositive or negative integer.

Graph positive and negative numbers on anumber line.

Demonstrate how to find the sum of twointegers.

Identify right, acute and obtuse angles.

Classify a set of quadrilaterals asparallelograms, rectangles, rhcebuses,squares or trapezoids.

Use the symbol (n) to express therelationship between congruent figures.

Explain the difference between equal andcongruent figures.




GEOMETRY (Cont.)

MATH SENTENCESKnow how to write and solve math

sentences.


139

Understand data gathering, organizationand graphing.

65

Sketch examples of parallel, intersectingand perpendicular lines, using astraightedge.

Construct a plane figure congruent to agiven line segment, angle or triangle,using a straightedge and compass.

Construct a circle, semi- or quartercircle with a given center and radius ordiameter, using a compass.

Use ,17, is, and i to make true numbersentences involving whole numbers,fractions, decimals, ratios and percents.

Determine the solution set for opensentences with the replacement set ofwhole numbers.

Collect, organise, analyse and illustratedata compiled from opinion polls,experiments, reference books, etc.

140


The Learner will:

PROBABILITY AND

STATISTICS (Cont.)

PROBLEM SOLVING


141


66


The Learner will:

Develop an extended recordkeeping projectthat includes collecting, orgar.izing andgraphing data.

Report on the use of probability andstatistics in careers.

Discuss the importance of unbiasedsampling while studying real-life issues.

Demonstrate the multiplication principleof probability through experiments withtree diagrams or rosters.

Use estimation to determine if solutionsto word problems are reasonable.

Interpret variations in a model in termsof the original problem situation.


TOP IC /CONCEPT LEARNING OUTCOME SAMPLE LEARNING OBJ3CTIvE


CALCULATORS AND

COMPUTERS

143

Know how to use a calculator. (See

Computer Education Curriculum Guide.)

67

Use a calculator to find sums,differences, products or quotients ofintegers or decimals.

Find the percent of a number using acalculator.

Find the square root of a number using acalculator.

144



The Learner will:


Understand concepts related to counting,reading, writing and recognising whole

numbers.

Understand expanded notation.

Understand divisibility rules.


145

68


The Learner will:

Identify, name, read and write different

names for the same number, usingdifferent numeration systems and formats.

Write an expanded numeral using

exponential notation.

Use divisibility rules for 2, 3, 5, 9 and10 as an aid in factoring.

Tint all the factor of a given wholenumber lens than 1000.

List multiples of a given whole numberless thAn 1000.

Determine the greatest common factor of aset of three numbers having less thanfour digits.



The Learner will:

WHOLE NUMBERS - COUNTINGAND NUMERATION (Cont.)

Understand prime numbers andcomposites.

Understand scientific notation.

Understand squares and square roots.


Know how to add, subtract, multiplyand divide whole numbers.

147


The Learner will:

Determine the least common multiple of aset of numbers having less than fourdigits.

Determine the complete primefactorisation for any whole number havingless than four digits.

Write any number, having less than sevendigits, in scientific notation.

Find the square of any whole number lessthan 100.

Find the square root of a perfect squarewhole number less than 200.

Perform any basic operation involvingwhole numbers.



The Learner will:


Understand decimal notation.

Understand terminating decimals andfraction equivalents.

Know how b3 add, subtract, multiplyand divide fractions and decimate.

RATIO, PERCENT,

AND PROPORTION

Understand ratio, percent and proportion.

149

70


The Learner will:

Read a numeral such as 2,479.6305 andwrite it in words.

Determine the equivalents for commonfractions given a set of decimalfractions.

Write a'set of fractions and decimalfractions that are equivalent to 7/8.

Find the sum, difference, product andquotient of fractions, mixed numerals anddecimal fractions.

Use the properties of addition and

multiplication of decimal fractions.

Demonstrate that a proportion is astatement of two equivalent ratios.




RATIO, PERCENT,

AND PROPORTION (Cont.)

INTEGERS

Understand the concept of integers.


Understand the process of measuring.

151

71

Compute the percent of a number usingequivalent fractions or decimals.

Add, subtract, multiply and divideintegers.

Use various measuring devices to measurelength in whole and fractional parts ofcustomary or metric units.

Measure time and to

Solve problems involving money.

Find the perimeter of a given polygon andthe circumference of a given circle.

Measure the angles of polygons using aprotractor.

Estimate length, weight, time,temperature awl money using appropriateunits and terms.

152




GEOMETRYUnderstand complementary andsupplementary angles.

Know how to measure angles ingeometric figures.

MATH SENTENCESKnow how to write and solve mathsentences.

153

72

Measure an angle and find its complementor supplement.

Find the sum of the angles in a polygon.

Solve simple linear equations usingnon-negative, rational numbers in thereplacement set.

Apply the operational symbols, x

and II to form true sentences usingnon-negative rational numbers andintegers.

Solve simple inequalities.

Use brackets and parentheses to show theorder of operation in mathematicalexpressions involving addition,subtraction, multiplication and division.



The Learner will:


Know how to determine mean.

PROBLEM SOLVING


155


Know how to use computer hardware andsoftware to solve problems. (See ComputerEducation Curriculum Guide.)

73


The Learner will:

Find the arithmetic mean (average) for agiven set of numerical data.

Determine the rule for completing anumber pattern.

Construct flow charts to show steps inoperatilns and solutions of word problems.

Formulate math statements to describeproblem situations.

Select processes and formulas to solveword problems.

Use spread sheet software to performrepetitive calculations.

156



The Learner will:


Understand the basic operationsinvolving whole numbers.


157

Understand equivalent fractions andtheir order.

74


The Learner will:

Solve problems involving whole numbers todemonstrate proficiency in the basic

operations.

Write a set of fractions which areequivalent to 15/16 in common and decimalforms.

Order a set of ten common fractions and aset of ten decimal fractions from leastto greatest.

Determine the equivalent common fractionsof a set of terminating decimals.

Determine the equivalent decimalfractions of a set of canon fractions.

158

ELEME1TARY MATHGRADE 8


RATIO, PERCENT

AND PROPORTION

159

The Learner will:

Understand ratio and proportion.

Know how to solve percent problems.

75


The Learner will:

Write the ratio that describes thecomparison of any two quantities in bothforms and express it in words.

Determine the value of the missingcomponent of a proportion.

Find the percent of a number usingequivalent fractions or decimals.

Find the percentage given the base andrate.

Rename percents as equivalent forms.

Solve problems involving discount, 'mpleinterest, commission and sales tax.

160




INTEGERS

Understand concepts related to integers.


161

Understand the process of measuring.

76

Graph integer numbers on a number line.

Order a set of integers from greatest toleast.

Add, subtract, multiply and divideintegers.

Write the absolute value of each integerin a set.

Find the approximate area of an irregularfigure drawn on graph paper.

Compute the surface area of rectangularprisms, cubes, spheres, pyramids andcylinders using appropriate formulas.

Find the volume of cylinders, cubes andrectangular solids.

Use a conversion formula to changetemperature from Celsius to Fahrenheit.

Solve problems relating to speed.




GEOMETRYKnow how to apply basic mathematicaloperations to geometry.

MATH SENTENCESKnow how to write and solve mathsentences.

PROBLEM SOLVINGKnow how to solve problems.

163

77

Solve problems related to computation andmeasurement of Teometric figures todemonstrate proficiency.

Write and solve linear equations todemonstrate proficiency in applyingoperational symbols, constructingmathematical sentences, determiningsolution sets, using propk2rPton,translating English sentences intomathematical sentences, using parenthesesand brackets, determining averages andsimple probability.

Use diagrams as an aid to problem solving.

Interpret and find solutions for multipleproblems.

164


TCPIC/CONCEPT LEARNING OUTCOME SAMPLE LEARNING OBJECTIVE


CALCULATORS AND

COMPUTERS

165

Know how to use a hand calculator to solveproblems. (See also Computer EducationCurriculum Guide.)

Know how to write simple computer programsto solve problem .

78

Uee a hand calculator to solve simpleequations.

Program the computer to draw graphics.

Program the computer to perform mathoperations.

APPENDIX A

At the elementary level, the following

grade level placement for topics/concepts:

GRADES

framework

1 2 3

is employed,

4 5

indicating

6 7 8

Sets X X X X X

Whole Numbers - Counting and Numeration X X X X X X X

Whole Numbers - Operations X X X X X X X X

Fractions and Decimals X X X X X X X X

Fraction Operations X X X

Measurement and Estimation X X X X X X X

Geometry X X X X X X X X

Math Sentences X X X X X X X

Probability and Statistics X X X X X X X

Graphs and Scale Drawings X

Problem Solving X X X X X X X X

Calculators and Computers XXX%XXXXIntegers X X X

Ratio, Percent and Proportion X X X

RESPONDENTS

ALASKA CURRICULUM GUIDE: Elementary Math

PROSLEMSL ISSUES, CONCERNS DISPOSITION

Lyn MaslowBering Strait

Jerry Sjolander

Alaska PacificUniversity

168

Include more computer use at the first gradelevel.

Do not require students to master skills thesame year they are taught.

Teach concrete skills before abstract skills.

Specific suggestions were made directly on theguide.

Incorporate more concrete experiences forprimary grader.

There is too little emphasis on place valuein grades two and three.

The integration of common fractions and decimalconcepts in grade four is essential.

Terminology such as associative and commutativeis difficult.

Crass-tfersocing to computer guide hasbeen included throughout elementary andsecondary levels.

The guides have been designed to representsequential development of math skills.

The guides have been revised accordingly.

These suggestions have been incorporatedinto the material to the greatest extentpossible.

Done.

Additional objectives have been developedin this area and included in these grades.

Agreed, and the material has been revised.

The guides are intended for curriculumcomdinators or directors; however:, briefdefinitions of these terms have beenincluded.

169

RESPONDENTS


PROBLEMS, ISSUES, CONCERNS DISPOSITION

Carol H. Jerue

Iditarod Area S.D.Specific changes noted on draft; also submittedlist of objectives to add.

Adjustments needed between concept /topic andlearning outcomes; also between outcomes andobjectives.

Objectives that appear as examples or problemsneed to be rewritten.

The concept of computers needs to be addedthroughout.

Doris AyersJim SeitzCheryl GirardonAlaska Council of

Teachers of Mathematics(ACIM) Submitted guides with specific suggestions

noted directly on the guides.

Phyllis MarcheseCCS

170

Structure of guides should be concepts,objectives, outcomes (measurable).

The guides are inconsistent across all levels.

2

These changes have been incorporated intothe material.

These adjustments have been made.

Done.

Cross-referencing to the ElementaryComputer Guide has been added.

These suggestions have been incorporatedinto the material to the greatest extentpossible.

The following framework was agreed upon:Topic/Concept; Outcome; Objective (writtenin behavioral terms.

The guides have been revised to ensureconsistency.

171

RESPONDENTS


PROBLEMSt_ISSUES, CONCERNS DISPOSITION

Phyllis MarcheseCCS (cont.)

Margaret McKinnonCCS

4

There is a lack of basic instruction in remedial.skills and hands-on application and activities.

Nord problems are treated as an isolatedconcept.

Problem solving should be integrated servothe board.

Need examples for the learning objectives toclarify such terminology as commutative.

'Understand set theory is too intimidating;the processes relate to counting, adding andsubtracting.

For measurement, specify types and sizes ofunits to be measured at each grade level.

3

Additional objectives in this area havebeen added. It was decided by theDepartment in consultation with theCurriculum Cabinet that no remedialcourses or programs be included in theseguides as the learning outcomes sought arenot different from regular courses orprograms.

The guides have been revised to integratemore word problems across alltopic /concept areas.

Done.

As the guides are intended for use bycurriculum directors, it was determinedthat a listing of examples and activitieswould not be a function of the guides, butwould be left to the discretion ofindividual teachers.

Agreed and these changes have been made.

Done.

173


RESPONDENTS PROBLEMS,_ ISSU?Sb CONCERNS DISPOSITION

Margaret McKinnonCCS (cont.)

174

For geometry, specify types of figures to be Done.studied at each grade level.

Add more application objectives for consumer Done.topics and computer literacy.

Specific comments were written oirectly on the These were incorporated into the materialguides. to the greatest extent possible.

4

175

ALASKAMODEL

CURRICULUMGUIDE

PROJECT PERCENTAGE OPEDUCATIONAL OUTCOMES

Subject: MATHCourse:

Level: ELEMENTARYGrade(s): 1-8Date: 8-20-85

Histogram of Percentages

Objective N S 10 20 30 40 50 60 70 80 90 100

+ -+ +- +- +- +- + -+ +- +----+

COGNITIVE

1.10 Knowledge of specifics : 45 22 :***********

1.20 Knowledge of ways and : 5 2 :*

means of dealing with :

specifics

1.30 Knowledge of : 0 0 :

universalsand abstractions

2.00 Comprehension :110 54 :***************************

3.00 Application : 32 16 :********

4.00 Analysis : 8 4 :**

5.00 Synthesis 2 1 :*

6.00 Evaluation 0 0 :

SUBTOTAL :202 100 :

AFFECTIVE 0 0 :

PSYCHOMOTOR 0 0 :

Not Classifiable 0 0 :

TOTAL :202 100

II 6

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