Unit Fractions and Operations - My Savvas Training

ASSESSMENT RESOURCES

Unit Fractions and Operations

M A T H N A V I G A T O R ®

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UNIT FRACTIONS AND OPERATIONS iii

0Checkpoint XContents

Teacher Materials

Pre-Test/Post-Test Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Lesson 7: Checkpoint 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Lesson 14: Checkpoint 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Student Materials

Lesson 7: Checkpoint 1 and Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Lesson 14: Checkpoint 2 and Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Image Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Copyright © 2020 Savvas Learning Company LLC All Rights Reserved. Savvas™ and Savvas Learning Company™ are the exclusive trademarks of Savvas Learning Company LLC in the US and in other countries.

UNIT FRACTIONS AND OPERATIONS 1

Pre-Test/Post-Test Administration

test administration

For the pre-test, let students know that this test will help you determine what they already know. Explain that the module will help them learn how to solve problems that seem difficult now.

For the post-test, remind students that this test will help you determine what they have learned about unit fractions and operations.

Online Testing

Once your testing window has started, you can begin testing.

• Seat students individually in front of a computer.

• Give each student a piece of scratch paper.

• Make sure that students have pencils.

• Have students use their access codes to log in to the pre-test.

• Before each student begins the test, confirm that he or she istaking the correct test.

Tell students that:

• Each question will be displayed on the computer screen. Studentsshould select the answer they think is best by clicking on theoption choice and then clicking to confirm the choice.

• After students answer a question, the next question will appear on the computer screen.

• Students may choose to skip a question and flag it to come back to before ending the test.

During the test:

• Observe students as they work to make sure that they are actively engaged in the testing process.

• Support any students who seem to find the material challenging. Encourage them to make a goodestimate for any problem they find difficult. You may wish to provide manipulatives.

Once students have answered all the questions, they should follow the online prompts to conclude the test.

After the pre-test if some students finish early, pair each of them with another student. Give each student a Student Book. Tell the students to read the instructions on page 1 of the Student Book and start working.

➲


0Checkpoint XPre-Test/Post-Test Administration

Paper-and-Pencil Test

• Print copies of the test and answer sheets for each student from ARO.

• Seat students individually.

• Distribute tests, answer sheets, and scratch paper.

• Make sure that students have #2 pencils.

• Instruct students to fill in the answers on their answer sheets.

During the test:

• Observe students as they work to make sure that they are actively engaged in the testing process.

• Support any students who seem to find the material challenging. Encourage them to make a goodestimate for any problem they find difficult. You may wish to provide manipulatives.

After students finish, collect their tests, answer sheets, and scratch paper. You will need to upload students’ answers to the ARO system so you can analyze the results.

After the pre-test if some students finish early, pair each of them with another student. Give each student a Student Book. Tell the students to read the instructions on page 1 of the Student Book and start working.

analyzing results

Irrespective of the method (online or paper-and-pencil) that you chose to administer the test, your students must be enrolled in the ARO system in order for you to obtain computer-generated reports.

These reports:

• Offer rich, instructionally-relevant information to teachers and administrators at the individual student,class, grade, school, and district levels.

• Include total test score performance information and item-level analysis for each student and for allstudents combined.

• Are important references in helping you to assess the misconceptions your students are struggling withand decide what concepts to focus on during the module.

For results:

• Online Testing: ARO will automatically generate performance reports.

• Paper-and-Pencil Test: Upload students’ data to ARO. Once you have uploaded the data, ARO willgenerate performance reports.

Additional information about the online test reporting can be found on ARO.

Remember to give a copy of the reports to the students’ regular mathematics teachers to help them in planning subsequent instruction.

➲


0Checkpoint XPre-Test/Post-Test Administration

reflection

When students have finished working on their pre- or post-tests, ask them to open the Student Book to page 1 for the pre-test and page 89 for the post-test and write a response to the reflection prompt.

➲


Checkpoint 1 7preparation

• Make a copy of the Checkpoint 1 lesson and answer sheet for each student.

• Seat students individually and distribute the checkpoint lesson and the answer sheet to each student.

• Ask students to put their names on their answer sheets.

setting the direction

This lesson is the first checkpoint lesson of the module. Tell students that today’s lesson is a checkpoint lesson; it will help them see how well they understand the concepts they have recently learned.

Tell students to read the checkpoint problems to themselves. They should complete the problems by doing the work and circling the answers in the checkpoint lesson. Then they should fill in the answers on the answer sheet.

At the end of the lesson, collect the completed answer sheets. Enter the data from each checkpoint into ARO. Open-ended questions should be included in the summation and entered either as correct or incorrect. The report generated by ARO will help you assess whether students are on track and making sufficient progress.

➲

➲


7Checkpoint 1

checkpoint

Give students 6–10 minutes to complete

UNIT FRACTIONS AND OPERATIONS Copyright © 2012 Pearson Education, Inc. or its a�liate(s). All rights reserved. 12

Checkpoint 1 7➲ checkpoint

1. What fraction of the whole is shaded?

A 3

10B

37

C 73

D 107

2. What number is shown by the point on the number line?

0 4 521 3

A 23

B 63

C 4 D 423

3. Which equation does the number line show?

0 2 314

24

34

54

44

64

A 14

+ 14

+ 14

+ 14

+ 14

+ 14

= 624

B 14

+ 14

+ 14

+ 14

+ 14

+ 14

= 64

C 14

+ 24

+ 34

+ 44

+ 54

= 64

D 14

+ 14

+ 14

+ 14

+ 14

+ 14

= 246

4. Subtract 96

– 26

. Sketch a tape diagram or a number line to help.

Write your answer as an equation.

96

– 26

= 76

16

26

36

46

56

66

76

86

96

0

Assessment Resources, page 12

the problems.

Tell students to complete problems 1–4. Ask students to be sure they have circled or written their answers in their checkpoint lessons before you collect the answer sheets.

➲


7Checkpoint 1

learning from the checkpoint

Explain to the group that when students choose the wrong answer, it is usually because they have a misconception or have made a common mistake. Ask students to write a sentence or two explaining the misconception or mistake that makes the answer a common wrong answer.

Learning from Problem 1


7Checkpoint 1

➲ learning from the checkpoint

Problem 1

The correct answer to problem 1 is A . What error would cause a student to choose answer B for this problem?

Problem 2

The correct answer to problem 2 is D . What error would cause a student to choose answer B for this problem?

Problem 3

The correct answer to problem 3 is B . What error would cause a student to choose answer A for this problem?

The student counted the number of parts (3) correctly, but only counted

the unshaded parts (7) to find the total number of parts. The size of

each part is 110

, not 17

. The student needed to count the unshaded and

shaded parts (10) to find the total number of parts.

The student counted on from 4 using whole numbers (4, 5, 6) rather than

counting on from 4 using thirds (4, 4 13, 4 2

3).

The student added the numerators and then added the denominators to find the sum.


The correct answer is A .

Students should be able to represent a fraction using a tape diagram.

Answer choice B :

Possible misconception: A student might choose Answer B if he counted the number of equal

parts being considered (3) correctly, but then counted the number of unshaded parts (7) as the

number of equal parts in the whole. The size of each part is 110

, not 17

. The student needed to

count the unshaded and shaded parts (10) to find the total number of equal parts in the whole.

Suggestion: To prevent this error, have students identify the number of equal parts in the whole. Ask, “In a fraction, does the numerator or the denominator represent the number of equal parts in the whole?”



7Checkpoint 1


Problem 1


Problem 2


Problem 3




each part is 110

, not 17





3).



The correct answer is D .

Students should be able to represent a mixed number using a number line.

Answer choice B :

Possible misconception: A student might choose Answer B if she counted the lengths between

tick marks after 4 as whole numbers (4, 5, 6) rather than thirds (4, 4 13 , 4 2

3 ).

Suggestion: To prevent this error, have students explain into how many equal parts each whole length is divided. Ask, “What does the length between each tick mark represent?”

➲


7Checkpoint 1



7Checkpoint 1


Problem 1


Problem 2


Problem 3




each part is 110

, not 17





3).



The correct answer is B .

Students should be able to add unit fractions on a number line.

Answer choice A :

Possible misconception: A student might choose Answer A if he added the numerators and then added the denominators to find the sum.

Suggestion: To prevent this error, have students explain what the numerator and the denominator describe. Remind students that they should add the number of equal parts being considered, not the size of the parts. Ask, “What fraction does the length between each tick mark represent? How many of these lengths are you adding?”

reflection

When you have about 2 minutes left, stop the discussion, even if they are not finished. Have students respond to the reflection prompt in the Student Book.

➲


Checkpoint 2 14preparation

• Make a copy of the Checkpoint 2 lesson and answer sheet for each student.

• Seat students individually and distribute the checkpoint lesson and the answer sheet to each student.

• Ask students to put their names on their answer sheets.

setting the direction

This lesson is a checkpoint lesson. Use the ritual for checkpoints to conduct the lesson.

Seat students individually and ask them to put their names on their answer sheets.

At the end of the lesson, collect the completed answer sheets. Enter the data from each checkpoint into ARO. Open-ended questions should be included in the summation and entered either as correct or incorrect. The report generated by ARO will help you assess whether students are on track and making sufficient progress.

➲

➲


14Checkpoint 2

checkpoint

Give students 6–10 minutes to complete the problems.

Tell students to complete problems 1–4. Ask students to be sure they have circled or written their answers in their checkpoint lessons before you collect the answer sheets.

➲


0Checkpoint 2 14

➲ checkpoint

Solve each problem below. Write your answer on the answer sheet.Circle each answer in your checkpoint lesson, too.

1. Find the sum. 53

10 + 4

410

= ?

A 20710

B 9710

C 9720

D 11

10

2. Find the difference. 878

– 138

= ?

A 9108

B 748

C 568

D 478

3. Mrs. Chi is making a quilt. She has 314

yards of red fabric and 724

yards of pink

fabric. How much fabric does Mrs. Chi have for her quilt?

A Mrs. Chi has 414

yards fabric for her quilt.

B Mrs. Chi has 434


C Mrs. Chi has 854


D Mrs. Chi has 1034


4. Anna was on a hike with her family. The distance to the end of

the trail is 745

miles. They walked 515

miles and then stopped

for lunch. How much farther do Anna and her family

need to hike to get to the end of the trail?

7 45

– 5 15 = 2 3

5 Anna and her family need to

hike 2 35 miles farther.



14Checkpoint 2

learning from the checkpoint

Explain to the group that when students choose the wrong answer, it is usually because they have a misconception or have made a common mistake. Ask students to write a sentence or two explaining the misconception or mistake that makes the answer a common wrong answer.



Checkpoint 2 14


Problem 1

The correct answer to problem 1 is B . What error would cause a student to choose answer C ?

Problem 2

The correct answer to problem 2 is B . What error would cause a student to choose answer A ?

Problem 3

The correct answer to problem 3 is D . What error would cause a student to choose answer A ?

The student added the denominators. To add two fractions, the students should add the numerators and keep the same denominator.

The student added instead of subtracted.

The student subtracted the mixed numbers in the problem.To find the total amount of fabric, add the mixed numbers.



Students should be able to add mixed numbers.

Answer choice C :

Possible misconception: A student might choose Answer C if he added the numerators and the denominators.

Suggestion: To prevent this error have students explain what the numerator and the denominator describe. Remind students that they should add the number of equal parts being considered, not the size of the parts. Have students sketch a model to help them add.



Checkpoint 2 14


Problem 1


Problem 2


Problem 3




The student subtracted the mixed numbers in the problem.To find the total amount of fabric, add the mixed numbers.



Students should be able to subtract mixed numbers.

Answer choice A :

Possible misconception: A student might choose Answer A if she misread the problem and added instead of subtracted.

Suggestion: To prevent this error, have students circle the operation sign in the problem as a reminder.

➲


14Checkpoint 2



Checkpoint 2 14


Problem 1


Problem 2


Problem 3




The student subtracted the mixed numbers in the problem. To find the total amount of fabric, add the mixed numbers.


The correct answer is D .

Students should be able to add mixed numbers to solve problems.

Answer choice A :

Possible misconception: A student might choose Answer A if he misunderstood the problem situation and subtracted instead of added.

Suggestion: To prevent this error, have students sketch a diagram of the problem situation so that they understand what operation to use. Ask, “What does the problem ask you to find?”

reflection

When you have about 2 minutes left, stop the discussion, even if they are not finished. Have students respond to the reflection prompt in the Student Book.

➲


Checkpoint 1 7➲ checkpoint

1. What fraction of the whole is shaded?

A3

10B

37

C73

D 107

2. What number is shown by the point on the number line?

0 4 521 3

A23

B63

C 4 D 423

3. Which equation does the number line show?

0 2 314

24

34

54

44

64

A14

+ 14

+ 14

+ 14

+ 14

+ 14

= 624

B14

+ 14

+ 14

+ 14

+ 14

+ 14

= 64

C 14

+ 24

+ 34

+ 44

+ 54

= 64

D 14

+ 14

+ 14

+ 14

+ 14

+ 14

= 246

4. Subtract 96

– 26

. Sketch a tape diagram or a number line to help.

Write your answer as an equation.


7Checkpoint 1


Problem 1


Problem 2


Problem 3



Answer Sheet

Class Information

School ____________________________________________________________________________

City ______________________________________________________ State __________________

Teacher (mathematics class) _________________________________________________________

Student Information

Grade __________

First name ________________________________________________________________________

Last name ________________________________________________________________________

Date of birth ______ (month) ______ (day) ______(year)

Male o Female o

How many years have you been at this school? _______ years

Do you usually speak English at home? Yes o No o

Does anyone in your home usually speak a language other than English?

Yes o No o


Answer Sheet

Name _______________________________________

A B C D

1. m m m m

2. m m m m

3. m m m m

Problem 4. Write a complete solution below to this problem.


0Checkpoint 2 14

➲ checkpoint

Solve each problem below. Write your answer on the answer sheet. Circle each answer in your checkpoint lesson, too.

1. Find the sum. 53

10 + 4

410

= ?

A 20710

B 9710

C 9720

D 11

10

2. Find the difference. 878

– 138

= ?

A 9108

B 748

C 568

D 478

3. Mrs. Chi is making a quilt. She has 314

yards of red fabric and 724

yards of pink

fabric. How much fabric does Mrs. Chi have for her quilt?

A Mrs. Chi has 414


B Mrs. Chi has 434


C Mrs. Chi has 854


D Mrs. Chi has 1034


4. Anna was on a hike with her family. The distance to the end of

the trail is 745

miles. They walked 515

miles and then stopped

for lunch. How much farther do Anna and her family

need to hike to get to the end of the trail?


Checkpoint 2 14


Problem 1


Problem 2


Problem 3



Answer Sheet

Class Information

School ____________________________________________________________________________

City ______________________________________________________ State __________________

Teacher (mathematics class) _________________________________________________________

Student Information

Grade __________

First name ________________________________________________________________________

Last name ________________________________________________________________________

Date of birth ______ (month) ______ (day) ______(year)

Male o Female o

How many years have you been at this school? _______ years

Do you usually speak English at home? Yes o No o

Does anyone in your home usually speak a language other than English?

Yes o No o


Answer Sheet

Name _______________________________________

A B C D

1. m m m m

2. m m m m

3. m m m m

Problem 4. Write a complete solution below to this problem.


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Copyright © 2020 Savvas Learning Company LLC All Rights Reserved. Savvas™ and Savvas Learning Company™ are the exclusive trademarks of Savvas Learning Company LLC in the US and in other countries.

Unit Fractions and Operations - My Savvas Training

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