4

A Story of Units®

Fractional Units LEARN ▸ Module 5 ▸ Place Value Concepts for Decimal Fractions

Student

Talking Tool Share Your Thinking

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

Ask for Reasoning

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? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

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Great Minds® is the creator of Eureka Math®, Wit & 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 978-1-63898-512-9

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A Story of Units®

Fractional Units ▸ 4 LEARN

Module

EM2_0405SE_title_page.indd 1

1 2 3 4 5 6

Place Value Concepts for Addition and Subtraction

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

Foundations for Fraction Operations

Place Value Concepts for Decimal Fractions

Angle Measurements and Plane Figures

11/18/2021 4:35:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M5

Contents Place Value Concepts for Decimal Fractions Topic A

Topic C

Exploration of Tenths

Comparison of Decimal Numbers

Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Compare measurements expressed as decimal numbers.

Organize, count, and represent a collection of money.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Decompose 1 one and express tenths in fraction form and decimal form.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Represent tenths as a place value unit.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Use pictorial representations to compare decimal numbers.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Compare and order decimal numbers.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Write mixed numbers in decimal form with tenths.

Topic D

Topic B

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Apply fraction equivalence to add tenths and hundredths.

Tenths and Hundredths Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Decompose 1 one and express hundredths in

Addition of Tenths and Hundredths

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

fraction form and decimal form.

Apply fraction equivalence to add mixed numbers with tenths and hundredths.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Represent hundredths as a place value unit.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Solve word problems with tenths and hundredths.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Write mixed numbers in decimal form with hundredths.

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 114

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Represent decimal numbers in expanded form.

2

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© Great Minds PBC •

This document is the confidential information of Great Minds PBC provided solely for review purposes which may not be reproduced or distributed. All rights reserved.

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TA ▸ Lesson 1

1

Date

For this counting collection, I am partners with We are counting

. .

We think the total amount of the collection is

.

This is how we organized and counted the collection:

The total amount of the collection is An equation that describes how we found the total amount is

© Great Minds PBC •

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This document is the confidential information of Great Minds PBC provided solely for review purposes which may not be reproduced or distributed. All rights reserved.

. .

3

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 1

Self-Reflection Write one thing that worked well for you and your partner. Explain why it worked well.

Write one challenge you had. How did you work through the challenge?

© Great Minds PBC •

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This document is the confidential information of Great Minds PBC provided solely for review purposes which may not be reproduced or distributed. All rights reserved.

LESSON

5

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TA ▸ Lesson 1

Date

1

1. Explain how you counted your collection.

2. If you counted your collection again, would you choose the same strategy? Explain.

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7

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 2 ▸ Tenths in Decimal Form and Fraction Form

0.2 kg

__ 3 liters

0.6 kg

__ 2 liters

10

10

0.4 kg 8 __ liters 10

© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TA ▸ Lesson 2

2

Date

1.

2. Label the number line.

0

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1

11

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0.1 1 tenth

0

0 tenths tenths

tenths

tenths

tenths

tenths

tenths

tenths

tenths

10 tenths

1

10 10

Name

c. Circle the number written in decimal form that represents the shaded part.

b. Shade the first 8 units of the tape diagram.

a. Label the number line by using fraction form, decimal form, and unit form.

1 10

0 10

1. Use the tape diagram and number line to complete parts (a)–(c).

EUREKA MATH2 Tennessee Edition 4 ▸ M5 ▸ TA ▸ Lesson 2

Date

2

13

11/18/2021 10:02:24 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 2

2. Write the length of the bee in centimeters. The drawing is not to scale.

8

9

10

8

7

11

12

13

14

15

7

1

16

17

6

9

6

18

5

5

19

20 21

4

10

4

22

23

3

3

24

25

26

2

2

27

28

1

11

0 CM 1

29

30

Inch

0 CM 12

a. Fraction form: _____ cm

cm

b. Decimal form:

Write the amount of water in fraction form and decimal form. 4.

3.

1L

1L

_____ L =

14

PROBLEM SET

EM2_0405SE_A_L02_problem_set.indd 14

_____ L =

L

© Great Minds PBC •

L

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 2

Write each fraction in decimal form. Shade the bottle to show the correct amount of water. 6.

5.

1L

1L 5 __ L = 10

9 __ L =

L

10

L

Write the total weight of the food in fraction form or decimal form. 8.

7.

kg

0.7 kg

_____ kg

© Great Minds PBC •

EM2_0405SE_A_L02_problem_set.indd 15

4 __ kg 10

PROBLEM SET

15

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 2

9.

10.

Flour

0 kg

0 kg

0.5

0.5

kg

kg

Match the equivalent numbers. 11.

2 tenths

0.7

2 10

12.

7 tenths

0.9

5 10

13.

5 tenths

0.2

9 10

14.

9 tenths

0.5

7 10

16

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TA ▸ Lesson 2

2

Date

Write the amount of water in liters.

1L

a. Fraction form:

b. Decimal form:

© Great Minds PBC •

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L

17

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 3 ▸ Area Models for Tenths

Each area model represents 1. A

B

C

D

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19

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 3

Name

3

Date

Write the decimal fraction as a decimal number. 2. 5 tenths

1. 2 tenths

2 = __ 10

3. 8 tenths

5 = __ 10

8 = __ 10

Write the decimal number as a decimal fraction. 4. 3 tenths 0.1

5. 7 tenths

0.1

0.1

0.3 = _____

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EM2_0405SE_A_L03_problem_set.indd 21

0.1

0.1

0.1

0.1

6. 9 tenths 0.1

0.7 = _____

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.9 = _____

21

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 3

Complete the table. Unit Form 7.

Fraction Form

Decimal Form

1 tenth

How Much to Get to 1?

0.9 4 __

8.

10

9.

6 tenths

10.

0.7

Complete the statements. Write each answer in decimal form. 11. 1 tenth more than 0.2 is 12. 1 tenth less than 0.5 is 13.

is 0.1 more than 0.6.

14.

is 0.1 less than 0.4.

15. 0.6 is

more than 0.5.

16. 0.9 is

less than 1.

22

PROBLEM SET

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. .

© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 3

Name

Date

3

1. Write the decimal fraction as a decimal number.

6 tenths

6 __ = 10

2. Write the decimal number as a decimal fraction.

4 tenths 0.1

© Great Minds PBC •

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0.1

0.1

0.1

0.4 = _____

23

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ Sprint ▸ Make 1

Sprint Write the unknown part as a fraction. 1.

_2 + 6

2.

© Great Minds PBC •

=1 + _ = 1 0 6

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25

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ Sprint ▸ Make 1

A

Number Correct:

Write the unknown part as a fraction. 1.

1 + 3

_

=1

2.

_

23.

2 + 3

=1

24.

3. 4.

_1 +

6.

2 + 4

10.

3 + 5

27.

=1

28.

3 4

29.

4

30.

_

=1

31.

=1

32.

+ _2 = 1 5

33.

0 5

34.

+ _ = 1

13.

_1 +

14.

6

6

_3 +

15.

=1

35.

=1

36.

+ _4 = 1

_1 +

18.

8

10 __ + 10

10

12

EM2_0405SE_A_L04_removable_fluency_sprint_make_1_whole.indd 26

=1 + _1 = 1 3

_

1 + 2

8

26

=1

__

12 + 12

40.

44.

6 12

5 12

=1

=1

=1

+ __ = 1

8

43.

6 10

__ 2 +

_1 + _1 +

=1

=1

+ __ = 1

39.

42.

5 10

0 __ +

=1

0 8

+ __ = 1

+ __ = 1

6

+ _ = 1 10

10

_1 +

41.

=1

__ 2 +

38.

6 8

+ _ = 1

_

8 + 8

6 6

+ _ = 1

=1 5 8

_1 + _1 +

_4 +

__ 1 +

_

2 + 8

37.

8

19.

8

6

+ _ = 1

17.

22.

=1

+ _ = 1

5

11.

21.

26.

+ 4_ = 1

_1 +

20.

0 3

_

9.

16.

25.

4

7.

12.

3

+ _ = 1

5.

8.

+ _2 = 1

+ 4_ = 1

6

_2 +

10

+ 2_ = 1 6

=1

8

+ _ = 1 3 8

10

10

+ __ = 1 3 10

+ __ 1 + __ 2 = 1

__ 2 +

© Great Minds PBC •

=1

6

+ __ 1 + __ 2 = 1

3 __ +

12

=1

12

12

+ __ = 1 5 12

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ Sprint ▸ Make 1

B

Number Correct: Improvement:

Write the unknown part as a fraction.

_

=1

_1 +

23.

=1

24.

1.

2 + 3

2.

3

3. 4.

+ _1 = 1 3

25.

3 3

26.

+ _ = 1

5.

_3 +

6.

2 + 4

4

_

=1

27.

=1

28.

7.

+ _1 = 1

8.

0 + = 1 4

30.

=1

31.

=1

32.

4

_

9.

_4 +

10.

2 + 5

5

_

11. 12.

_5 +

14.

3 + 6

=1

35.

=1

36.

+ _2 = 1

18.

8

10

0 __ + 10

10

10

__

10 + 10

12

EM2_0405SE_A_L04_removable_fluency_sprint_make_1_whole.indd 28

3

=1

_ _

8

28

=1

2

40.

44.

7 12

_1 +

=1

=1

+ __ = 1

+ _2 = 1

8

43.

=1

0 __ +

_1 + _1 +

=1

+ __ = 1

__

10 + 12

39.

42.

=1 6 12

=1

8 8

=1 + __ 4 = 1

6

41.

5 10

8 __ +

_2 +

_

=1 + __ = 1

38.

+ _ = 1

9 __ +

8

0 6

+ 2 = 1 8

3 8

_0 +

1 1 + + 6 6

_4 +

=1 + _ = 1

37.

8

19.

8

6

+ _ = 1

_7 +

22.

34.

_

17.

21.

5 5

6

15.

20.

33.

8

_6 +

29.

3 5

+ _ = 1

13.

16.

+ _ = 1

+ 4_ = 1

_3 +

10

6

=1

8

+ _2 = 1 8

+ 2 + 1 = 1 10 10 + __ = 1 3 10

+ __ 2 + __ 1 = 1

5 __ +

© Great Minds PBC •

+ 1_ = 1

__ __

3 __ +

12

=1

12

12

+ __ 2 = 1 12

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 4

Name

4

Date

Write the number as a mixed number. 1. 1 one 2 tenths 0. 1

1

0. 1

2. 1 one 4 tenths 1

0. 1

3. 2 ones 7 tenths

0.1

0.1

1.4 =

1.2 =

0. 1

1

1

0. 1

0. 1

0. 1

0. 1

0. 1

0. 1

0.1

2.7 =

For problems 4–6, represent the number on the number line by completing the following steps: •

Partition and label the number line.

•

Plot and label the point.

•

Write the number in decimal form.

4. 1 one 3 tenths

3 1 __ = 10

5. 1 one 5 tenths

5 1 __ = 10

© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 4

6. 2 ones 9 tenths

9 2 __ = 10

Write the number in expanded form by using decimal form. 7. 1.8 =

+

8. 2.2 =

+

Complete the table.

9.

Unit Form

Fraction Form

1 one 1 tenth

1__ 1 1.6

0.4

9 1 __

11.

10

2 ones 1 tenth

0.9 2.3

13. 8 2 __

14.

30

How Much to Get to the Next One?

10

10.

12.

Decimal Form

10

PROBLEM SET

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© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TA ▸ Lesson 4

Name

4

Date

1. Write the number as a mixed number.

2 ones 6 tenths 1

1

0.1

0.1

0.1

0. 1

0.1

2.6 =

0.1

2. Partition the number line to plot and label the number. Then write the number in decimal form.

1 one 8 tenths

8 1 __ = 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 5 ▸ Hundredths in Fraction Form and Decimal Form

1 liter

0.07 kg

___ 34 liters 100 1 liter

0.85 kg

___ 7 liters 100 1 liter

0.70 kg

___ 50 liters 100 © Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 5

© Great Minds PBC •

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5

1

Date

2.

1.

1

Name

35

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EUREKA MATH2 Tennessee Edition

36

LESSON

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© Great Minds PBC •

0

0

1

1

4 ▸ M5 ▸ TB ▸ Lesson 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 5

© Great Minds PBC •

EM2_0405SE_B_L05_problem_set.indd 37

1 0

10

0.01 0.00

5

hundredths hundredth hundredths hundredths hundredths hundredths hundredths hundredths hundredths hundredths hundredths

1 100 0 100

1

1. Label the number line by using fraction form, decimal form, and unit form.

0.10

Date

10 100

Name

37

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 5

Complete the number bond. Write each part as a decimal fraction. 2.

1

0.13

10 100

3.

1

4.

1

38

PROBLEM SET

EM2_0405SE_B_L05_problem_set.indd 38

100

0.24

0.46

© Great Minds PBC •

11/18/2021 10:18:48 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 5

Write the weight of the animal in fraction form or decimal form. 6.

5.

7.

kg

0.24 kg

____ kg

___ 68 kg 100

____ kg

Match the equivalent numbers. 8.

4 hundredths

0.14

9.

40 hundredths

0.40

10.

14 hundredths

0.41

11.

41 hundredths

0.04

© Great Minds PBC •

EM2_0405SE_B_L05_problem_set.indd 39

0.97 kg

41 ___ 100

14 ___ 100

4 ___ 100 40 ___ 100

PROBLEM SET

39

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 5

Name

Date

5

Write the shaded amount in unit form, fraction form, and decimal form.

1

a. Unit form: b. Fraction form: ____ c. Decimal form:

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41

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 6 ▸ Area Models for Hundredths

Each area model represents 1.

A

B

C

© Great Minds PBC •

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43

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 6

Name

6

Date

Write the decimal fraction in decimal form. 1. 8 hundredths

2. 48 hundredths

8 ___ 100 =

___ 48 = 100

4. 70 hundredths

3. 50 hundredths

___ 50 =

70 ___ = 100

100

5. Use division to show ___ = __ . 50 100

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5 10

6. Use multiplication to show __ = ___ . 7 10

70 100

45

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 6

Write the decimal number in fraction form. 7. 2 hundredths

8. 12 hundredths

0.02 = ____

0.12 = _____

Use the place value disks, unit form, and number bond to answer problems 9 and 10. •

Circle hundredths to compose as many tenths as you can.

•

Complete the unit form.

•

Use the number bond to break apart the tenths from the hundredths.

9.

14 hundredths =

tenth

hundredths

0.14

0.1

46

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11/18/2021 10:35:16 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 6

10.

26 hundredths =

tenths

hundredths

0.26

Complete the table. Unit Form 11.

Fraction Form

5 hundredths

12.

tenths

hundredths

13.

tenths

hundredths

14.

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Decimal Form

50 ___ 100

0.25

5 tenths 2 hundredths

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 6

Complete the statements. Write the answer in decimal form. 15. 1 hundredth more than 0.04 is 16. 1 hundredth less than 0.14 is 17.

is 0.01 more than 0.27.

18.

is 0.01 less than 0.07.

19. 0.09 is 20. 0.9 is

48

.

more than 0.08. less than 0.91.

PROBLEM SET

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.

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 6

Name

6

Date

1. Write the decimal fraction in decimal form.

39 hundredths

39 ___ 100 =

2. Write the decimal number in fraction form.

17 hundredths 0.17 = ____

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49

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EUREKA MATH2 Tennessee Edition 4 ▸ M5 ▸ TB ▸ Lesson 7 ▸ Open Number Line

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 7

Name

Date

7

Write the number in unit form and decimal form. 1.

one

tenths

hundredths =

2.

ones

tenths

ones

hundredths =

hundredths =

3.

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53

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 7

Write the number in unit form and fraction form. 4.

one

tenths

hundredths =

5.

ones

tenths

ones

hundredths =

hundredth =

6.

54

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11/18/2021 10:35:44 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 7

Represent the number on the number line. •

Partition and label the number line.

•

Plot and label the point.

7. 2 ones 3 tenths 7 hundredths

8. 1 one 8 hundredths

Complete the table.

9.

10.

11.

12.

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Unit Form

Fraction Form

1 one 6 tenths 4 hundredths

64 1 ___

ones

tenth

Decimal Form

100

3.17

hundredths

2 ones 9 hundredths

ones

hundredths

5 5 ___ 100

PROBLEM SET

55

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 7

Match the equivalent numbers. 13.

6 ones 8 hundredths

6.13

80 6 ___

14.

6 ones 8 tenths

6.03

8 6 ___

15.

6 ones 3 hundredths

6.08

13 6 ___

16.

6 ones 1 tenth 3 hundredths

6.80

3 6 ___

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PROBLEM SET

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100

100

100

100

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 7

Name

Date

7

Write the number in unit form, decimal form, and fraction form. a.

Unit form:

one

tenths

hundredths

Decimal form: Fraction form:

b.

Unit form:

ones

tenths

hundredths

Decimal form: Fraction form:

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57

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 8

Name

8

Date

Write an expression to show the total value of the place value disks. Use unit form. 1.

2.

Write an expression to show the total value of the place value disks. Use decimal form. 3.

3 ones

6 tenths +

4 hundredths +

4.

2 tens

8 hundredths +

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59

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 8

Write each number in expanded form. Use decimal form or fraction form. 5. 3 ones 2 tenths

6. 5 ones 4 tenths 9 hundredths

7. 1 ten 3 tenths 3 hundredths

8. 3 tens 1 one 8 hundredths

Write the value of each digit. Use decimal form. 9.

60

10.

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 8

Use the place value chart to complete each statement. Express the value of each digit in decimal form. 11.

tens

ones

tenths

hundredths

9

2

5

a. The digit

is in the ones place. It has a value of

b. The digit

is in the tenths place. It has a value of

c. The digit

is in the hundredths place. It has a value of

12.

tens

ones

tenths

hundredths

4

0

7

6

. .

a. The digit 4 is in the

place. It has a value of

.

b. The digit 0 is in the

place. It has a value of

.

c. The digit 7 is in the

place. It has a value of

.

d. The digit 6 is in the

place. It has a value of

.

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PROBLEM SET

61

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TB ▸ Lesson 8

Name

8

Date

1. Use the place value chart to complete each statement. tens

ones

tenths

hundredths

7

4

9

a. The digit

is in the ones place. It has a value of

b. The digit

is in the tenths place. It has a value of

c. The digit

is in the hundredths place. It has a value of

. . .

2. Write 7.49 in expanded form. Use unit form, decimal form, or fraction form.

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63

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 9 ▸ Blank Tape Diagrams, Area Models, and Number Line

1

1

1

Each area model represents 1.

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 9

Name

9

Date

Write the lengths of the shaded parts in decimal form. Then complete the statement.

1 meter

1.

meters

1 meter meters meters is longer than

meters.

1 meter

2.

meters

1 meter meters meters is shorter than

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meters.

67

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 9

3. Use the scales to complete parts (a)–(c). Grapes

Lettuce

Carrots

Bananas

0 kg

0 kg

0 kg

0 kg

0.5

0.5

0.5

0.5

0.17 kg

0.41 kg

0.4 kg

0.71 kg

a. Write an X over the items that are lighter than the lettuce. b. Write the mass of each item in the table. Mass of Food (kilograms)

Food Grapes Lettuce Carrots Bananas

c. Complete the statements by using the words heavier than or lighter than. The grapes are The lettuce is

68

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the bananas. the carrots.

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11/18/2021 10:58:38 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 9

4. Use the graduated cylinders to complete parts (a) and (b).

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A

B

C

1L

1L

1L

0.86 L

0.2 L

0.8 L

D

E

F

1L

1L

1L

0.35 L

0.18 L

0.5 L

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 9

a. Complete the table by writing the liquid volume of the water in each graduated cylinder. Cylinder

Liquid Volume of Water (liters)

A B C D E F

b. Circle the larger amount of water.

70

PROBLEM SET

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0.2 L

0.18 L

0.35 L

0.5 L

0.8 L

0.86 L

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11/18/2021 10:58:38 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 9

Name

9

Date

Use the scales to complete parts (a) and (b).

A

B

C

0 kg

0 kg

0 kg

0.5

0.5

0.5

0.15 kg

0.48 kg

0.32 kg

a. Write the mass of each package in the table. Package

Mass of Package (kilograms)

A B C b. Complete the statements by using the words heavier than or lighter than. Package A is

package B.

Package B is

package C.

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EUREKA MATH2 Tennessee Edition

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4 ▸ M5 ▸ TC ▸ Lesson 10 ▸ Area Models and Number Line

73

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 10

Name

10

Date

Use >, =, or < to compare the numbers. Shade the area models to help you. Each square represents 1. 1. 0.26

0.2

2. 0.80

0.8

Use >, =, or < to compare the numbers. 3.

0.1

0.1

0.1

0.1

0.1

0.01

0.5

4.

1

0.1

0.1

0.1

0.01

0.01

EM2_0405SE_C_L10_problem_set.indd 75

0.01

0.05

0.01

0.01

0.01

0.01

0.01

0.01

0.01

1.37

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0.01

1

0.1

0.1

0.1

0.1

0. 1

0. 1

0.1

0.01

0.01

0.01

1.73

75

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 10

Use >, =, or < to compare the numbers. Locate the numbers on the number line to help you. 5. 6.03

6.3

6.0

6. 15.68

6.1

6.2

6.3

15.7

15.8

15.9

15.8

15.6

Use >, =, or < to compare the numbers. 7. 0.79

0.9

8. 0.41

0.38

9. 1.85

1.92

10. 1.06

1.6

11. 7.23

7.32

12. 3.5

3.50

13. 34.9

34.19

14. 25.28

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25.2

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 10

Name

10

Date

1. Use >, =, or < to compare the numbers. 0.1

0.1

0.1

0.01

0.01

0.32

0.1

0.1

0.01

0.01

0.01

0.23

2. Use >, =, or < to compare the numbers. Locate the numbers on the number line to help you.

4.2

4.0

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4.02

4.1

4.2

4.3

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EUREKA MATH2 Tennessee Edition

8.2

A

0.49

A

7.2

A

8.04

A

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100

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31 ___ 2

4 ▸ M5 ▸ TC ▸ Lesson 11 ▸ Comparison Cards

B

2.1

B

1.09

B

2 __ 1 10

B

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 11

Name

11

Date

1. Use the scales to complete parts (a)–(c).

Rice

Rice

Rice

Rice

0 kg

0 kg

0 kg

0 kg

0.5

0.5

0.5

0.5

0.13 kg

0.3 kg

0.25 kg

0.1 kg

a. Plot numbers to represent the weight of each bag of rice. Label each point.

0

0.1

0.2

0.3

b. Use >, =, or < to compare the numbers.

0.3

0.1

0.13

0.25

0.25

0.3

c. List the numbers from least to greatest.

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 11

2. Use the numbers to complete parts (a)–(c).

1.2, 1.18, 1.02, 1.28 a. Plot and label the numbers.

1.0

1.1

1.2

1.3

b. Use >, =, or < to compare the numbers.

1.18

1.28

1.02

1.18

1.2

1.02

c. List the numbers from greatest to least.

Arrange the numbers from least to greatest. 3. 2.5, 0.85, 2.8, 2.05

4. 1.31, 13.01, 1.3, 13.1

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 11

List the numbers from greatest to least. 49 __6 ___ 5. 6.08, 5 , 4.95, 6.2, 5 10 100

37 7 ___ __1 ___ 6. 43 , 71.04, 70 , 7 , 47.3 100 10 100

7. Four students record the weights of their rocks, as shown in the table. Jayla

__

13 kg 10

Tom

Amy

Shen

1.38 kg

1 and 4 tenths kg

104 kg 100

___

a. Whose rock is the lightest?

b. Jayla says her rock weighs more than Amy’s because 13 tenths is greater than 4 tenths. Do you agree? Explain.

c. List the weights of the rocks from the lightest to the heaviest.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 11

8. Eva records her 100-meter dash times for the week. On Monday, she runs the dash in 16.01 seconds. On Tuesday, she runs it in 15.58 seconds. On Wednesday, she runs it in 15.56 seconds. On Thursday, she runs it in 16.1 seconds. a. On which day does Eva run the fastest?

b. Arrange Eva’s times from the slowest to the fastest.

84

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TC ▸ Lesson 11

Name

Date

11

Use the numbers to complete parts (a) and (b).

2.36, 2.5, 2.05, 2.46 a. List the numbers from least to greatest.

b. Use >, =, or < to compare the numbers.

2.36 2.5

2.05

2.46

2.5

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2.46

85

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TD ▸ Lesson 12

Date

12

Add.

2 ___ 10 + 100 4 1. __

2. ___ 48 + __ 3 100 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TD ▸ Lesson 12

Name

12

Date

Add. 1. 1 hundredth + 7 hundredths =

2. 6 hundredths + 3 hundredths =

hundredths

hundredths

3. 14 hundredths + 72 hundredths =

hundredths

4. 61 hundredths + 35 hundredths =

hundredths

Add. Shade the area model to help you. 5. __ 1 + ___ 4 = _____ + _____ 10 100 100 100

6. ___ 27 + __ 3 100 10

= _____ 100

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TD ▸ Lesson 12

Add. Use the number line to help you.

4 + ___ 7 7. __ 10 100

8. __ 4 + ___ 17 10 100

90

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Add.

4 ▸ M5 ▸ TD ▸ Lesson 12

9 + ___ 2 9. __ 10 100

10. ___ 7 + __ 4 100 10

11. __ 2 + ___ 9 10 100

12. ___ 37 + __ 4 100 10

13. __ 3 + ___ 40 10 100

14. ___ 60 + __ 4 100 10

3 67 15. Miss Diaz walks ___ kilometers to the library. Then she walks __ kilometers to the gym. 100

How many kilometers does Miss Diaz walk altogether?

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10

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TD ▸ Lesson 12

Date

12

Add.

5 + ___ 7 1. __ 10 100

2. ___ 25 + __ 6 100 10

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EUREKA MATH2 Tennessee Edition 4 ▸ M5 ▸ TD ▸ Lesson 13 ▸ Methods Recording Page

=

=

Method 1

Method 2

Method 3

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TD ▸ Lesson 13

Date

Add.

6 2 + 3 __ 1. 1 __ 10 10

25 64 2. 1 ___ + 3 ___ 100 100

3. __ 7 + ___ 21 10 100

83 4. ___ + __ 7 100 10

7 5. 1 __ + ___ 51 10 100

83 6. __ 6 + 1 ___ 10 100

46 4 7. 1 __ + 3 ___ 10 100

96 4 8. 1 __ + 3 ___ 10 100

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13

97

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TD ▸ Lesson 13

6 64 9. 3 __ + 3 ___ 10 100

85 2 10. 3 ___ + 4 __ 100 10

98 8 11. Zara and David find the sum of 4 ___ and 5 __ . Who made a mistake? Explain. 100

10

Zara’s Work 98

8

78

9 100 + 10 = 10 100 2 100

98

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78 100

David’s Work 98

8

6

9 100 + 10 = 10 10 2 10

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6 10

11/18/2021 11:06:36 AM

EUREKA MATH2 Tennessee Edition

Name

Add. 1.

4 ▸ M5 ▸ TD ▸ Lesson 13

Date

13

__3 + ___ 98 10

100

57 7 2. 4 ___ + 1 __ 100 10

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99

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ Sprint ▸ Equivalent Fractions

Sprint Write the unknown numerator or denominator. 1. 2. 3. 4.

© Great Minds PBC •

1_ = ___ 6

3 9 3_ = ___ 4

_3 = ___ 2 6 3 6 __ = ___ 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ Sprint ▸ Equivalent Fractions

A

Number Correct:

Write the unknown numerator or denominator. 2_3 = ___ 9

1.

1_2 = ___ 4

21.

2.

1_3 = ___ 9

22.

_4 = ___

4_5 = ___ 10

3

6

3.

3 _1 = ___ 4

23.

4.

2 1_5 = ___

24.

4_6 = ___

5.

_1 = ___ 6 12

25.

2 __ = ___ 10 100

6.

2_3 = ___ 6

26.

3_ ___ 6 = 2

7.

2_4 = ___ 8

27.

2 _4 = ___ 6

__ = ___ 12 3

8

8.

9 _3 = ___ 4

28.

9.

_5 = ___

29.

__ = ___ 12

10.

_6 = ___ 12

30.

___ = ___ 100 10

11.

2_4 = ___ 2

31.

1_2 = ___

12.

2_6 = ___ 3

32.

1_3 = ___

3

6

3

8

10

5

30

3 3

13.

__ = ___ 1 12

33.

14.

__ 2 = ___ 1

1_2 = ___ 8

10

34.

__ = ___ 12 4

15.

2 __ = ___ 12 6

35.

2_4 = ___

16.

4_6 = ___ 3

36.

__ = ___ 1 10

37.

__ = ___ 10 100

3

9

6

5

18.

_6 = ___ 3 9 9 3 __ 12 = ___

19.

4 2 __ = ___ 10

39.

__ = ___ 10

20.

8 __ = ___

40.

___ = ___ 100

17.

12

6

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38.

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6

___ = ___ 100 10 40 7

90

70 9

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ Sprint ▸ Equivalent Fractions

B

Number Correct: Improvement:

Write the unknown numerator or denominator. 1.

1_2 = ___ 2

21.

2.

1_3 = ___

22.

3.

_1 = ___ 4 12

23.

3_ ___ 4 = 8 8 _4 = ___ 5

24.

4_6 = __ 12

3

5.

_1 = ___ 5 10 1_6 = ___ 2

6.

4.

2_3 = ___ 6

25.

2 __ = ___ 10

4 2_3 = ___

26.

_6 = ___ 1

7.

4 2_4 = ___

27.

8.

3_ ___ 4 = 12

28.

_4 = __ 3 6 8 2 __ = ___ 12

29.

__ = ___ 12 6

10.

_3 = ___ 5 10 3_ ___ 6 6 =

11.

9.

20

3

10

30.

30 3 ___ = ___

1 _2 = ___ 4

31.

2 1_2 = ___

12.

1 2_6 = ___

32.

2 _1 = ___ 3

13.

__ = ___ 12 4

33.

4 _1 = ___

14.

__ 2 = ___

34.

9 3 __ = ___

15.

2 __ = ___ 1 12

35.

16.

2 _4 = ___ 6

_2 = __ 4 12

36.

17.

_9 = ___ 2

__ = __ 10 2

37.

__ = ___ 10

18.

__ = ___ 12 4

38.

4 ___ = ___ 100

19.

__ 4 = ___

39.

20.

3

10

5

6

9

5 10 8 __ = ___ 4 12

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40. © Great Minds PBC •

100

2

12

5 6

60

40

__ = ___ 10 100 7

___ = ___ 100 10 90

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TD ▸ Lesson 14

Date

14

Use the Read–Draw–Write process to solve the problem. Write the solution statement by using a decimal number. A wall in Mrs. Smith’s living room is 0.78 meters longer than a wall in her bedroom. The wall in Mrs. Smith’s bedroom is 4.32 meters long. How long is the wall in her living room?

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TD ▸ Lesson 14

Date

14

Use the Read–Draw–Write process to solve each problem. Write the solution statement by using a decimal number. 1. Mr. Endo’s chicken drink 5.6 liters of water on Monday. They drink 6.17 liters on Tuesday. In total, how many liters of water do the chickens drink on both days?

2. A watermelon weighs 4.79 kilograms. A pineapple weighs 1.4 kilograms. What is the combined weight of the watermelon and pineapple?

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TD ▸ Lesson 14

3. A sheep is 1.17 meters long. A pig is 0.47 meters longer than the sheep. What is the length of the pig?

4. Gabe solves a magic cube puzzle in 7.64 seconds. That is 4.93 seconds faster than the time it takes his brother to solve the puzzle. How long does it take Gabe’s brother to solve the puzzle?

108

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M5 ▸ TD ▸ Lesson 14

5. Robin jogs 5.3 kilometers on Saturday. She jogs 1.85 kilometers more on Sunday than she jogs on Saturday. How many kilometers does Robin jog on Sunday?

6. Pablo has 4 one-dollar bills, 3 dimes, and 9 pennies. Mia has 4 one-dollar bills and 4 pennies. How much money do they have altogether?

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PROBLEM SET

109

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M5 ▸ TD ▸ Lesson 14

Date

14

Use the Read–Draw–Write process to solve the problem. Write the solution statement by using a decimal number. Miss Diaz’s class drinks 2.9 liters of juice. Mrs. Smith’s class drinks 3.15 liters of juice. How many liters of juice do both classes drink altogether?

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EUREKA MATH2 Tennessee Edition

4 ▸ M5

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, Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Arts, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York; 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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4 ▸ M5

Acknowledgments Kelly Alsup, Leslie S. Arceneaux, Lisa Babcock, Adam Baker, Christine Bell, Reshma P. Bell, Joseph T. Brennan, Dawn Burns, Leah Childers, Mary Christensen-Cooper, Nicole Conforti, Jill Diniz, Christina Ducoing, Janice Fan, Scott Farrar, Gail Fiddyment, Ryan Galloway, Krysta Gibbs, Torrie K. Guzzetta, Kimberly Hager, Jodi Hale, Karen Hall, Eddie Hampton, Andrea Hart, Rachel Hylton, Travis Jones, Jennifer Koepp Neeley, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Ashley Meyer, Bruce Myers, Marya Myers, Geoff Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Marlene Pineda, Elizabeth Re, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Tara Stewart, Mary Swanson, James Tanton, Julia Tessler, Jillian Utley, Saffron VanGalder, Rafael Velez, Jackie Wolford, Jim Wright, Jill Zintsmaster Trevor Barnes, Brianna Bemel, 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

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Talking Tool Share Your Thinking

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

Ask for Reasoning

? 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?

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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?

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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 Addition and Subtraction Module 2 Place Value Concepts for Multiplication and Division Module 3 Multiplication and Division of Multi-Digit Numbers Module 4 Foundations for Fraction Operations Module 5 Place Value Concepts for Decimal Fractions Module 6 Angle Measurements and Plane Figures

What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/ Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

ISBN 978-1-63898-512-9

9

781638 985129