# EM2 Tennessee Learn | Grade 5 Module 3

5

A Story of Units®

Fractions Are Numbers LEARN ▸ Module 3 ▸ Multiplication and Division with Fractions

Student

I know . . . . I did it this way because . . . . The answer is

because . . . .

My drawing shows . . . . Agree or Disagree

I agree because . . . . That is true because . . . . I disagree because . . . . That is not true because . . . . Do you agree or disagree with

Why did you . . . ? Can you explain . . . ? What can we do first? How is

Say It Again

related to

?

I heard you say . . . . said . . . . Another way to say that is . . . . What does that mean?

Content Terms

Place a sticky note here and add content terms.

? Why?

What does this painting have to do with math? Color and music fascinated Wassily Kandinsky, an abstract painter and trained musician in piano and cello. Some of his paintings appear to be “composed” in a way that helps us see the art as a musical composition. In math, we compose and decompose numbers to help us become more familiar with the number system. When you look at a number, can you see the parts that make up the total? On the cover Thirteen Rectangles, 1930 Wassily Kandinsky, Russian, 1866–1944 Oil on cardboard Musée des Beaux-Arts, Nantes, France Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY

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Great Minds® is the creator of Eureka Math®, Wit &amp; Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2022 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Printed in the USA 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-516-7

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A Story of Units®

Fractions Are Numbers ▸ 5 LEARN

Module

EM2_0503SE_title_page.indd 1

1 2 3 4 5 6

Place Value Concepts for Multiplication and Division with Whole Numbers

Multiplication and Division with Fractions

Place Value Concepts for Decimal Operations

Addition and Multiplication with Area and Volume

Foundations to Geometry in the Coordinate Plane

03-Dec-21 11:55:26 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3

Contents Multiplication and Division with Fractions Topic A

Topic C

Multiplication of a Fraction by a Whole Number

Division with Fractions and Whole Numbers

Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Find fractions of a set with arrays.

Divide a nonzero whole number by a unit fraction to find the number of groups.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Interpret fractions as division to find fractions of a set with tape diagrams and number lines.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Multiply a fraction less than 1 by a whole number. Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Multiply a fraction by a whole number.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Convert larger customary measurement units to smaller measurement units.

Topic B Multiplication of Fractions

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Divide a nonzero whole number by a unit fraction to find the size of the group.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Divide a unit fraction by a nonzero whole number.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Divide by whole numbers and unit fractions.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Reason about the size of quotients of whole numbers and unit fractions and quotients of unit fractions and whole numbers. Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Multiply unit fractions by fractions less than 1 pictorially.

Divide whole numbers by non-unit fractions.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Multiply fractions less than 1 pictorially.

Problem Solving with Fractions

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Solve word problems involving fractions with multiplication and division.

Multiply unit fractions by fractions by making simpler problems.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Multiply fractions by fractions greater than 1. Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Multiply fractions.

2

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Topic D Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Create and solve one-step word problems involving fractions. Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Solve multi-step word problems involving fractions.

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12/14/2021 11:38:19 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3

Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Evaluate expressions involving nested grouping symbols. (Optional)

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 188

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12/14/2021 11:38:19 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

Name

1.

a. _1 of 12 is 3

.

Use the array to find the value. Draw lines to show your work. 2.

a. _1 of 18 is

.

c. _5 of 18 is

.

a. _1 of 15 is

.

c. _4 of 15 is

.

6 6

3.

5 5

EM2_0503SE_A_L01_classwork.indd 5

1

Date

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b. _2 of 12 is

.

b. _3 of 18 is

.

b. _2 of 15 is

.

3

6

5

5

03-Dec-21 11:56:14 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

4. There are 20 people on a bus. _3 of the people are adults. The rest are children. 5

a. How many adults are on the bus?

b. What fraction of the people on the bus are children?

c. How many people on the bus are children?

5. Julie has 16 balloons. _3 of Julie’s balloons are blue. How many of Julie’s balloons are not blue? 8

6

LESSON

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03-Dec-21 11:56:14 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

Name

1

Date

Use the array to find the value. Draw lines to show your work if needed. 1.

a. _1 of 9 is

.

c. _3 of 9 is

.

3 3

2.

.

c. _3 of 18 is

.

a. _1 of 20 is

.

c. _4 of 20 is

.

a. _1 of 24 is

.

c. _5 of 24 is

.

3

3.

5

5

4.

6

6

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3

a. _1 of 18 is 3

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b. _2 of 9 is

.

b. _2 of 18 is

.

b. _2 of 20 is

.

b. _3 of 24 is

.

3

5

6

7

12/21/2021 10:36:01 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

5. Use the array to complete parts (a)–(e).

a. _1 of 15 is

.

b. _2 of 15 is

.

c. _1 of 15 is

.

d. _2 of 15 is

.

e. _4 of 15 is

.

3 5 5

3 5

Find the value. Draw lines or boxes to show your work if needed. 7.

6.

_2 of 12 is 3

.

_3 of 16 is

.

4

9.

8.

_2 of 27 is 3

8

PROBLEM SET

EM2_0503SE_A_L01_problem_set.indd 8

_3 of 24 is 4

.

.

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12/21/2021 10:36:23 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

10. How does knowing _1 of 27 help you find _4 of 27? 9

9

Complete the statement to find the value.

11. _3 of 14 7

Because _1 of 14 is 7

12. _5 of 28 7

Because _1 of 28 is 7

13. _7 of 32 8

Because _1 of 32 is 8

EM2_0503SE_A_L01_problem_set.indd 9

, then _3 of 14 is 3 × 2 or

.

7

, then _5 of 28 is

or

.

, then _7 of 32 is

or

.

7

8

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PROBLEM SET

9

12/21/2021 10:36:32 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

Use the Read–Draw–Write process to solve the problem.

14. There are 25 students in Miss Baker’s class. _1 of the students bring their lunch from home. 5

The rest of the students get a school lunch. How many students bring their lunch from home? a. Should the answer be more than or less than _1 of the class? Explain. 2

b. How many students bring their lunch from home?

c. What fraction of the students get a school lunch?

d. How many students get a school lunch?

10

PROBLEM SET

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12/21/2021 10:36:42 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 1

Name

Date

1

1. Use the array to find _4 of 15. Draw lines or boxes to show your work. 5

_4 of 15 is

.

5

2. Yuna reads 20 books during the summer. _3 of the books she reads are fiction. How many fiction books does Yuna read?

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4

fiction books.

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11

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03-Dec-21 11:57:02 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 2

Name

2

Date

Find the value by using the number line. 1. _1 of 3 is

.

5

0

1

2

3

Find the value by using the number line. 2. _2 of 4 is

.

5

0

1

2

3

4

Find the value. 3. _3 of 35 is 5

EM2_0503SE_A_L02_classwork.indd 13

.

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13

03-Dec-21 11:58:48 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 2

4. Blake has 19 yards of fabric. He uses _1 of the fabric to make a quilt. How many yards of fabric does Blake use for the quilt?

14

LESSON

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3

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03-Dec-21 11:58:49 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 2

Name

2

Date

Find the value by using the number line. Write your answer as a whole number when possible. 1. _1 of 4 is _4 or

.

4

4

0

2. _2 of 3 is _____ or

1

0

3

or

0

4. _3 of 3 is 4

EM2_0503SE_A_L02_problem_set.indd 15

4

1

2

3

.

1

2

3

4

5

6

.

0

3

.

3

3. _2 of 6 is

2

1

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2

3

15

03-Dec-21 12:00:30 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 2

Complete the tape diagram and find the value. Write your answer as a whole number when possible. 5. _1 of 16 4

16

?

4 units =

1 unit =

_____

=

6. _1 of 32 4

units = unit =

=

? 7. _2 of 24 3

units = unit = 2 units = 2 ×

= =

8. _5 of 24 6

units = unit = units =

16

PROBLEM SET

EM2_0503SE_A_L02_problem_set.indd 16

= ×

=

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03-Dec-21 12:00:32 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 2

Find the value. Write your answer as a whole number when possible. 9. _2 of 28 is

.

10. _3 of 48 is

.

11. _5 of 72 is

.

12. _2 of 45 is

.

13. _5 of 42 is

.

14. _1 of 8 is

7

9

6

EM2_0503SE_A_L02_problem_set.indd 17

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8

5

3

.

PROBLEM SET

17

03-Dec-21 12:00:32 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 2

Use the Read–Draw–Write process to solve each problem.

15. A baker makes 36 cookies. _7 of the cookies have chocolate chips. How many cookies have 9

chocolate chips?

16. A band has 56 members. _3 of the members play a brass instrument. How many members play a brass instrument?

18

PROBLEM SET

EM2_0503SE_A_L02_problem_set.indd 18

7

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03-Dec-21 12:00:33 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TA ▸ Lesson 2

Date

2

Find each value. Show your work by using a tape diagram. 1. _1 of 5 is 5

.

2. _4 of 25 is

.

3. _2 of 16 is

.

5

3

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19

03-Dec-21 11:59:28 AM

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03-Dec-21 11:59:28 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply Whole Numbers by Fractions

Sprint Write the sum or product. Use a whole or mixed number when possible. 1.

_1 + _1 + _1 8

8

2.

8 × _1

3.

8

8

8

9 × _1

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EM2_0503SE_A_L03_removable_fluency_sprint_multiply_fractions_by_whole_numbers.indd 21

21

03-Dec-21 12:06:26 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply Whole Numbers by Fractions

A

Number Correct:

Write the sum or product. Use a whole or mixed number when possible. 1.

_1 + _1 5

23.

_3 + _3

2.

5

24.

3 5

5

2 × _1

5

5

2×_

3.

_1 + _1 7

25.

_4 + _4

4.

7

26.

5

7

2 × _1

5.

_1 + _1 + _1

6.

3×1 5

5

5

_

5

7.

_1 + _1 + _1

8.

3×1 4

4

4

_

4

9.

_1 + _1 + _1 + _1

10.

4×1 7

7

7

7

7

_

_1 + _1 + _1

11.

3

3

5

2 × _4

27.

_2 + _2 + _2

28.

3×2 3

3

3

_

_3 + _3 + _3

30.

3 3× 5

5

5

_

_2 + _2 + _2 + _2

32.

4×2 7

7

7

7

_

3

3

3

12.

3

34.

13.

3

35.

3 × _2 3

36.

6 × _2 3

3 4

_1 + _1 + _1 + _1

15.

4×1 4

37.

5×_

16.

4

38.

7×_ 3 4

39.

6×_ 5 5 5

4

4

_

5 × _1

_1 + _1 + _1 + _1 + _1

17.

5

5

5

5

5

18.

5 × _1 5

40.

8 × _4

19.

6×1 5

41.

9 × _4 6

42.

9×_ 6 7 5 8

20.

_

_1 + _1 + _1 + _1 + _1 + _1 6

6

6

6

6

6

21.

6 × _1 6

43.

7×_

22.

6

44.

7 9

7 × _1

22

EM2_0503SE_A_L03_removable_fluency_sprint_multiply_fractions_by_whole_numbers.indd 22

3

3

14.

4

7

_1 + _1 + _1 + _1 4 × _1

4

5

31.

3 × _1 4 × _1

3

29.

33.

3

5

8×_

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03-Dec-21 12:06:30 PM

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03-Dec-21 12:06:30 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply Whole Numbers by Fractions

B

Number Correct: Improvement:

Write the sum or product. Use a whole or mixed number when possible. 1.

_1 + _1 3

23.

2.

3

24.

3

2 × _1

_2 + _2 3

3

2 × _2 3

3.

_1 + _1 5

25.

_3 + _3

4.

5

26.

3 5

5

2 × _1

5.

_1 + _1 + _1

6.

3×1 4

4

4

_

4

7.

_1 + _1 + _1

8.

3×1 5

5

5

_

5

9.

_1 + _1 + _1 + _1

10.

5

5

5

2×_

27.

_2 + _2 + _2

28.

3×2 3

3

3

_

29.

_2 + _2 + _2

30.

3×2 5

5

5

_

_2 + _2 + _2 + _2

4×1 5

32.

4×2 5

2

5

5

_

5

5

5

_1 + _1 2

12.

2 × _1

33.

2

34.

3 × _1

13.

2

35.

2 × _2 2

36.

4 × _2 2 3

3 × _1

_1 + _1 + _1 2

2

_1 + _1 + _1

15.

3×1 3

37.

5 × _2

16.

3

38.

7 × _2 3

39.

6 × _4 4 5

_

3

4 × _1

_ _ _ _ 1 1 1 1 + + + 4 4 4 4

18.

4 × _1 4

40.

7 × _4

19.

5×1 4

41.

6×_ 5 6

42.

8×_ 6 7 5 8

20.

_

_1 + _1 + _1 + _1 + _1 5

5

5

5

5

21.

5 × _1 5

43.

5×_

22.

5

44.

7 9

6 × _1

24

EM2_0503SE_A_L03_removable_fluency_sprint_multiply_fractions_by_whole_numbers.indd 24

2

2

14.

3

5

_

11.

17.

5

31.

5

3

3

7×_

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03-Dec-21 12:06:32 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 3

Name

3

Date

Use the number line to find the product. Then write a repeated addition sentence to check your work. Write your answer as a whole number when possible. 1.

_

1 ×4= 2

0

1

2

3

4

3

4

= 2.

_

3 ×4= 4

0

1

2 =

3. Use the tape diagram to fill in the blanks. Then complete the equation to find the product. Write your answer as a whole number when possible. a.

_1 × 20 4

20

1 × (_4 × 20) = 1 × _____ 1

?

b.

=

×

=

_

3 × 20 4

20

?

3 × (_4 × 20) = 1

=

× _____ ×

= © Great Minds PBC •

EM2_0503SE_A_L03_problem_set.indd 25

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25

03-Dec-21 12:04:47 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 3

Fill in the blanks. Then complete the equation to find the product.

_1

4. 5 of 15 is 1 part when

_

1 × 15 = 1 × 5

_3

5. 5 of 15 is

_

3 × 15 = 5

____ = 5

is partitioned into 5 equal parts.

×

=

parts when

× ____ =

is partitioned into

×

equal parts.

=

_

3 × 60 = 4

2_ 8. 5 × 8 =

26

PROBLEM SET

EM2_0503SE_A_L03_problem_set.indd 26

_

7.

5 ×6= 9

9.

7 × 64 = 8

_

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03-Dec-21 12:04:48 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 3

_

_

10.

5 × 18 = 6

11.

3 × 12 = 8

12.

3 × 12 = 4

_

4_ 13. 5 × 60 =

14. The measure of ∠A is 120°. The measure of ∠B is 3 of the measure of ∠A. What is the measure of ∠B?

_2

A

B

_5

15. The trampoline park sold 84 tickets. 7 of the tickets sold were for children. How many of the tickets sold were for children?

EM2_0503SE_A_L03_problem_set.indd 27

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PROBLEM SET

27

03-Dec-21 12:04:49 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 3

_3

16. Blake correctly found 4 × 36 = 27. He was surprised that his answer was less than 36 because he thought multiplication resulted in a number greater than both factors. Explain why Blake’s answer was less than 36.

28

PROBLEM SET

EM2_0503SE_A_L03_problem_set.indd 28

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03-Dec-21 12:04:49 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TA ▸ Lesson 3

Date

3

Multiply. Show your work. 1. 2_ × 15 = 3

3×8= 2. _ 5

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29

03-Dec-21 12:01:16 PM

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03-Dec-21 12:01:16 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 4 ▸ Multiplication Expression Cards

4_ ×4 5

5_ ×4 4

1_ ×4 3

_1 × 4 2

1_ ×4 5

_3 × 4 8

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31

03-Dec-21 12:09:21 PM

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03-Dec-21 12:09:21 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TA ▸ Lesson 4

4

Date

Use the Read–Draw–Write process to solve each problem.

_3

1. Scott spent 4 of his money on comic books. He spent \$9 on comic books. How much money did Scott have before he bought the comic books?

_8

2. Tyler drew the angle shown. Kayla draws an angle with a measure that is 5 the measure of Tyler’s angle. What is the measure of Kayla’s angle?

60°

EM2_0503SE_A_L04_classwork.indd 33

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33

03-Dec-21 12:07:02 PM

EM2_0503SE_A_L04_classwork.indd 34

03-Dec-21 12:07:02 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 4

Name

4

Date

Use the number line to represent the multiplication. Then write a repeated addition sentence to find the product. 1. _1 ​​ × 5 4

0

1

2

3

4

5

= 2. ​​ _ ​​

0

1

2

3

4

= Use the tape diagram to complete the statement. Then find the product. 3. _ ​​  ​​

is

part when 5 is partitioned into

5 ​​

equal parts.

_1 × 5 = 4

×5

5 × ​​ _____  ​​ = ​​_______  ​​ =

?

EM2_0503SE_A_L04_problem_set.indd 35

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35

03-Dec-21 12:08:17 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 4

4. ​​ _ ​​

parts when 4 is partitioned into

is

equal parts.

4 ​​

​​

​​

​​

? 5. ​​ _

parts when 11 is partitioned into

​ is

equal parts.

11 × 11

11 × ​​ _____  ​​ = ​​________  ​​ =

3 × 11 = ​_ 4

? 6. ​​ _

​ is

parts when

is partitioned into

equal parts.

11 5 × 11 = ​_ 4

×

× 11

= ________  ​​ =

? Complete the statement. Then find the product. 7. _ ​​

​ is

7_ × 12 = 5

8. ​​

​ is

9_ × 10 = 7

36

parts when

×

equal parts.

×

​​ = = __________

parts when

is partitioned into

×

=

PROBLEM SET

EM2_0503SE_A_L04_problem_set.indd 36

is partitioned into

=

equal parts.

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03-Dec-21 12:08:20 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 4

Multiply. 11

10. _3 × 9​ =

11. _3 × 7​ =

12. _5 × 6​ =

13. _ ​​

14. __ ​​

9.

__1 × 8​ =

8

5

3

15. _ ​​  ​​

16. Sana drew the angle shown. Riley draws an angle that is __ ​​ 11 ​​ 5

a. Is the measure of Riley’s angle greater than or less than the measure of Sana’s angle? How do you know?

45° b. What is the measure of Riley’s angle?

EM2_0503SE_A_L04_problem_set.indd 37

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PROBLEM SET

37

03-Dec-21 12:08:22 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 4

Use the Read–Draw–Write process to solve each problem. ​​  17. Mr. Evans makes 10 pints of salsa. _ ​

​​  ​ 18. Lisa breaks _

38

PROBLEM SET

EM2_0503SE_A_L04_problem_set.indd 38

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03-Dec-21 12:08:22 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 4

Name

Date

4

Multiply. Show your work. 1. _ ​​  4 × 8 = 5

2. _ ​​  7 × 15 = 5

3. Which expression results in a product greater than 4? Explain how you know.

​​ _3​​ × 4   ​​ _5​​ × 4 4

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4

39

03-Dec-21 12:07:37 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5 ▸ Mathematics Reference Sheet

Grade 5 Mathematics Reference Sheet Conversions 1 mile = 5,280 feet

1 pound = 16 ounces

1 cup = 8 fluid ounces

1 mile = 1,760 yards

1 ton = 2,000 pounds

1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts 1 liter = 1,000 cubic centimeters

Volume Formula Right rectangular prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V = B × h or V = l × w × h

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41

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5

Name

Date

5

Convert. 1.

_2 lb = 3

oz 1 pound

1 ounce

2.

_7 c = 4

fl oz 1 cup

1 fluid ounce

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43

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5

Use the Read–Draw–Write process to solve each problem.

_3

3. Mr. Sharma spends 8 of a day at work. He spends the rest of the day at home. How many hours does he spend at home?

4. Ryan is in a 2-mile race. He jogs 1 __ miles and walks the rest of the distance. How many yards 3 10

does Ryan walk?

44

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5

Name

5

Date

Convert each measurement.

1 yard 1. _1 yd = 3

2. _2 yd =

ft

ft

3

3. _1 yd = 4

ft

1 foot

1 foot

4.

__

1 ft = 12

6. _3 ft = 4

1 inch

in

in

5. _1 ft =

in

7. _7 ft =

in

2

8

8. Tyler buys _3 yards of ribbon for a project. How many feet of ribbon does Tyler buy? 4

Convert each measurement.

1 pound

9.

__

1 lb = 16

11. _3 lb =

1 ounce

8

oz

oz

10. _1 lb =

oz

12. _1 lb =

oz

2

3

13. A hamburger weighs _1 pound. How many ounces does the hamburger weigh? 4

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45

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5

Convert each measurement.

1 gallon 14. _3 gal = 4

qt

15. _1 gal = 2

qt

1 quart 1 quart 16. _1 qt =

pt

17. _5 qt =

pt

18. _1 pt =

c

19. _3 pt =

c

4

2

1 pint 1 pint 2

4

1 cup

20. Mrs. Chan needs _1 gallon of milk. The store only sells quarts of milk. Mrs. Chan buys 1 quart 8

of milk. Does she have enough milk? How do you know?

46

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5

Use the Read–Draw–Write process to solve each problem.

21. Toby buys 3 gallons of juice. He uses 2  ​  _3 ​ gallons of it to make punch. How many quarts of juice 8 does he have left?

22. Julie buys a piece of wood that is 12 feet long. She cuts the wood into 8 equal pieces. How many inches long is each piece of wood?

EM2_0503SE_A_L05_problem_set.indd 47

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PROBLEM SET

47

03-Dec-21 12:11:32 PM

EM2_0503SE_A_L05_problem_set.indd 48

03-Dec-21 12:11:32 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TA ▸ Lesson 5

Name

Date

5

Convert each measurement. Use the tape diagrams or reference sheet if needed. 1. ​​ _5​​ yards =

feet

6

1 yard

1 foot

2. ​​ 3_​​ pounds = 4

ounces 1 pound

1 ounce

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49

03-Dec-21 12:10:48 PM

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03-Dec-21 12:10:48 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

Name

Date

6

1. Mr. Evans plants flowers in _25 of his garden. _13 of the flowers are roses. What fraction of the garden is roses? Garden

Roses

1 3 2 5 Flowers

Draw an area model to find the product. 1 1 _ 2. _ 2 ​ × ​  2 ​ =​

EM2_0503SE_B_L06_classwork.indd 51

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51

03-Dec-21 12:12:53 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

3 1 _ 3. _ 4 ​ × ​  5 ​ =

Find the product by using the area model and the number line. 3 1 _ 4. _ 2 ​ × ​  4 ​ =​

0

52

LESSON

EM2_0503SE_B_L06_classwork.indd 52

1 4

2 4

3 4

4 4

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03-Dec-21 12:12:54 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

Name

6

Date

Use the number line to complete the multiplication equation. 1​​ ​​ of _ 1​​ 1. _ 2 3

1​​ ​​ of _ 1​​ 2. _ 3 4

0

1 3

2 3

3 3

1 4

0

_ _ _____​​

2 4

3 4

4 4

_ _ _____​​

1 1 ​​ ​​ × ​​ ​​ = ​​ 2 3

1 1 ​​ ​​ × ​​ ​​ = ​​ 3 4

Complete the area model to find the product. Each diagram represents 1. 3.

4.

_ _

​​_____​​ × 2_​​ ​​ =

1 1 ​​ ​​ × ​​ ​​ = 2 4

1 2

4

2 4

1 4

5.

6.

×

EM2_0503SE_B_L06_problem_set.indd 53

=

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​​1_​​ × 4

=

53

03-Dec-21 12:14:06 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

Draw a model to find the product. 1 _ ×1= 7. _ 2 5

3 = 8. 1_ × _ 2 5

1 _ 9. _ ×2= 3 3

3 10. 1_ × _ = 2 4

1 11. 1_ × _ = 4 4

12. 3_ × 1_ = 5 4

54

PROBLEM SET

EM2_0503SE_B_L06_problem_set.indd 54

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03-Dec-21 12:14:08 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

13. Adesh needs to find _1 of _3 . He estimates the answer is about 1 because he thinks the value is 5 4 _1 greater than _3 . Is Adesh correct? Explain. 5

4

Use the Read–Draw–Write process to solve each problem.

14. Jada has _3 gallons of lemonade. She pours _1 of the lemonade into a bottle. How many gallons 4

6

EM2_0503SE_B_L06_problem_set.indd 55

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PROBLEM SET

55

03-Dec-21 12:14:08 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

15. _4 of the food items on the lunch table are sandwiches. _2 of the sandwiches are peanut butter and 5

3

the rest are cheese. What fraction of the food items on the lunch table are cheese sandwiches?

56

PROBLEM SET

EM2_0503SE_B_L06_problem_set.indd 56

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03-Dec-21 12:14:09 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 6

Name

6

Date

1. Use the number line to find the product. Then complete the equation.

1 5

0

2 5

3 5

4 5

5 5

_ _ _____ 1 1 × = 3 5

2. Draw an area model to find the product. Then complete the equation.

_1 × _2 = _____ 4

3

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57

03-Dec-21 12:13:24 PM

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03-Dec-21 12:13:24 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 7

Name

1.

7

Date

_ _

3 2 × = 4 5

0

1 5

2 5

3 5

4 5

5 5

2. Sasha buys a bag of almonds that weighs _2 pound. She uses _3 of the bag to make trail mix. 3

4

How many pounds of almonds does Sasha use to make the trail mix?

EM2_0503SE_B_L07_classwork.indd 59

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59

03-Dec-21 12:15:25 PM

EM2_0503SE_B_L07_classwork.indd 60

03-Dec-21 12:15:25 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 7

Name

7

Date

Use the number line to find the product. Then complete the equation. 2 _ ​​ ​​ × 2​​ ​​ = 1. _ 3 3

1 3

0

2 3

3 3

2 2_ 2. _ ​​ ​​ × ​​ ​​ = 3 4

0

1 4

2 4

3 4

4 4

2 2_ 3. _ ​​ ​​ × ​​ ​​ = 4 3

0

EM2_0503SE_B_L07_problem_set.indd 61

1 3

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2 3

3 3

61

03-Dec-21 12:16:35 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 7

Use the area model to find the product. Then complete the equation. Each model represents 1. 2 3_ ​​ ​​ × ​​ ​​ = 4. _ 3 4

2 3_ 5. _ ​​ ​​ × ​​ ​​ = 3 5

2 3

3 4

3 _ 6. _ ​​ ​​ × 3​​ ​​ = 4 4

62

PROBLEM SET

EM2_0503SE_B_L07_problem_set.indd 62

2 2_ 7. _ ​​ ​​ × ​​ ​​ = 5 3

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03-Dec-21 12:16:37 PM

EUREKA MATH2 Tennessee Edition

Multiply. Draw a model to find the product.

5 ▸ M3 ▸ TB ▸ Lesson 7

​​ ​​ × _4​​ ​​ = 8. 3_ 4 5

4 2_ 9. _ ​​ ​​ × ​​ ​​ = 5 3

2 5_ 10. _ ​​ ​​ × ​​ ​​ = 3 6

3 3_ 11. _ ​​ ​​ × ​​ ​​ = 4 5

EM2_0503SE_B_L07_problem_set.indd 63

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PROBLEM SET

63

03-Dec-21 12:16:39 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 7

3 _ 12. _ ​​ ​​ × 5​​ ​​ = 5 6

3 4_ 13. _ ​​ ​​ × ​​ ​​ = 8 5

Use &gt;, =, or &lt; to compare the expressions. Explain how you can compare the expressions without evaluating them.

​​_2​​

4 _ ​​ ​​ × 2​​ ​​ 14. _ 5 7

7

Explain:

15. 3 × 5_​​ 8

​​5_​​ 8

Explain:

​​3_​​ × 4

16. 4 Explain:

64

4

PROBLEM SET

EM2_0503SE_B_L07_problem_set.indd 64

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03-Dec-21 12:16:40 PM

EUREKA MATH2 Tennessee Edition

6 5_ 17. _ ​​ ​​ × ​​ ​​ 6 9

5 ▸ M3 ▸ TB ▸ Lesson 7

_5​​ ​​ 9

Explain:

18. Noah’s mom told him he could have _1​​ of a candy bar. She told Noah’s sister she could have 4

_1​​ of the rest of the candy bar. Noah says it is not fair because he only gets _1​​ , but his sister gets _1​​ . 3

4

Explain why Noah’s reasoning is not correct.

3

Use the Read–Draw–Write process to solve each problem.

19. Scott spends _2​​ of his allowance. Of the money he spends, he uses _3​​ of it to buy a toy. What fraction 5

of his allowance does Scott spend on the toy?

EM2_0503SE_B_L07_problem_set.indd 65

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4

PROBLEM SET

65

03-Dec-21 12:16:40 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 7

20. Tara has _5​​ gallons of glue. She uses _2​​ of the glue to make blue slime, _1​​ of the glue to make green 8

5

5

slime, and the rest of the glue to make purple slime. How many gallons of glue does Tara use to make purple slime?

66

PROBLEM SET

EM2_0503SE_B_L07_problem_set.indd 66

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03-Dec-21 12:16:41 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 7

Name

7

Date

1. Show the product by using a number line. Then complete the equation.

1 6

0

2 6

3 6

4 6

5 6

6 6

_ _ _____​​ 3 5 ​​ × ​​ ​​ = ​​ 4 6

2. Show the product by using an area model. Then complete the equation.

_ _ _____​​ 2 3 ​​ ​​ × ​​ ​​ = ​​ 5 4

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67

03-Dec-21 12:15:57 PM

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03-Dec-21 12:15:57 PM

EUREKA MATH2 Tennessee Edition

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5 ▸ M3 ▸ TB ▸ Lesson 8 ▸ Using Known Products

69

03-Dec-21 12:18:37 PM

EM2_0503SE_B_L08_removable_using_known_products.indd 70

03-Dec-21 12:18:37 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 8

Name

Date

8

1. Use a known product to make a simpler problem. Show your thinking. 1 _ ​​5 ​​ × 17​​  ​​ = a. _ 1 _ b. _ ​​5 ​​ × 27​​  ​​ = 1 3_ c. _ ​​5 ​​ × 7​​  ​​ = 1 _ d. _ ​​5 ​​ × 47​​  ​​ = 1 _ e. _ ​​5 ​​ × 57​​  ​​ =

2. Fill in the blanks to find the product _ ​​   ​ ​ _

_​​ ​ of 4 is _​ of 4 fifths is ​​

fifths.

3. Fill in the blanks to find the product _ ​​   ​ ​ _

_​​ ​ of 8 is _​ ​ of 8 ninths is ​​

. ninths.

4. Fill in the blanks to find the product _ ​​   ​ ​ __

_ _​ of 10 elevenths is ​​

​​  ​ of 10 is

EM2_0503SE_B_L08_classwork.indd 71

elevenths.

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71

03-Dec-21 12:17:10 PM

EM2_0503SE_B_L08_classwork.indd 72

03-Dec-21 12:17:10 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 8

Name

8

Date

1. Use the number line to find the product. Then complete the equation. 1 _ ​​ ​​ × 1​​ ​​ a. _ 2 3

0

1 3

2 3

3 3

0

1 3

2 3

3 3

_1​​ ​​ × _1​​ ​​ = 2

3

1 2_ b. _ ​​ ​​ × ​​ ​​ 2 3

_ _ _____​​ × ​​_____​​ × 1 2 ​​ ​​ × ​​ ​​ = ​​ 2 3

=

×

=

c. 1_ ​​ ​​ × 4_​​ ​​ 2 3

0

1 3

2 3

3 3

4 3

_ _

1 4 ​​ ​​ × ​​ ​​ = 2 3

×

×

= =

EM2_0503SE_B_L08_problem_set.indd 73

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73

03-Dec-21 12:18:08 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 8

Use the model to complete the statements. The diagram represents 1.

_​​ 1​​ of 4 fifths is

2.

fifth.

4

_ _ _____​​

4 5

1 4 ​​ ​​ × ​​ ​​ = ​​ 5 4 5

Fill in the blanks.

​​  1​​ of 3 is 3. _ 3

4. _ ​​  1​​ of 4 is 2

.

5. _ ​​  1​​ of 9 is 3

74

PROBLEM SET

EM2_0503SE_B_L08_problem_set.indd 74

_​​ 1​​ of 3 fifths is 3

fifth.

_1​​ ​​ × _3​​ ​​ =

_​​ 1​​ of 4 fifths is

fifths.

_1​​ ​​ × _4​​ ​​ =

2

3

2

5

5

_1​​ ​​ × _9​​ ​​ =

_​​ 1​​ of 9 sevenths is

3

3

7

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03-Dec-21 12:18:09 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 8

Make a simpler problem by using a known product or unit language. Show your thinking. Then multiply. 1 3_ ​​ ​​ × ​​ ​​ = 6. _ 6 2

1 __ 7. _ ​​ ​​ × ​​  4 ​​ = 2 10

1 7_ 8. _ ​​ ​​ × ​​ ​​ = 7 9

1 __ ​​ ​​ × ​​  6 ​​ = 9. _ 5 11

1 _ 10. _ ​​ ​​ × 2​​ ​​ = 8 5

11. __ ​​  1 ​​ × 5_​​ ​​ = 10 3

1 _ 12. _ ​​ ​​ × 4​​ ​​ = 2 6

__ 13. __ ​​  1 ​​ × 12 ​​ ​​ = 5 12

1 7_ ​​ ​​ × ​​ ​​ = 14. _ 3 9

1 12 15. _ ​​ ​​ × __ ​​ ​​ = 7 6

EM2_0503SE_B_L08_problem_set.indd 75

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PROBLEM SET

75

03-Dec-21 12:18:10 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 8

Use the Read–Draw–Write process to solve the problem.

16. Kayla plays her video game for _ ​​ ​​ hours on Sunday. She spends _​​ ​​

a. Does Kayla spend more time or less time playing her video game on Monday than on Sunday? Explain your reasoning.

b. What fraction of an hour does Kayla spend playing her video game on Monday?

c. For how many minutes does Kayla play her video game on Monday?

76

PROBLEM SET

EM2_0503SE_B_L08_problem_set.indd 76

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03-Dec-21 12:18:10 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TB ▸ Lesson 8

Date

8

Make a simpler problem by using a known product or unit language. Then multiply. 1 5_ 1. _ ​​ ​​ × ​​ ​​ = 5 7

1 __ 2. _ ​​ ​​ × ​​  6 ​​ = 3 10

3. 1_ ​​ ​​ × 6_​​ ​​ = 9 7

4. 1_ ​​ ​​ × 4_​​ ​​ = 8 7

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77

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03-Dec-21 12:17:37 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 9 ▸ Using Known Products with Fractions Greater Than 1

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79

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TB ▸ Lesson 9

Date

9

1. Use a known product to make a simpler problem. Show your thinking.

_1 _6

a. 5 ​ × ​ 7 ​ =

_1 _7

b. 5 ​ × ​ 7 ​ =

_1 _8

c. 5 ​ × ​ 7 ​ =

2. Use a known product to make a simpler problem. Show your thinking.

_2 _6

a. 5 ​ × ​ 7 ​ =

_3 _8

b. 5 ​ × ​ 7 ​ =

_4 _9

c. 5 ​ × ​ 7 ​ =

_3 _6

a. 4 ​ × ​ 5 ​ =

__9 _5

b. 10 ​ × ​ 4 ​ = 13 __2 __

c. 11 ​ × ​  5 ​ = 4 10 _ __

d. 13 ​ × ​ 3 ​ =

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81

03-Dec-21 12:19:49 PM

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03-Dec-21 12:19:49 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TB ▸ Lesson 9

9

Date

1. Use the area model to find the product. Then complete the equation. 1 2 ​ × _ a. _ 3 4

_2 ​ × 1_ ​ = ​​_____​​ × ​​_____​​ × 3 4 2 3

= 1 4

b. 2_ ​ × 3_ 3 4 2_ ​ × 3_ ​ = ​​_____​​ × ​​_____​​ × 3 4 2 3

= 3 4

EM2_0503SE_B_L09_problem_set.indd 83

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×

×

=

83

03-Dec-21 12:20:49 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 9

5 2 ​ × _ c. _ 3 4

_2 ​ × 5_ ​ = 3 4

×

×

×

=

2 3

= 5 4

Make a simpler problem. Show your thinking. Then multiply. 3 ​ × 8_ ​ = 2. _ 4 5

4.

84

9  ​ × 6_ ​ = __ 11 5

PROBLEM SET

EM2_0503SE_B_L09_problem_set.indd 84

6 5 ​ × _  ​ = 3. _ 6 2

1 ​ × 11 __ ​ = 5. _ 5 2

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03-Dec-21 12:20:51 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 9

Multiply. 6.

4  ​ × 8_ ​ = __

10 3 ​ × __ 7. _  ​ = 8 5

8.

_8 ​ × 8_ ​ = 9 7

3 ​ × 3_ ​ = 9. _ 5 4

2  ​ × 5_ ​ = 10. __ 11 3

5 ​ × 3_ ​ = 11. _ 6 7

7  ​ × 11 __ ​ = 12. __ 10 10

12 ​ × __ 13. __ ​  7  ​ = 12 5

13

3

EM2_0503SE_B_L09_problem_set.indd 85

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PROBLEM SET

85

03-Dec-21 12:20:52 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 9

14. Eddie runs for _3 hours on Friday. He runs _5 as much on Saturday. 5

4

a. Does Eddie run for more time or less time on Saturday than he did on Friday? How do you know?

​  5​is greater than 1 because _5 is greater than 1. Explain why his reasoning b. Eddie says _3 ​ × _ 5 4 4 is incorrect. What advice would you give to Eddie?

86

PROBLEM SET

EM2_0503SE_B_L09_problem_set.indd 86

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03-Dec-21 12:20:52 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 9

Use the Read–Draw–Write process to solve each problem.

15. _5 of the animals in the pet show are dogs. _3 of the dogs are poodles. What fraction of the animals 9

in the pet show are poodles?

5

16. At a summer camp, ​​ _

_​​  ​play football and the rest play basketball. What fraction of the campers

EM2_0503SE_B_L09_problem_set.indd 87

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PROBLEM SET

87

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03-Dec-21 12:20:52 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TB ▸ Lesson 9

Date

9

Make a simpler problem. Then multiply. 9​ × __ 1. _ ​  2 ​ = 2 10

4​ × 6_​ = 2. _ 9 6

3.

9 ​ × 5_​ = __ 10

3

7​ × 8_​ = 4. _ 6 9

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89

03-Dec-21 12:20:17 PM

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03-Dec-21 12:20:17 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 10

Name

10

Date

1. Use the clues in part (a) to complete the equation in part (b). a. Analyze the clues and fill in the blanks. The clues represent equivalent expressions. Clue A

Clue B

_1​​ ​​ × ​​ 1_ × 4 × 5 3

Clue C

_______ ×3

b. Write the multiplication expression that is represented by the clues. Then find the product to complete the equation.

​​ _____​​ × ​​_____​​ = ​​_____​​

EM2_0503SE_B_L10_classwork.indd 91

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91

03-Dec-21 12:21:54 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 10

Use the Read–Draw–Write process to solve each problem.

_1

_3

2. Mrs. Chan has 4 gallons of paint. She uses 3 of it to paint her bedroom. She uses 4 ​of the

remaining paint for her living room. What fraction of the paint does Mrs. Chan use for her living room?

_3

_1

3. Blake has 3 feet of ribbon. He uses 4 of the ribbon for a project. He gives his friend 2 of the remaining ribbon. What fraction of the ribbon does Blake give to his friend?

92

LESSON

EM2_0503SE_B_L10_classwork.indd 92

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03-Dec-21 12:21:55 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 10

Name

10

Date

Consider the statement. Circle to show whether the product is less than or greater than _ ​​  ​​  1. _ ​​ as much as _

2. ​​ _ ​ ​as much as _3

4

less than _ ​​

×

3. ​​ _ ​ ​as much as _ ​​

4

greater than _3 4

=

less than _3​ 4

×

greater than _3 4

=

less than ​​ _​

×

greater than _ ​​

=

Multiply. 4. _1 ​ × _8 ​ = 4 9

5. _2 ​ × _3 ​ = 3 5

6. _5 ​ × _6 ​ = 8 4

7. _5 ​ × _4 ​ = 6 3

8.

9. _2 ​ × _8 ​ = 9 7

3= 7  ​ × _ __  ​ 10 2

EM2_0503SE_B_L10_problem_set.indd 93

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93

03-Dec-21 12:24:22 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 10

10. Lacy thinks _2 ​ × _ ​  9​ &gt; _​  2 ​. 3

8

3

a. Explain why Lacy might think the product is greater than ​​ ​

b. Find _2 ​ × _ ​  9 . 3

8

Use &gt;, =, or &lt; to compare the expressions. Explain how you can compare the expressions without evaluating them.

__​​ 11. _1 ​ × ​​13 2 15

_4 ​ × 13 __ ​​ ​​ 5 15

Explain:

41 13 ​ × __  ​ 12. __ 9 50

41 __​​ × __ ​​18 19

50

Explain:

11 ​ × ___ ​  67  ​ 13. __ 10 100

11 __ ​  7  ​ × __ 10 10

Explain:

94

PROBLEM SET

EM2_0503SE_B_L10_problem_set.indd 94

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03-Dec-21 12:24:23 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TB ▸ Lesson 10

Use the Read–Draw–Write process to solve each problem.

​​ of the brownies to his family. He gives his friends 14. Tyler bakes 1 pan of brownies. He gives _

_5​ as much of the brownies as he gives his family. What fraction of the brownies is left? 4

​  7​​ pounds. She buys 1 bag 15. Miss Song’s favorite brand of almonds is sold in bags that weigh _

of almonds at the store and she has _ ​​  1​​ of a bag of almonds at home. What is the total weight 8

of Miss Song’s almonds?

EM2_0503SE_B_L10_problem_set.indd 95

2

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PROBLEM SET

95

03-Dec-21 12:24:23 PM

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03-Dec-21 12:24:23 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TB ▸ Lesson 10

Date

10

Multiply.

3 ​ × 5_ ​ = 1. _ 4 4

2. 3_ ​ × 8_ ​ = 4 9

Compare the expressions by using &gt; , =, or &lt; . Explain how you can compare the expressions without evaluating them. 3. 1_ ​ × ​​1_ ​​ 2 3

1_ 7_  ​ × 2 8

Explain:

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97

03-Dec-21 12:22:22 PM

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03-Dec-21 12:22:23 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 11

Name

Date

11

Use the Read–Draw–Write process to solve each problem. 1. A family makes 3 pans of brownies for a bake sale. They plan to sell gift bags that each hold

_

​​  ​ of a pan of brownies. How many gift bags can the family make?

2. Julie paints birdhouses. She uses _1 pint of paint for each birdhouse. How many birdhouses can Julie paint with 6 pints of paint?

EM2_0503SE_C_L11_classwork.indd 99

4

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99

03-Dec-21 12:25:16 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 11

3. Ryan makes bags of peanuts for snacks. He has 4 pounds of peanuts. He puts _ ​​ pound of peanuts into each bag. How many bags can he make?

100

LESSON

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03-Dec-21 12:25:17 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 11

Name

11

Date

Use the model to help you complete each statement and divide. 1. There are

halves in 1.

There are

halves in 2.

2 ÷ _1​​ = 2

2. There are

thirds in 1.

There are

thirds in 2.

2 ÷ _1​​ = 3

0

3. There are

thirds in 1.

There are

thirds in 3.

3 ÷ 1_​​ = 3

fourths in 1.

There are

fourths in 3.

4

EM2_0503SE_C_L11_problem_set.indd 101

3 2

1

1 3

2 3

1

4 3

2

5 3

2

3

1 3

4. There are

3 ÷ _1​​ =

1 2

0

3

1 4

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101

03-Dec-21 12:26:18 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 11

Draw a model to find the quotient. Then complete the statements to check your work. 1 ​​ = 5. 5 ÷ _ 2

6. 2 ÷ 1_​​ = 6

groups of _ ​​ ​​ make 5.

groups of

make

7. Solve the related problems.

a. 1 gallon of juice is poured equally into containers. Each container holds _1​​ gallon. How many 8

containers can be filled with juice?

b. 4 gallons of juice are poured equally into containers. Each container holds _1​​ gallon. How many containers can be filled with juice?

102

PROBLEM SET

EM2_0503SE_C_L11_problem_set.indd 102

8

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03-Dec-21 12:26:19 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 11

8. The chart shows the ingredients needed to make a small pizza. Use the chart to write an expression. Then evaluate the expression and use a sentence to write your answer. Ingredient

Amount

Dough

_​​ 1​​ pound

Sauce

_​​ 1​​ of a jar

Cheese

_​​ 1​​ cup

3

5

4

a. How many pizzas can be made with 5 pounds of dough?

b. How many pizzas can be made with 4 jars of sauce?

c. How many pizzas can be made with 4 cups of cheese?

EM2_0503SE_C_L11_problem_set.indd 103

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PROBLEM SET

103

03-Dec-21 12:26:20 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 11

Use the Read–Draw–Write process to solve each problem. 9. A family orders 6 large sandwiches. They cut each large sandwich into thirds to make smaller sandwiches. How many smaller sandwiches does the family have?

10. A bag of cat food holds 12 cups. Mrs. Chan feeds her cat _1​​ cup at each meal. How many meals can Mrs. Chan feed her cat from the bag of cat food?

2

​​  ​​ 11. The only measuring cup Mr. Evans has is a _

104

PROBLEM SET

EM2_0503SE_C_L11_problem_set.indd 104

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 11

Date

11

Use the Read–Draw–Write process to solve the problem.

_​​ yard of ribbon to make each bow. Jada buys 7 yards of ribbon to make bows. She uses ​​  How many bows can Jada make?

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105

03-Dec-21 12:25:47 PM

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03-Dec-21 12:25:47 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 12

Name

Date

12

Use the Read–Draw–Write process to solve each problem.

1. Lacy reads 12 pages of a book. This is _1 of the number of pages in the book. How many pages are 5

in Lacy’s book?

2. Tyler has 5 lemons. This is _1 of the number of lemons he needs to make a pitcher of lemonade. 4

How many lemons does Tyler need to make a pitcher of lemonade?

EM2_0503SE_C_L12_classwork.indd 107

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107

03-Dec-21 12:29:02 PM

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03-Dec-21 12:29:02 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 12

Name

12

Date

Use the model to help you complete each statement and divide. 1. 2 is _1 of what number?

?

3 2÷1= 3

_

2

_

1 of 3

is 2. 1 3

0

2 3

2. 2 is _1 of what number?

3 3

?

4 2÷1= 4

_

2

_

1 of 4

is 2. 1 4

0 3. 4 is _1 of what number?

3 4

4 4

?

2 1 4÷ = 2

_

4 of

is

.

4. 4 is _1 of what number?

?

4 4÷1= 4

_

4 of

EM2_0503SE_C_L12_problem_set.indd 109

2 4

is

.

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109

03-Dec-21 12:29:58 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 12

Draw a tape diagram to find the quotient. Then complete the division equation. 5. 3 is _1 of what number? 5

3 ÷ 1_ =

6. 5 is _1 of what number? 4

5 ÷ _1 =

5

4

Use the Read–Draw–Write process to solve each problem.

7. 3 miles is _1 of the distance Sana rides her bike. How far does Sana ride her bike? 4

110

PROBLEM SET

EM2_0503SE_C_L12_problem_set.indd 110

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 12

8. 4 reams of paper is _1 of the paper a school uses in a week. How many reams of paper does the 5

school use in a week?

9. Noah passes 12 levels in a game. This is _1 of the total levels in the game. How many levels are in Noah’s game?

EM2_0503SE_C_L12_problem_set.indd 111

6

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PROBLEM SET

111

03-Dec-21 12:29:59 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 12

10. An elephant can hold 8 liters of water in its trunk. This is _1 of the liters of water the elephant 9

drinks in one day. How many liters of water does the elephant drink in one day?

11. Mr. Perez mows _1 of his lawn in 15 minutes. If he continues at the same pace, how long does 5

it take Mr. Perez to mow his whole lawn?

112

PROBLEM SET

EM2_0503SE_C_L12_problem_set.indd 112

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03-Dec-21 12:29:59 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 12

Name

Date

12

Use the Read–Draw–Write process to solve the problem.

Each package holds 6 slices of cheese. This is _1 of the number of slices Lacy needs for her party. 5

How many slices of cheese does Lacy need for her party?

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113

03-Dec-21 12:29:26 PM

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03-Dec-21 12:29:26 PM

EUREKA MATH2 Tennessee Edition

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5 ▸ M3 ▸ TC ▸ Lesson 13 ▸ Blank Tape Diagram

115

03-Dec-21 12:31:51 PM

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03-Dec-21 12:31:51 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply a Fraction by a Whole Number

Sprint Write the product. Use a whole number or mixed number when possible. 1.

_

1 of 15 is 3

2.

_

.

1 × 15 3

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117

03-Dec-21 12:32:59 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply a Fraction by a Whole Number

A

Number Correct:

Write the product. Use a whole number or mixed number when possible. 1. 2. 3. 4. 5. 6.

_

1 of 6 is 3

_

_

1 ×6 3

1 of 9 is 3

_

_

.

.

1 ×9 3

1 of 12 is 3

.

_

_

1 × 12 3

_

23.

1 ×6 2

24.

1 ×7 2

25.

1 ×9 3

26.

1 × 10 3

27.

1 × 12 4

28.

1 × 13 4

_ _ _ _ _ _

7.

1 of 6 is 2

.

29.

1 × 15 5

8.

2 of 6 is 2

.

30.

1 × 17 5

9.

1 of 9 is 3

.

31.

1 × 18 6

10.

2 of 9 is 3

.

32.

1 × 20 6

11. 12.

_ _ _ _

_ _ _

1 of 12 is 4

.

33.

_1 × 21

2 of 12 is 4

.

34.

1 × 23 7

_

_

7

_

_

13.

1 × 12 3

35.

14.

_

1 ×8 2

3 × 12 3

36.

15.

_

2 × 11 2

1 × 16 4

37.

16.

_

2 ×8 3

3 × 16 4

38.

17.

_

3 × 12 3

1 × 15 5

39.

18.

_

2 × 11 4

3 × 15 5

40.

19.

_

3 × 11 4

5 × 15 5

41.

20.

_

2 ×9 5

1 × 18 6

42.

21.

_

4 × 11 5

3 × 18 6

43.

22.

_

2 × 11 6

5 × 18 6

44.

5 × 13 6

118

EM2_0503SE_C_L13_removable_sprint_multiply_whole_number_by_fraction.indd 118

_

_

_ _ _

_

_ _ _

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03-Dec-21 12:33:01 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply a Fraction by a Whole Number

B

Number Correct: Improvement:

Write the product. Use a whole number or mixed number when possible. 1. 2. 3. 4. 5. 6.

_

1 of 4 is 2

_

_

1 ×4 2

1 of 6 is 2

_

_

.

1 ×6 2

1 of 8 is 2

_

_

.

.

1 ×8 2

_

23.

1 ×4 2

24.

1 ×5 2

25.

1 ×6 3

26.

1 ×7 3

27.

1 ×8 4

28.

1 ×9 4

_ _ _ _ _ _

7.

1 of 4 is 2

.

29.

1 × 10 5

8.

2 of 4 is 2

.

30.

1 × 12 5

9.

1 of 6 is 3

.

31.

1 × 12 6

10.

2 of 6 is 3

.

32.

1 × 14 6

11.

1 of 8 is 4

.

33.

1 × 14 7

12.

2 of 8 is 4

.

34.

1 × 16 7 1 ×6 2

_ _ _ _ _

_

_ _ _ _ _

_

13.

1 ×9 3

35.

14.

3 ×9 3

36.

2 × 10 2

15.

1 × 12 4

37.

2 ×7 3

16.

3 × 12 4

38.

3 × 11 3

17.

1 × 10 5

39.

2 ×9 4

18.

3 × 10 5

40.

3 × 10 4

19.

5 × 10 5

41.

2 ×8 5

20.

1 × 12 6

42.

4 ×9 5

21.

3 × 12 6

43.

2 × 10 6

22.

5 × 12 6

44.

5 × 11 6

_ _ _ _ _ _ _ _ _

120

EM2_0503SE_C_L13_removable_sprint_multiply_whole_number_by_fraction.indd 120

_

_

_

_

_

_ _

_ _

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03-Dec-21 12:33:03 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 13

Name

Date

13

1.

1 2

0

1

a. Partition the tape diagram into 3 equal units.

b. Write a division expression that represents the model.

c. What is the size of one unit?

Use the Read–Draw–Write process to solve each problem.

2. Mr. Perez has _1 gallon of water. He pours the water equally into 4 bottles. How much water 4

is in each bottle?

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121

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 13

3. Lacy and Adesh share _1 quart of ice cream equally. How much ice cream does each person get? 2

122

LESSON

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03-Dec-21 12:30:41 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 13

Name

13

Date

Use the model to divide. 1 ÷2= 1. _ 2

?

0

1 2

1

0

1 2

1

1 2. _ ÷4= 2

1 3. _ ÷2= 3

0

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1 3

2 3

1

123

03-Dec-21 12:32:24 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 13

Draw a model to divide. 1 ÷2= 4. _ 4

5. 1_ ÷ 4 = 4

1 6. _ ÷3= 5

124

PROBLEM SET

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03-Dec-21 12:32:25 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 13

Use the Read–Draw–Write process to solve each problem.

7. In 2 minutes, Tara runs _1 mile. She runs an equal distance each minute. How far does Tara run in 1 minute?

6

8. Ryan has half of a pie. He eats an equal amount of the pie after dinner each day for 3 days. How much of the pie does Ryan eat each day?

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PROBLEM SET

125

03-Dec-21 12:32:25 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 13

9. Miss Song uses _1 gallon of olive oil to make 4 equal bottles of salad dressing. How many gallons 4

of olive oil does Miss Song use for each bottle?

10. Ms. Baker shares _1 pound of fudge equally between her and 4 friends. How much fudge does each person get?

126

3

PROBLEM SET

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03-Dec-21 12:32:25 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 13

Date

13

Draw a model to divide.

_

1÷2= 8

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127

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03-Dec-21 12:31:08 PM

EUREKA MATH2 Tennessee Edition

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5 ▸ M3 ▸ TC ▸ Lesson 14 ▸ Blank Tape Diagram

129

03-Dec-21 12:36:35 PM

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03-Dec-21 12:36:35 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 14

Date

14

Use the Read–Draw–Write process to solve the problem.

_1

1. Miss Song has 4 of a pan of lasagna in the refrigerator. She wants to cut the lasagna into equal slices so she can have it for dinner for 3 nights. How much of the pan of lasagna will she eat

each night?

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131

03-Dec-21 12:34:25 PM

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03-Dec-21 12:34:25 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 14

Date

14

_1

1. Scott pours 4 gallon of lemonade equally into 2 glasses. How much lemonade is in each glass? a. Draw a model to represent the problem.

b. Is the quotient less than or greater than the dividend? Explain.

c. Write an equation to find how many gallons of lemonade are in each glass. Then write a statement to answer the question.

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133

03-Dec-21 12:37:21 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 14

_1

2. Tara makes 2 gallons of lemonade by using 4 of a container of powdered lemonade. How many gallons of lemonade can she make with the whole container of powdered lemonade? a. Draw a model to represent the problem.

b. Is the quotient less than or greater than the dividend? Explain.

c. Write an equation to find how many gallons of lemonade Tara can make with the whole container of powdered lemonade. Then write a statement to answer the question.

134

PROBLEM SET

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03-Dec-21 12:37:22 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 14

Use the Read–Draw–Write process to solve each problem.

_1

3. Sasha does 7 problems. This is 3 of all the problems on her math homework. How many problems are on Sasha’s math homework?

_1

4. A 2 -mile relay race is run by a team of 4 students. Each student runs an equal distance. How many miles does each student run?

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PROBLEM SET

135

03-Dec-21 12:37:22 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 14

_1

5. Toby eats 8 pound of raisins each day. He buys a 3-pound bag of raisins. How many days will Toby’s bag of raisins last?

_1

6. The perimeter of a square is 5 meter. What is the length of each side of the square?

136

PROBLEM SET

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03-Dec-21 12:37:23 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 14

Name

Date

14

Use the Read–Draw–Write process to solve each problem.

1. There are 4 children who share _1 gallon of milk equally. How much milk does each child get? 2

2. How many _1 -foot pieces can be cut from 3 feet of string? 3

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137

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12/14/2021 11:39:16 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 15

Name

15

Date

Circle the expression that can be used to solve the word problem.

1. How many _1 -pound servings of shrimp can Miss Song make with 6 pounds of shrimp? 2

6 ÷ _2

_1 ÷ 6

greater than 8

less than 8

1

2

1 2. 8 ÷ _ 3

3.

_1 ÷ 6 6

_1

greater than 6

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_1

less than 6

139

03-Dec-21 12:37:54 PM

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03-Dec-21 12:37:54 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 15

Name

15

Date

Circle the expression that could be used to solve each word problem.

_1

1. Kayla and her 2 brothers share 2 of a pan of lasagna equally. What fraction of the pan of lasagna does each person get?

3 ÷ _21

_1 ÷ 3 2

2. How many _1 -pound burgers can Mr. Evans make with 5 pounds of meat? 4

5 ÷ _41

_1 ÷ 5 4

In each pair, circle the description in which the pieces are longer. Explain how you know. 3. Rope A: 4-foot rope cut into fourths

Rope B: 2-foot rope cut into fourths

Explain:

4. Rope C: _1 -foot rope cut into 4 equal pieces 2

Rope D: 4-foot rope cut into _1 -foot pieces 2

Explain:

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141

03-Dec-21 12:38:52 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 15

Use &gt;, =, or &lt; to compare the expressions. Explain how you can compare the expressions without evaluating them. 5.

1_ ÷3 2

1 __ ÷3 10

Explain:

1 6. 4 ÷ _ 5

_1 ÷ 4 5

Explain:

7. 4 ÷ 2

4 × 1_2

Explain:

8.

1_ ÷2 6

1_ 1_ × 6 2

Explain: 1 9. 4 ÷ _ 3

4 ÷ 1_4

Explain:

10.

_1 × 2 8

_1 ÷ 2 8

Explain:

142

PROBLEM SET

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03-Dec-21 12:38:53 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 15

11. Write the expressions in order from least to greatest. Then explain how you know which expression has the least value.

_1 ÷ 5 2

5 ÷ 1_5

5 ÷ 1_2 ,

,

1_ ÷5 5

,

Explain:

Consider the expression. Write a word problem that can be represented by the given expression. 1 12. 5 ÷ _ 4

13.

_1 ÷ 4 3

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PROBLEM SET

143

03-Dec-21 12:38:54 PM

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03-Dec-21 12:38:54 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 15

Date

15

Use &gt;, =, or &lt; to compare the expressions. Explain how you can compare the expressions without evaluating them. 1 1. 6 ÷ __ 12

6 ÷ 1_ 2

Explain:

2. 1_ ÷ 4 5

1_ ÷4 3

Explain:

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145

03-Dec-21 12:38:21 PM

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03-Dec-21 12:38:21 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 16

Date

16

1. How many _ -foot pieces of string can be cut from 4 feet of string? 2 3

2. Tyler freezes 6 cups of strawberries. This amount is _ of the total cups of strawberries he picked. How many cups of strawberries did Tyler pick in all?

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3 4

147

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12/14/2021 10:35:08 AM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 16

16

Date

Use the Read–Draw–Write process to solve each problem.

1. A bag of dog food has 16 cups of food. Pablo feeds his dog _4 cups of food each day. How many days can Pablo feed his dog from the bag of dog food?

8

2. Toby used 3 kilograms of flour to make pasta. This is _3 of the total amount of flour in the pantry. 4

How much flour was in the pantry before Toby makes pasta?

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149

12/21/2021 10:41:04 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 16

3. Mr. Sharma uses 8 meters of ribbon to make bows. He uses _4 meters of ribbon for each bow. How many bows does Mr. Sharma make?

5

4. 4 miles is _2 of the distance Blake runs. How far does Blake run? 5

150

PROBLEM SET

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12/21/2021 10:45:56 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TC ▸ Lesson 16

5. Zara has 6 liters of carrot juice. She drinks _3 liters every day. How many days will it take for Zara 4

to drink all 6 liters?

6. Sasha chopped 10 logs of wood. This is _5 of the total number of logs she chops in a week. How many logs does Sasha chop in a week?

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PROBLEM SET

151

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12/14/2021 10:35:01 AM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TC ▸ Lesson 16

16

Date

Use the Read–Draw–Write process to solve each problem.

1. The principal ordered 9 boxes of pencils. This amount is _3 of the total number of boxes of pencils 4

the students need. How many boxes of pencils do the students need?

2. Ryan has 6 kilograms of beans and some containers. He puts _2 kilograms of beans into 3

each container. How many containers of beans does Ryan have?

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153

12/21/2021 10:51:20 AM

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12/14/2021 10:35:35 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 17

Name

Date

17

_1

1. Ms. Baker has 4 yards of fabric. It takes 4 yard to make a pencil pouch. Does Ms. Baker have enough fabric to make one pencil pouch for each of her 24 students? Explain how you know.

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155

12/14/2021 10:38:28 AM

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12/14/2021 10:38:28 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 17

Name

Date

17

Use the Read–Draw–Write process to solve each problem.

_1

1. Jada pours 2 gallon of fruit punch equally into 4 containers. How many gallons of fruit punch are in each container?

_1

2. Eddie has 45 bottles of water. He drinks 9 of them. How many bottles of water does Eddie drink?

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157

12/14/2021 10:39:29 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 17

3. A chef makes 4 pizzas. They slice each pizza into eighths. How many slices of pizza are there?

_1

4. Mr. Sharma spends 5 minutes driving to the gym. This is 4 of the time he spends driving to work. How many minutes does Mr. Sharma spend driving to work?

158

PROBLEM SET

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12/14/2021 10:39:29 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 17

_1

5. A student misses 5 of the 5 dozen baseballs their coach pitches to them. How many baseballs do they miss?

_1

6. Julie uses 5 of her beads to make 2 necklaces. a. What fraction of her beads does Julie use to make 1 necklace?

b. If Julie has 160 beads, how many beads does she use to make 1 necklace?

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PROBLEM SET

159

12/14/2021 10:39:30 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 17

_7

7. Mr. Perez needs to put 24 books on his bookshelf. Each book is 8 inches wide. The bookshelf is 22 inches wide. Will all the books fit on the shelf? Explain.

160

PROBLEM SET

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12/14/2021 10:39:30 AM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TD ▸ Lesson 17

Date

17

Use the Read–Draw–Write process to solve each problem.

1. Kayla has a wooden board that is 12 feet long. She uses _1 of the board to make a sign. How many 3 feet long is the sign?

2. Eddie makes 5 cups of rice. Each serving of rice measures _1 cup. How many servings of rice does 2 Eddie make?

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161

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12/14/2021 10:40:21 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

Name

Date

18

Write a word problem to match each model. 1.

Saturday

? Sunday

5

2. 1 4

... ? fourths

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163

12/14/2021 10:41:05 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

Write a word problem to match each equation. 3. 4_ × 30 = x 5

1 4. 4 ÷ _3 = w

164

LESSON

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12/14/2021 10:41:05 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

Name

Date

18

Use the Read–Draw–Write process to solve each problem.

9 liters of vinegar. _2 of the vinegar spills. How many liters of vinegar spill? 1. A container has __ 10

3

2. Lisa wants to cut _1 -foot boards from a piece of wood that is 8 feet long. How many boards can she cut?

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3

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165

12/14/2021 10:42:38 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

3 3. A dog and a cat go to the vet. The dog weighs 48 pounds. The vet says the cat weighs __ as much 16

as the dog. How much does the cat weigh?

4. A music teacher spends _1 of their workday teaching piano lessons. If they teach 6 lessons that 2

are each the same length, what fraction of their workday do they spend teaching one lesson?

166

PROBLEM SET

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12/14/2021 10:42:38 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

5. Adesh reads _1 of his book each night. If he reads 28 pages each night, how many pages are in the book?

8

6. Ryan completes a race in 17 minutes. Jada completes the same race in _7 as much time as Ryan. How many minutes does Jada take to complete the race?

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8

PROBLEM SET

167

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

1 of a race. She has run 500 meters so far. How long 7. A long distance runner has completed __

is the race?

10

1 as much in one week. 8. A bakery sells 6,000 pies in one week in November. They usually sell __

How many pies does the bakery usually sell in one week?

168

PROBLEM SET

EM2_0503SE_D_L18_problem_set.indd 168

10

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12/14/2021 10:42:38 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

9. The line plot shows the distances, in miles, that a student runs. Distances a Student Runs

0

× × ×

× × × ×

× ×

1 4

1 2

3 4

× 1

Distance (miles)

a. Write an expression that includes multiplication to represent the total distance the student runs.

b. Evaluate your expression to find the total distance the student runs.

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PROBLEM SET

169

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 18

Name

Date

18

Write a word problem that can be solved by evaluating _2 × 20. Then solve the word problem. 5

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171

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 19

Name

19

Date

Construct a tape diagram to match the story. 1. Sana has 4 pounds of green beans. She gives 2 pounds of them to her friend. Sana’s family eats

_3 of the remaining green beans. How many pounds of green beans does Sana have left? 4

Use the Read–Draw–Write process to solve each problem.

_1

_3

2. Tyler has 6 cups of blueberries. He uses 2 2 cups of blueberries for pancakes. He uses 7 of the

_1

remaining blueberries for muffins. Tyler puts the rest of the blueberries into bags. He puts 4 cup

of blueberries into each bag. How many bags of blueberries can Tyler make?

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173

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 19

1 _1 3. Lacy’s cat weighs 8 pounds. Her cat weighs _ as much as her dog. Noah’s dog weighs 2 2 pounds 3 less than Lacy’s dog. How much does Noah’s dog weigh?

174

LESSON

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12/14/2021 10:44:49 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 19

Name

19

Date

Use the Read–Draw–Write process to solve each problem. 1. Tara has 15 state quarters and 10 silver dollars in her coin collection. After Tara’s dad gives her

_1

more silver dollars, she finds that 5 of her collection is state quarters. How many silver dollars did Tara’s dad give her?

_4

_1

2. 270 muffins were made for a school bake sale. After 5 of the muffins were sold, 3 of the

remaining muffins were given away. The rest of the muffins are shared equally between the

8 students working the bake sale. How many muffins does each student get?

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175

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 19

_1

3. The farmer cooks 6 carrots. The carrots that the farmer cooks is 7 of his total carrots.

_1

The farmer gives 2 of the remaining carrots to a neighbor. The rest of the carrots are divided

equally among his 8 pet rabbits. How many carrots does each rabbit get?

4. The measure of ∠ABC is 147°, and the angle is decomposed into smaller angles as shown. The measure of ∠DBC is 7 the measure of ∠ABC. The measure of ∠EBD is 3 the measure

_1

_1

of ∠ABD. What is the measure of ∠ABE?

E

A D C

B

176

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 19

Name

19

Date

Use the Read–Draw–Write process to solve the problem.

Shen bought 20 pounds of ground beef. He used __1 of the beef to make tacos. He used _2 of the 4

remaining beef to make __1 -pound burgers. How many burgers did he make?

3

4

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177

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply Fractions

Sprint Write the product as a fraction.

_ _

1.

1 1 × 3 3

2.

3 2 × 4 3

_ _

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply Fractions

A

Number Correct:

Write the product as a fraction. 1. 2.

​​ 1_​​ × ​​1_​​ 2

2

23.

​​ 2_​​ × ​​ _​​ 5

5 3

2

3

24.

3 5

5 2

2

4

25.

​​ 1_​​ × ​​ 1_​​ 3

3

​​1_​​ × ​​1_​​

​​ _​​ × ​​_​​

3.

​​ 1_​​ × ​​ 1_​​

4.

​​ 1 ​​ × ​​ 1​​ 2 7

5.

​​ 1_​​ × ​​ 1_​​

26.

​​ 1​​ × ​​ 2​​ 3 3

7

27.

​​2_​​ × ​​ 2_​​ 3

6.

​​ 1​​ × 1​​ ​​ 3 2

28.

3 ​​ 2​​ × ​​  ​​ 3 2

3

29.

​​ 2_​​ × ​​ 4_​​ 5 ​​ 2 ​​ × ​​ ​​ 3 3

_ _ 2

_ _

_ _ 3

_ _

7.

​​1_​​ × ​​ 1_​​

8.

​​ 1​​ × ​​ 1 ​​ 3 6

30.

9.

1 1 ​​ ​​ × ​​ ​​ 3 5

31.

​​ _​​ × ​​  _​​ 3 2

3 5

3 4

5

3 4

5

3 4

5 5

3

_ _

_ _

10.

​​ 1_​​ × ​​ 1_​​ 5

3

32.

11.

5

3

33.

​​ 1_​​ × ​​ 2_​​

3

3

_ _

​​ _​​ × 1_​​ ​​

​​ _​​ × 4_​​ ​​

12.

​​ 2_​​ × ​​ 2_​​ 5

3

34.

13.

4

3

35.

3 6 ​​ ​​ × ​​  ​​ 4 5

4

3

36.

​​ 1_​​ × _​​ ​​ 4

6 5

3 4

3

37.

​​ 1_​​ × ​​ 1_​​ 7

7

6

3

38.

​​ 1_​​ × _​​ ​​ 8

3 5

5 6

4

14. 15. 16.

​​ 1_​​ × 1_​​ ​​ ​​ 1_​​ × 2_​​ ​​ ​​ _​​ × ​​ 2_​​ ​​ 1_​​ × ​​ 1_​​

​​ _​​ × ​​  _​​

_ _

17.

​​ _​​ × 1_​​ ​​ 5 6

3

39.

18.

5 6

3

40.

3 3 ​​ ​​ × ​​  ​​ 4 4

5 4

3

6 6

​​ _​​ × ​​ 2_​​

​​ _​​ × 1_​​ ​​

_ _

19.

​​ _​​ × ​​ 2_​​ 3

41.

20.

1 1 ​​ ​​ × ​​  ​​ 5 5

42.

​​ _​​ × ​​_ ​​ 3 4

6 2

21.

5

5

43.

7 8

7 9

5

3 5

44.

12

8

22.

_ _ ​​ 2_​​ × ​​ 2_​​

​​ 2_​​ × _

180

EM2_0503SE_D_L20_removable_fluency_sprint_multiply_fractions.indd 180

​​ 2_​​ × _​​ ​​

​​_​​ × ​​ _​​

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ Sprint ▸ Multiply Fractions

B

Number Correct: Improvement:

Write the product as a fraction.

_ _

1.

1 1 ​​ ​​ × 2 3

23.

2.

2

4

24.

2

5

25.

​​ 1_​​ × ​​1_​​

_ _ 3 5 ​​ ​​ × ​​  ​​ 5 4

​​4_​​ × ​​ _​​ 5

5 3

4

4

3.

​​ 1_​​ × ​​ 1_​​

4.

​​ 1​​ × ​​ 1​​ 2 9

26.

3 ​​1 ​​ × 4 4

5.

1 1 × 9 2

27.

3 3 × 4 4

6.

1 1 × 5 2

28.

3 4 × 4 3

7.

1 1 × 7 5

29.

3 5 × 4 4

8.

1 1 × 5 7

30.

3 6 × 4 4

9.

1 1 × 5 3

31.

4 4 × 3 6

10.

1 1 × ​​ ​​ 3 5

32.

​​ 2_​​ × ​​ 1_​​ 3

5

_ _ _ _ _ _ _ _

_ _ _ _ _ _

​​ 1_​​ × ​​ 1_​​

_ _ _ _

_ _

_ _ _ _

_ _

11.

​​ 1_​​ × 2_​​ ​​ 3

5

​​ 2_​​ × 4_​​ ​​ 3

5

12.

​​ 2_​​ × 2_​​ ​​

33.

3

5

34.

3

5 5

13.

3

4

35.

​​2_​​ × ​​ _​​ 3

6 5

3

6 5

9

9

​​1_​​ × 1_​​ ​​

​​2_​​ × _​​ ​​

14.

​​ 1_​​ × ​​_​​ 3

3 4

36.

15.

3

3 4

37.

3

6

38.

​​ 1_​​ × _​​ ​​ 5

3 8

3 4

6

3

3

16.

​​ 2_​​ × _​​ ​​ ​​ 1_​​ × ​​ 1_​​

​​ 1_​​ × _​​ ​​ ​​ 1_​​ × 1_​​ ​​

17.

​​2_​​ × 1_​​ ​​ 3

6

18.

​​ 2_​​ × ​​ _​​

39.

3

5 6

40.

​​ 2_​​ × ​​ 2_​​

19.

3 3 ​​ ​​ × ​​  ​​ 2 4

41.

3 8 ​​  ​​ × ​​ ​​ 4 8

20.

5

5

42.

​​ 2_​​ × ​​ _​​ 3

6 3

6 7

8 9

7 12

8 7

_ _ ​​ 1_​​ × ​​1_​​

21.

​​ _​​ × ​​ _​​ 3 5

3 5

43.

22.

3 5

5

44.

​​ _​​ × ​​ 4_​​

182

EM2_0503SE_D_L20_removable_fluency_sprint_multiply_fractions.indd 182

​​ _​​ × ​​1_​​

_ _

​​ _​​ × ​​_​​ ​​ __​​ × ​​_​​

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12/14/2021 11:30:07 AM

EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 20

Name

20

Date

Fill in the blanks to show how to evaluate the expression. 1. 20 − ((7 + 3) ÷ 2) = 20 − (

÷ 2)

= 20 −

2. 9 × ((1_ + 7_) − 2_) = 9 × ( 3 2 6

− 2_) 3

=9×

=

=

Evaluate the expression. 3. 20 + [(2 × 6) − 4]

4. [(20 + 2) × 6] − 4

5. ((2_ − 5_) ÷ 4) × 36 3 9

6. [(2_ + 1_) × 2] − 2_ 3 5 5

7. {1_ − [2 × (1 ÷ 8)]} × 10 4

8. [91 + (36 ÷ (2 + 2))] ÷ 10

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EUREKA MATH2 Tennessee Edition

5 ▸ M3 ▸ TD ▸ Lesson 20

9. [(4 ÷ 1_) ÷ 2] × 2_ 3 4

4 11. {[9 ÷ (_ − (3 ÷ 5))] − 44} × 2,000 5

10. 24 − {2 × [(15 + 5) ÷ 5]}

7 12. 4,628 × [((3 ÷ 5) − 3_) + (__ − (14 ÷ 26))] 5 13

Place parentheses and brackets to make each equation true. 13.

184

60 − 3 × 4 ÷ 2 = 24

PROBLEM SET

EM2_0503SE_D_L20_problem_set.indd 184

14.

5 × 40 ÷ 4 − 2 = 40

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M3 ▸ TD ▸ Lesson 20

Date

20

Evaluate each expression. 1. 15 + [3 × (1 ÷ 4)]

3 2. [(1_ ÷ 4) × (12 3_ − 3_)] + _ 5 5 3 4

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185

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EUREKA MATH2 Tennessee Edition

5 ▸ M3

Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. Cover, Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musee des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY.; page 99, Atsushi Hirao/Shutterstock.com; All other images are the property of Great Minds. For a complete list of credits, visit http://eurmath.link/media-credits.

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EUREKA MATH2 Tennessee Edition

5 ▸ M3

Acknowledgments Kelly Alsup, Adam Baker, Agnes P. Bannigan, Christine Bell, Reshma P Bell, Joseph T. Brennan, Dawn Burns, Amanda H. Carter, David Choukalas, Mary Christensen-Cooper, Nicole Conforti, Cheri DeBusk, Lauren DelFavero, Jill Diniz, Mary Drayer, Christina Ducoing, Karen Eckberg, Melissa Elias, Danielle A Esposito, Janice Fan, Scott Farrar, Gail Fiddyment, Ryan Galloway, Krysta Gibbs, January Gordon, Torrie K. Guzzetta, Kimberly Hager, Jodi Hale, Karen Hall, Eddie Hampton, Andrea Hart, Stefanie Hassan, Tiffany Hill, Christine Hopkinson, Rachel Hylton, Travis Jones, Laura Khalil, Raena King, Jennifer Koepp Neeley, Emily Koesters, Liz Krisher, Leticia Lemus, Marie Libassi-Behr, Courtney Lowe, Sonia Mabry, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Ashley Meyer, Pat Mohr, Bruce Myers, Marya Myers, Kati O’Neill, Darion Pack, Geoff Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Brian Petras, April Picard, Marlene Pineda, DesLey V. Plaisance, Lora Podgorny, Janae Pritchett, Elizabeth Re, Meri Robie-Craven, Deborah Schluben, Colleen Sheeron-Laurie, Michael Short, Erika Silva, Jessica Sims, Tara Stewart, Heidi Strate, Theresa Streeter, Mary Swanson, James Tanton, Cathy Terwilliger, Saffron VanGalder, Rafael Vélez, Jessica Vialva, Allison Witcraft, Jim Wright, Jackie Wolford, Caroline Yang, Jill Zintsmaster Trevor Barnes, Brianna Bemel, Lisa Buckley, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

188

EM2_0503SE_acknowledgements.indd 188

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I know . . . . I did it this way because . . . . The answer is

because . . . .

My drawing shows . . . . I agree because . . . .

Agree or Disagree

That is true because . . . . I disagree because . . . . That is not true because . . . . Do you agree or disagree with

? Why?

Why did you . . . ? Can you explain . . . ? What can we do first? How is

Say It Again

related to

?

I heard you say . . . . said . . . . Another way to say that is . . . . What does that mean?

EM2_0503SE_acknowledgements.indd 189

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12/14/2021 11:37:16 AM

Thinking Tool When I solve a problem or work on a task, I ask myself Before

Have I done something like this before? What strategy will I use? Do I need any tools?

During

Is my strategy working? Should I try something else? Does this make sense?

After

What worked well? What will I do differently next time?

At the end of each class, I ask myself

What did I learn? What do I have a question about?

EM2_0503SE_acknowledgements.indd 190

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12/14/2021 11:37:16 AM

MATH IS EVERYWHERE Do you want to compare how fast you and your friends can run? Or estimate how many bees are in a hive? Or calculate your batting average? Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars. Fueled by your curiosity to understand the world, math will propel you down any path you choose. Ready to get started?

Module 1 Place Value Concepts for Multiplication and Division with Whole Numbers Module 2 Addition and Subtraction with Fractions Module 3 Multiplication and Division with Fractions Module 4 Place Value Concepts for Decimal Operations Module 5 Addition and Multiplication with Area and Volume Module 6 Foundations to Geometry in the Coordinate Plane

What does this painting have to do with math? Color and music fascinated Wassily Kandinsky, an abstract painter and trained musician in piano and cello. Some of his paintings appear to be “composed” in a way that helps us see the art as a musical composition. In math, we compose and decompose numbers to help us become more familiar with the number system. When you look at a number, can you see the parts that make up the total? On the cover Thirteen Rectangles, 1930 Wassily Kandinsky, Russian, 1866–1944 Oil on cardboard Musée des Beaux-Arts, Nantes, France Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY

ISBN 978-1-63898-516-7

9

781638 985167

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