EM2 Tennessee Learn | Grade 5 Module 2 by General

A Story of Units®

Fractions Are Numbers LEARN ▸ Module 2 ▸ Addition and Subtraction with Fractions

Student

L1uuKA7 MATH 2··

TENNESSEE

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

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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

L1uREKA7 MATH 2··

TENNESSEE

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GREAT MINDS

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 978-1-63898-515-0

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/ 1uREKA7 MATH 2-

A Story of Units®

TENNEssee

Fractions Are Numbers ▸ 5

LEARN

Module

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1 2 3 4 5 6

Place Value Concepts for Multiplication and Division with Whole Numbers

Addition and Subtraction with Fractions

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

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EUREKA MATH2 Tennessee Edition

5 ▸ M2

Contents Addition and Subtraction with Fractions Topic A

Topic C

Fractions and Division

Addition and Subtraction of Fractions, Whole Numbers, and Mixed Numbers

Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Interpret a fraction as division.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Add whole numbers and mixed numbers and add mixed numbers with related units.

Interpret a fraction as division by writing remainders as fractions.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Represent fractions as division by using models.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Solve word problems involving division and fractions.

Topic B Addition and Subtraction of Fractions by Making Like Units Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Add and subtract fractions with related units by using pictorial models.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Add and subtract fractions with related units by using area models to rename fractions.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Add mixed numbers with unrelated units.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Subtract whole numbers from mixed numbers and mixed numbers from whole numbers. Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Subtract mixed numbers from mixed numbers with related units.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Subtract mixed numbers from mixed numbers with unrelated units.

Topic D Problem Solving and Line Plots with Fractional Measurements Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Represent data on a line plot.

Add and subtract fractions with related units by finding equivalent fractions numerically.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Solve problems by using data from a line plot.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Add and subtract fractions with unrelated units by finding equivalent fractions pictorially.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Solve problems by equally redistributing a total amount.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Add and subtract fractions with unrelated units by finding equivalent fractions numerically.

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Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 160

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EUREKA MATH2 Tennessee Edition

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5 ▸ M2 ▸ TA ▸ Lesson 1 ▸ Pizza Slices

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 1

Date

1. Complete the model to represent 1 waffle shared equally among 5 friends.

2. 6 waffles are shared equally by 5 people. Each waffle is a different flavor, and each person wants to try every flavor. Use the model to find how many waffles each friend gets. Express your answer as a fraction.

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 1

Date

1. Draw a line to match the expression with the model. Each circle represents 1.

[QQ]

~+lool

3÷5

1000001

ICJCJCJCJCJI

~ 0•1000001

2÷3

1\/\/\/ I<)<)<)

®•ll>l>l>

5÷3

IQQQ

1666

1\/\/1

®[Qg]

LDI-.IL>L>I

2÷5

CIY

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lvvl 1661 7

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 1

Draw a model to show how to equally share the pizzas. Then complete the equation. 2. 3 small pizzas are shared equally by 4 people.

3 ÷ 4 = _____

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 1

3. 3 small pizzas are shared equally by 2 people. Each pizza has a different topping: mushrooms, olives, or pineapple. Each person wants to try each pizza.

3 ÷ 2 = _____

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 1

Draw a model to represent the division expression. Then complete the equation. 4. 1 ÷ 3

1 ÷ 3 = _____

5. 4 ÷ 5

4 ÷ 5 = _____ 6. 5 ÷ 4

5 ÷ 4 = _____

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 1

7. 7 ÷ 2

7 ÷ 2 = _____

Write each division expression as a fraction. 8. 1 ÷ 8 =

9. 7 ÷ 10 =

10. 13 ÷ 6 =

11. 15 ÷ 5 =

Write each fraction as a division expression. 12.

2_ = 3

14.

12 __ = 9

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13.

1_ = 5

15.

11 __ = 4

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 1

Use the Read–Draw–Write process to solve the problem. 16. Mr. Evans has 3 liters of water. He pours an equal amount of water into each of 4 containers. How many liters of water are in each container?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 1

Date

1. Draw a model to show the quotient. Then complete the equation.

2÷3

2 ÷ 3 = _____

2. Write each division expression as a fraction. a. 15 ÷ 6 = b. 9 ÷ 19 = 3. Write each fraction as a division expression. a. b.

3_ = 8

13 __ = 12

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 2

Date

1. Adesh is training for a 22-mile relay race. He will run the race on a 4-person team. Each team member runs the same number of miles. How many miles will each team member run?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 2

Name

Date

1. 4 granola bars of the same flavor are shared equally by 3 friends. a. Circle to show how many whole granola bars each friend gets. Each square represents 1 granola bar.

□□□□ b. How many granola bars are left to share equally?

c. Draw on the remaining square in part (a) to show how the 3 friends can equally share the remaining granola bar.

d. What fraction of the remaining granola bar does each friend get?

e. How many granola bars does each friend get in all?

Complete the division equation.

4÷3=

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 2

Complete the equation and the statement by using a mixed number. Draw a model to help you. Then divide. 2. 3 boxes of paper are shared equally by 2 teachers.

Divide: T

3÷2= Each teacher gets

boxes of paper.

3. 5 treats are shared equally by 3 dogs.

Divide: T

5÷3= Each dog gets

PROBLEM SET

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treats.

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 2

Divide, and express the quotient as a mixed number. Use vertical form to help you. 4. 5 ÷ 2 =

5. 8 ÷ 3 =

n 5

8 +

6. 33 ÷ 4 =

7. 59 ÷ 6 =

). 3

TT9 5

8. Blake and Kayla find 13 ÷ 5. Blake’s Way

13 ÷ 5 = 5

Kayla’s Way

2 5 13 –10 3

13 ÷ 5 = 2 5

Whose quotient is correct? How do you know?

9. Find 43 ÷ 8. Express the quotient as a mixed number.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 2

Date

1. Divide. Express any remainder as a fraction.

5÷2=

2. A cook pours 9 gallons of soup equally into 4 pots. How many gallons of soup does the cook pour into each pot? Express the number of gallons as a fraction and a mixed number.

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 3

Date

Use the Read–Draw–Write process to solve each problem. 1. Miss Song pours 5 liters of water equally into 4 containers. How many liters of water are in 1 container?

2. Mr. Perez pours 3 liters of water equally into 4 containers. How many liters of water are in 1 container?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 3

3. Mr. Evans pours 11 liters of water equally into 4 containers. How many liters of water are in 1 container?

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 3

Name

Date

Complete the equation and statement. Rename fractions as whole or mixed numbers when possible. 1. 1 meter of ribbon is cut into 4 equal pieces.

1 meter

I I=====r====;=-==71~= I I ? ÷

= ____

Each piece of ribbon is

meter long.

2. 3 meters of ribbon are cut into 4 equal pieces.

3 meters

I=====r====r===s1r=-_1 I I --,_, ?

= _____

Each piece of ribbon is

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meters long.

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 3

3. 8 meters of ribbon are cut into 4 equal pieces.

8 meters

? ÷

= _____ =

Each piece of ribbon is

meters long.

4. 5 meters of ribbon are cut into 4 equal pieces.

5 meters

___., ?

= _____ =

Each piece of ribbon is

PROBLEM SET

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meters long.

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 3

Draw a tape diagram to represent the expression. Estimate which two whole numbers the quotient is between. Then divide. Express the quotient as a mixed number. 5. 7 ÷ 6

Divide:

The quotient is between

and

6. 9 ÷ 5

Divide:

The quotient is between

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and

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 3

7. 8 ÷ 3

The quotient is between

Divide:

and

Use the Read–Draw–Write process to solve the problem. 8. The relay team has 4 members. They run a total of 6 kilometers for a race. Each team member runs an equal number of kilometers. a. What fraction of the race does each team member run?

b. How many kilometers does each team member run?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 3

Date

Noah has 15 meters of rope. He cuts it into 8 equal-size pieces to make jump ropes. How long is each jump rope?

Each jump rope is

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meters long.

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 4

Date

Use the Read–Draw–Write process to solve each problem. 1. Mrs. Chan uses 13 yards of fabric to make 4 identical quilts. How many yards of fabric does Mrs. Chan use for each quilt?

2. 40 students share 5 pizzas equally. How much pizza does each student get?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 4

3. Mr. Evans cuts 17 feet of wire into 6 equal pieces. What is the length of each piece of wire?

4. Lacy has 10 gallons of water. She pours an equal number of gallons of water into each of 3 fish tanks. Lacy’s blue fish tank already had _1 gallon of water in it. How many gallons of water 3 are in her blue fish tank now?

LESSON

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 4

Date

1. Lisa cuts a board that is 1 meter long into 5 equal pieces. How many meters long is each piece? a. Draw a tape diagram to represent the problem.

b. Is the quotient less than 1 or greater than 1?

c. Write an equation to find the length of each piece. Then write a solution statement.

d. Use your answer from part (b) to explain how you know your answer for part (c) is reasonable.

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 4

2. Mr. Perez buys 8 liters of juice for his class. The 24 students in his class equally share all the juice. a. Draw a tape diagram to represent how many liters of juice each student gets.

b. Complete the equation to find how many liters of juice each student gets.

= _____

c. Express your answer to part (b) as an equivalent unit fraction.

d. Which fraction helps you better understand how many liters of juice each student gets? Why?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 4

Use the Read–Draw–Write process to solve each problem. 3. Eddie bakes 5 pies for a party. The 30 people at the party equally share the pies. How much pie does each person get?

4. Tara practices soccer for a total of 9 hours in 4 days. She practices for the same number of hours each day. How many hours does Tara practice each day?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TA ▸ Lesson 4

5. A team of fifth graders cleans up trash along a 15-kilometer road. It takes them 7 days to finish. The team cleans the same number of kilometers of the road each day. How many kilometers of the road do they clean each day?

6. Mr. Sharma puts 33 pounds of birdseed equally into 8 bird feeders. His yellow bird feeder

already had _5 pounds of birdseed in it. How many pounds of birdseed are in Mr. Sharma’s yellow 8

bird feeder now?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TA ▸ Lesson 4

Date

Use the Read–Draw–Write process to solve each problem. 1. Lacy uses 5 pounds of clay to make 6 identical vases. How many pounds of clay does she use for each vase?

Lacy uses

pounds of clay for each vase.

2. Yuna uses 23 inches of string to make 3 identical bracelets. How many inches of string does she use to make each bracelet?

Yuna uses

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inches of string to make each bracelet.

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Add and Subtract Fractions or Mixed Numbers

Sprint Add or subtract. Write the sum or difference as a whole number when possible.

_ _

3 2 + = 4 4

8 2 − = 6 6

3. 4.

_ _

1_ + 1_ = 2 5

3 5

6 8

5 8

2_ − 1_ =

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Add and Subtract Fractions or Mixed Numbers

Number Correct:

Add or subtract. Write the sum or difference as a whole number when possible.

_ _

1 1 + = 3 3

23.

1 1 + = 4 4

24.

1 3 + = 5 5

25.

2 3 + = 6 6

26.

3 3 + = 8 8

27.

_ _ _ _ _ _ _ _

__2 + __5 =

2 1 − = 3 3

29.

3 1 − = 4 4

30.

4 2 − = 5 5

31.

10.

5 2 − = 6 6

32.

11.

7 3 − = 8 8

33.

12.

8 − 4 = 10 10

34.

13.

1 4 + = 5 5

35.

14.

3 3 + = 6 6

36.

15.

4 5 + = 8 8

37.

_ _

_ _ _ _

__ __ _ _ _ _ _ _

__5 + __6 = 10

17.

__6 + __8 =

38.

39.

18.

5 2 − = 5 5

40.

19.

6 2 − = 6 6

41.

20.

9 3 − = 8 8

42.

21.

12 − 2 = 10 10

43.

22.

5 14 − = 12 12

44.

_ _ _ _

__ __

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1 3

1 4

2 5

1 6

4 6

2 8

5 8

3 10

6 10

2 3

1 3

3 4

1 4

4 5

1 5

4 6

2 6

7 8

2 8

9 10

4 10

1 5

2 6

3 8

5 8

4 10

6 10

5 12

6 12

20 100

70 100

1_ + 2_ = 1_ + 2_ = 2_ + 2_ = 1_ + 4_ = 2 __ + 3 __ =

28.

16.

_ _

1_ + 1_ =

2_ − 1_ = 3_ − 1_ = 3_ − 2_ = 4_ − 2_ = 5_ − 1_ = 5 __ − 2 __ = 1_ + 1_ = 1_ + 1_ = 2_ + 4_ = 5 __ + 2 __ = 2 __ + 5 __ = 3 ___ + 6 ___ = 6_ − 1_ = 8 8

2 8

10 10

3 10

16 12

7 12

170 100

80 100

8 __ − 2 __ = 9 __ − 4 __ = 13 ___ − 7 ___ =

11/22/2021 3:03:12 PM

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Add and Subtract Fractions or Mixed Numbers

Number Correct: Improvement:

Add or subtract. Write the sum or difference as a whole number when possible.

_ _

1 1 + = 3 3

23.

1 1 + = 4 4

24.

1 2 + = 5 5

25.

2 2 + = 6 6

26.

3 2 + = 8 8

27.

2 + 4 = 10 10

28.

2 1 − = 3 3

29.

2 1 − = 4 4

30.

3 2 − = 5 5

31.

10.

4 2 − = 6 6

32.

11.

6 3 − = 8 8

33.

_ _

_ _ _ _

_ _

__ __ _ _ _ _

_ _

12.

__7 − __4 =

13.

4 1 + = 5 5

35.

14.

3 3 + = 6 6

36.

15.

5 4 + = 8 8

37.

_ _

__6 + __5 =

17.

8 6 + = 12 12

39.

18.

5 3 − = 5 5

40.

19.

6 4 − = 6 6

41.

20.

9 6 − = 8 8

42.

21.

11 − 1 = 10 10

43.

22.

9 14 − = 12 12

44.

__ ___ _ _

_ _

__ __

EM2_0502SE_B_L05_removable_fluency_sprint_add_and_subtract_fractions_or_mixed_numbers.indd 42

1 3

1 4

2 5

4 6

1 6

5 8

2 8

6 10

3 10

2 3

1 3

3 4

2 4

4 5

3 5

4 6

2 6

7 8

5 8

9 10

5 10

1 4

2 5

5 8

3 8

6 10

4 10

6 12

5 12

70 100

20 100

2_ + 1_ = 2_ + 1_ = 2_ + 2_ = 4_ + 1_ = 3 __ + 2 __ = 2_ − 1_ = 3_ − 1_ = 3_ − 2_ = 4_ − 2_ = 5_ − 1_ = 5 __ − 2 __ =

34.

16.

1_ + 1_ =

1_ + 1_ = 1_ + 1_ = 4_ + 2_ = 2 __ + 5 __ =

38.

5 __ + 2 __ = 6 ___ + 3 ___ = 6_ − 1_ = 8 8

6 8

10 10

7 10

16 12

9 12

170 100

90 100

8 __ − 2 __ = 9 __ − 4 __ = 13 ___ − 7 ___ =

11/22/2021 3:03:13 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 5

Name

Date

Consider the expression. Mentally estimate the sum or difference. Circle to show your estimate. 1.

3_ 1_ + 8 4

less than 1

between 1 and 2

greater than 2

between 1 and 2

greater than 2

between 1 and 2

greater than 2

3_ 3_ − 4 8

less than 1

greater than 2

5_ 2_ + 9 3

less than 1

between 1 and 2

15 __ − 4_ 10 5

less than 1

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 5

Complete the model to make like units. Then add or subtract. Each tape diagram represents 1. 5.

1_ 1_ + = 2 4

_1 − 3_ = 2 8

1 2

4_ 1_ + = 9 3

−

1 2

7 __ − 2_ = 10 5

−

1 3

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 5

Draw a model to make like units. Then add or subtract. 9.

3_ __ + 5 = 4 12

10.

11 __ − 2_ = 12 6

−

11.

7_ 2_ + = 9 3

EM2_0502SE_B_L05_problem_set.indd 45

PROBLEM SET

11/18/2021 3:02:08 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 5

12.

8_ __ − 8 = 5 10

−

Use the Read–Draw–Write process to solve the problem. 13 __

13. Noah draws a line 16 inches long. He erases 8 inches from the line. How many inches long is the line now?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 5

Name

Date

Draw a model to help you make like units. Then add or subtract. 1 5+_ = 1. _ 8 4

5 1_ − = 2. _ 8 2

−

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EUREKA MATH2 Tennessee Edition

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5 ▸ M2 ▸ TB ▸ Lesson 6 ▸ Equivalent Fractions

11/18/2021 3:07:47 PM

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TB ▸ Lesson 6

Date

Add or subtract. Show your work. 1.

_7 − 2_ 6 3

6 __ + 4_ 15 5

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 6

1_ 18 + __ 7 14

15 1_ __ −

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 6

Name

Date

Complete the area model to make like units. Then add or subtract. Each area model represents 1. 1. _1 + _5 = 4 8

2. _1 − _2 = 2 6

1 4

−

1 2

1×

× _1 = 1_______ = ____

_1 = _______ = ____

7 __ + 1_ = 10

1×

4×

_1 = _______ = ____

EM2_0502SE_B_L06_problem_set.indd 53

2×

4. 4_ − 1_ = 6 3

−

2×

4÷

_4 = _______ = ____ 6

6÷

11/18/2021 3:05:52 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 6

Draw an area model to make like units. Then add or subtract. 6 3 + __ 5. _ = 4 12

1 7−_ 6. _ = 9 3

3 7. 4_ + __ = 5 10

__ + 1_ = 8. 12 4 8

PROBLEM SET

EM2_0502SE_B_L06_problem_set.indd 54

−

11/18/2021 3:05:53 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 6

Add or subtract. Show your work. 2 + 2_ = 9. _ 9 3

1 − 1_ = 10. _ 2 8

−

1 + 3_ = 11. _ 2 4

__ − 3_ = 12. 21 12 4

EM2_0502SE_B_L06_problem_set.indd 55

−

PROBLEM SET

11/18/2021 3:05:53 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 6

__4

13. Jada and Scott use different strategies to find like units to add 10 and 5 . They both have correct answers. Jada’s Way

Scott’s Way

4 1 + 10 5 1 1×2 2 = = 5 5 × 2 10 4 2 6 + = 10 10 10

4 1 + 10 5 4 4÷2 2 = = 10 10 ÷ 2 5 2 1 3 + = 5 5 5

Explain why Jada’s and Scott’s answers look different but are equivalent.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 6

Name

Date

Draw an area model to make like units. Then add or subtract. 15 __ − 1_ = 12 3

−

3 12 _ __ 2. 15 +5=

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EUREKA MATH2 Tennessee Edition

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5 ▸ M2 ▸ TB ▸ Lesson 7 ▸ Equivalent Fractions

11/18/2021 3:11:06 PM

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 7

Name

Date

Decompose to make like units. Then add or subtract. 1.

15 __ __ − 9 8

6 21 _ __ +5 2. 15

Compose to make like units. Then add or subtract. 3.

6 21 + _ __ 4. 15 5

9 15 − __ __ 8

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 7

Name

Date

Decompose to make like units. Then add or subtract. 1.

2 × 3 __ 3 _2 + __ + 3 = ____ 4

4×3

2× __ − 2_ = 12 __ − _______ 2. 12 15 5 15 5×

−

5 + 16 __ = 3. _ 6 24

37 − 5_ = 4. __ 28 7

−

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 7

Compose to make like units. Then add or subtract. 3÷3 3 2 + __ 5. _ = _2 + _____ 4 12 4 12 ÷ 3

12 ÷ 2 12 − 2_ = ________ − _ 6. __ 5 15 5 15 ÷

−

__ = 7. 5_ + 16 6 24

__ − 5_ = 8. 36 28 7

−

PROBLEM SET

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11/18/2021 3:10:19 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 7

Make like units. Then add or subtract. 4 20 + __ 9. __ = 50 10

3 21 − _ 10. __ = 27 9

17 8 + __ 11. __ = 14 28

28 10 − __ 12. __ = 35 5

24 11 + __ 13. __ = 36 9

7 53 − _ 14. __ = 45 9

16 = 54 + __ 15. __ 8 48

17 = 9 − __ 16. _ 7 42

EM2_0502SE_B_L07_problem_set.indd 65

PROBLEM SET

11/18/2021 3:10:19 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 7

32 _ 6 __

17. Leo and Tyler both correctly found 56 + 7 . Look at their work. Which method would you use? Explain why. Leo’s Way

Tyler’s Way

32 6 × 8 32 48 80 + = + = 56 56 7 × 8 56 56

32 ÷ 8 6 4 6 10 + = + = 56 ÷ 8 7 7 7 7

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

__1

18. Sana spent 5 of her money on a pair of shoes, 5 of her money on a pair of pants, and 10 of her money on a shirt. What fraction of her money did Sana spend?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TB ▸ Lesson 7

Date

1. Add.

2_ 5_ + = 3 6

2. Subtract. 11 − 1_ = __ 8

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

Name

Date

Add or subtract.

_ _

−

1 1 + = 3 5

2 2 − = 4 6

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

_ _

5 3 + = 4 5

Use the Read–Draw–Write process to solve the problem. 4. Blake buys 2 trays of brownies for a party. He cuts each tray into fifths. At the end of the party,

_6 of a tray of brownies is left. He gives _2 of a tray of the remaining brownies to his friends. What 5

fraction of a tray of brownies does Blake keep for himself?

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

Name

Date

Complete the area models to make like units. Then add or subtract. Each area model represents 1. 1. 1_ + 1_ = 2 3

× _ 1_______ = _____ 1 = 2

2×

EM2_0502SE_B_L08_problem_set.indd 71

2. 1_ − 1_ = 3 4

× _1 = 1_______ = _____ 3

3×

−

× _ 1_______ = _____

1 = 3

3×

× _1 = 1_______ = _____ 4

4×

11/18/2021 3:12:28 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

Draw an area model to represent each fraction. Use the area models to make like units. Then add or subtract. 2 _ +3= 3. _ 6 4

× _ 2_______ = _____

2 = 6

6×

8 _ −4= 4. _ 9 6

× _3 = 3_______ = _____ 4

4×

−

× _ 8_______ = _____

8 = 9

9×

× _4 = 4_______ = _____ 6

6×

Draw area models to make like units. Complete the equation to add or subtract. 2× 1× 2 1_ ________ _______ 5. _ + = + 5 2 5× 2×

PROBLEM SET

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2× 3× 2 _ 6. _ − 3 = _______ − _______ 3 5 3× 5×

−

11/18/2021 3:12:29 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

× 1× _ _ 4_______ + _______

7. 4 + 1 = 3 4

3×

× 3× _ _ 6_______ − _______

8. 6 − 3 = 5 4

4×

5×

4×

−

Mentally estimate the sum or difference and circle to show your estimate. Then add or subtract. Show your work. 1 _ +2= 9. _ 2 7

Estimate: less than 1

between 1 and 2

greater than 2

between 1 and 2

greater than 2

9 10. __ − 3_ = 10 4

Estimate: less than 1

EM2_0502SE_B_L08_problem_set.indd 73

PROBLEM SET

11/18/2021 3:12:30 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

5 _ 11. _ −1= 3 7

Estimate: less than 1

between 1 and 2

greater than 2

between 1 and 2

greater than 2

11 _ 12. __ +9= 10 8

Estimate: less than 1

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

13. Kelly’s water bottle is filled with _3 liters of water. She drinks _1 liter of water after her walk and

_1 liter of water with her snack.

a. How many liters of water does Kelly drink in all?

b. How many liters of water are left in Kelly’s water bottle?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 8

Name

Date

Draw an area model to represent each fraction. Use the area models to make like units. Then add or subtract. 1. _2 + _1 = 3 4

5 3_ − = 2. _ 6 5

−

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TB ▸ Lesson 9

Date

Add or subtract. Show your work. 1.

_1 + _1 = 4 6

_8 + _7 = 9 6

_4 − _2 = 5 7

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 9

5 3 __ + __ + _3 = 20 12 4

1 _2 + _1 + __ =

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 9

Name

Date

Make like units. Then add or subtract. 1.

× 4 1____ _5 + 1_ = 5____ + ×7 7 4 7×4 4×7

5 7 3. _ + _ = 6 9

5×

7×

6×

9×

_______ + _______

3 4 4. _ − _ = 2 9

EM2_0502SE_B_L09_problem_set.indd 79

4×

2×

9×

_______ − _______ −

3 __ + _5 = _______ + _______

3×

−

× 3 1____ 3_ _ − 1 = 3____ − ×2 4 6 4×3 6×2

15 __ − 11 __ = 9 8

_______ − _______ −

11/18/2021 3:14:15 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 9

Mentally estimate the sum or difference and circle to show your estimate. Then add or subtract. Show your work. 7.

2_ 2_ + = 8 5

Estimate: less than 1

between 1 and 2

greater than 2

10.

between 1 and 2

greater than 2

between 1 and 2

greater than 2

15 11 __ − __ = 12 9

Estimate: between 1 and 2 greater than 2

PROBLEM SET

EM2_0502SE_B_L09_problem_set.indd 80

greater than 2

13 __ − _5 = 6 8

less than 1

12.

Estimate:

between 1 and 2

Estimate:

7_ 9_ + = 6 7

less than 1

Estimate:

11.

Estimate:

6_ 3_ + = 7 5

less than 1

8 __ − 2_ =

less than 1

between 1 and 2 greater than 2

11/18/2021 3:14:15 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 9

Make like units to add or subtract. Show your work. 13.

_1 + 3_ + 4_ = 3 5 5

1 2 4 14. (_ + _) − _ = 5 2 3

11 __

15. Toby correctly added 12 and 8 . 11 × 8 7 × 12 88 84 172 = + + = 12 × 8 8 × 12 96 96 96

a. Explain how Toby chose the units he used and why he could have used other units.

7 11 _ __

b. Find 12 + 8 by using different units than Toby.

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PROBLEM SET

11/18/2021 3:14:16 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TB ▸ Lesson 9

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

16. Riley has 4 gallons of lemonade at a lemonade stand. Yuna brings an additional 3 gallons

of lemonade to the stand. Together, they sell 2 gallon of lemonade. How many gallons

of lemonade do they have left?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TB ▸ Lesson 9

Date

1. Add.

_2 + _3 = 5 8

2. Subtract. 5_ 3_ − = 6 4

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Equivalent Fractions

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

_ ___

1 = 3 6 3 9 = 4

_ ___ _ ___

3 = 2 6 3 6 = 10

__ ___

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Equivalent Fractions

Number Correct:

Write the unknown numerator or denominator. 1.

1 = 2 4

_ ___

21.

_ ___

22.

1 = 3 9 3 1 = 4

1 2 = 5

24.

4 = 5 10 8 4 = 6

1 = 12 6

_ ___

25.

__2 = ___

_2 = ___

26.

_2 = ___

27.

28.

3 6 = 5

29.

8 = 12 3 5 10 = 12

30 ___ = ___

8. 9.

_ ___ _ ___

3 4

6 8

9 _3 = ___

_ ___

23.

_ ___

2 = 3 9 3 6 = 4

_ ___ _ ___

_ ___ 10

100

_ ___

3 = 2 6 4 2 = 6

_ ___

__ ___ __ ___

10.

3 = 12 6

_ ___

30.

11.

2 = 2 4

_ ___

31.

100 10 3 1 = 2

12.

_ ___

32.

3 1 = 3

13.

2 = 3 6 3 1 = 12

33.

_1 = ___

14.

34.

15.

__2 = ___

35.

16.

4 = 3 6

_ ___

36.

17.

_ ___

37.

18.

6 = 3 9 9 3 = 12

38.

19.

4 2 = 10

39.

20.

__8 = ___

40.

__ ___ 1 __2 = ___

__ ___ __ ___ 12

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_ ___

_ ___ 2

__ ___

9 = 12 4 6 2 = 4

_ ___

1 __5 = ___ 10

__ ___

6 = 10 100

40 ___ = ___ 100 10 70 7 = 10

__ ___

90 9 ___ = ___ 100

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Equivalent Fractions

Number Correct: Improvement:

Write the unknown numerator or denominator.

_ ___

6 _2 = ___

1 2 = 2

21.

3 1 = 3

22.

1 = 12 4

_ ___

23.

4 8 8 4 = 5

_ ___

24.

_4 = ___

1 = 5 10 1 2 = 6

2 4 = 3

26.

2 4 = 4

27.

3 = 12 4

_ ___

28.

3 = 5 10 3 6 = 6

_ ___

29. 30.

10 = 12 6 30 3 = 100

31.

1 2 = 2

12.

2 1 = 6

32.

13.

__3 = ___

33.

14.

__2 = ___

34.

10. 11.

_ ___

_ ___ _ ___

_ ___

_ ___ 1 _2 = ___

_ ___ 12

25.

_3 = ___

_ ___ 6

20 __2 = ___ 10

_ ___ 3 1 = 6

_ ___

4 = 3 6 8 2 = 12

__ ___ __ ___

___ ___ _ ___

2 _1 = ___ 3

_ ___ 1 4 = 2

3 __9 = ___ 12

15.

5 10 2 1 = 12

16.

4 2 = 6

36.

17.

6 2 = 9

37.

18.

__9 = ___

38.

__ ___

39.

__7 = ___

40.

90 ___ = ___

19. 20.

__ ___ _ ___ _ ___

4 = 5 10 8 4 = 12

__ ___

EM2_0502SE_C_L10_removable_fluency_sprint_equivalent_fractions.indd 88

35.

_ ___ 2 = 12 4

__5 = ___ 10

60 __6 = ___

40 4 ___ = ___ 100 10

100

11/22/2021 3:04:45 PM

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 10

Date

Add. Show your work. 12 + 3 _1 = 1. 12 __ 5 30

2. 2 3_ + 8 7_ = 4 8

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11/18/2021 3:15:05 PM

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 10

Name

Date

1. Consider the expression.

1 + 1 2_ 5

a. Estimate the sum. Circle to show your estimate. between 1 and 2

between 2 and 3

greater than 3

b. Use the number line to find the sum 1 + 1 _2 . 5

,I I I I I •,._++---l-t--++-t-+-t-++-t----t-11,1 I I I I I I I I I I I I I 0

►

1 + 1 2_ = 5

2. Consider the expression.

1 5_ + 2 6

a. Estimate the sum. Circle to show your estimate. between 1 and 2

between 2 and 3

b. Use the number line to find the sum 1 _5 + 2.

greater than 3

1 5_ + 2 = 6

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 10

Make like units and then add. 1 3. 3 _ + 2 _1 = 3 2 4

_____ + 2 _1 4

= 3 + 2 + _____ + _1 4

= 5 + _____ =

1 4. 9 _ + 17 _5 = 9 _____ + 17 _____ 4 8

+ _____

+ _____ + _____

PROBLEM SET

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11/18/2021 3:15:33 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 10

Add. Use the arrow way or a number bond to help you make the next whole number.

__ = 1 _____ + 11 __ = 5. 1 1_ + 11 2 8 8

2 6. 2 _ + 1 _4 = 2 _____ + 1 _4 = 3 9 9

9 7. 6 1_ + 9 __ = 6 _____ + 9 _____ = 10 2

10 4 8. 5 _ + 7 __ = 5 _____ + 7 _____ = 12 6

Add.

9. 4 5_ + 7 = 7

4 10. 3 + 1 _ = 9

11. 6 1_ + 3 2_ = 3 9

6 6 12. _ + 9 __ = 5 10

EM2_0502SE_C_L10_problem_set.indd 93

PROBLEM SET

11/18/2021 3:15:34 PM

EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 10

3 13. 5 _ + 2 _3 = 4 8

14. 13 2_ + 8 7_ = 3 9

3 15. 2 _ + 1 _7 + 4 _1 = 2 4 8

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

3 kilometers from her home to the store. She rides her bike 3 _4 kilometers 16. Jada rides her bike 2 __ 10

from the store to the park. How many kilometers does Jada ride her bike in all?

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 10

Date

1. Add. Use the arrow way or a number bond to help you make the next whole number.

4 1_ + 6 _5 = 4 _____ + 6 _5 = 2

2. Add. Show your work. 2 3 _2 + 2 __ = 5 15

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 11

Name

Date

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

1. A banana muffin recipe uses 2 _1 cups of flour. A blueberry muffin recipe uses 2 _3 cups of flour. 3

How many cups of flour are needed to make both recipes?

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 11

Date

Make like units. Then represent the equation with like units on the number line and add. 1 = 2 _____ + 1 _____ = 1. 2 1_ + 1 _ 2 3

1× _1 = ________ = _____ 2

2×

× _1 = 1_______ = _____ 3

3×

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 11

2 2. 1 3_ + 3 _ = 1 _____ + 3 _____ = 3 4

3× _ ________ = _____

3 = 4

4×

2× _2 = ________ = _____ 3

3×

Make like units and then add.

3. 3 1 + 2 1 = 3 + 5 2

1× 1× ________ ________ +2+ 5×

2×

6×

4×

= 3 + 2 + _____ + _____

= 4 + 7 + _____ + _____

100

2× 1× 2 1_ _ ________ ________ 4 +7 =4+ +7+

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 11

Add. Use the arrow way or a number bond to help you make the next whole number. 5 5. 4 _ + 1 _1 = 4 _____ + 1 _____ = 7 2

4 6. 3 _ + 1 3_ = 3 _____ + 1 _____ = 5 4

2 7. 6 _ + 2 _2 = 6 _____ + 2 _____ = 5 3

5 8. 4 _ + 7 5_ = 4 _____ + 7 _____ = 9 6

Add.

1 9. 2 _ + 1 _4 = 2 9

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3 10. 1 _ + 1 _1 = 5 2

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 11

13 11. __ + 2 _1 = 3 8

9 12. 5 1_ + 8 __ = 10 4

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

3 1 hours in school. He spends 1 _ hours at his piano lesson. How many hours does 13. Adesh spends 5 _ 3 4 Adesh spend in school and at his piano lesson in all?

102

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 11

Date

Add. Show your work. 1 1. 1 _ + 1 _4 = 5 4

3 2. 4 _ + 12 _2 = 3 4

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 12

Date

Subtract. Show your work. 1. 28 5_ − 6 = 7

2 2. 7 − 3 _ = 7

3 3. 15 − 6 _ = 8

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105

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 12

Date

Subtract like units to find the difference. 1. 5 7_ − 5 = 8

2. 5 7_ − 3 = 8

Decompose the part to take away from the total. Use the number line to show your work. 3. 2 − 1 1_ = 8

I I I I I I I - ~~+H+~K~l~l71 0 1

•

I I I I• 2

4. 12 − 4 3_ = 5

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107

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 12

Use the arrow way to add on to find the unknown part. 7 = 5. 2 − _ 8

6. 5 − 2 5_ = 7

Arrow way:

Subtract the whole-number parts. Then decompose the total to take from 1 to subtract. 1

5 –16 =

8 – 2 13 =

5 –1= 4

8–

4– 6 =

= -

–

13– 6 11 =

–

108

= =

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 12

Subtract. 3 −4= 10. 7 __ 10

5 11. 7 − 2 __ = 12

12. 3 − 1 2_ = 7

9 13. 24 __ − 17 = 13

7 14. 21 − 6 __ = 15

__ = 15. 13 − 19 9

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 12

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

3 kilograms of the flour to make bread. How many 16. Noah buys 3 kilograms of flour. He uses 1 __

kilograms of flour does Noah have left?

110

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 12

Date

Subtract.

1. 7 3_ − 2 = 8

3 2. 7 − 2 _ = 8

2 3. 22 − 4 _ = 5

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111

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 13

Date

Subtract. Show your work. 5 3 1. 4 _ − 2 __ = 16 8

10 1 2. 9 _ − 4 __ = 12 6

7 1 3. 8 _ − 5 __ = 12 4

3 5 4. 18 __ − 7 _ = 4 16

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 13

Name

Date

4 1. Consider the expression 9 _5 − 4 __ . Between what two whole numbers do you estimate is the 6

difference? Explain your reasoning. The difference is between

and

Rename the mixed numbers so the fractional parts have like units. 1 2. 2 7_ − 1 _ = 2 ____ − 1 ____ 4 8

__ = 3. 4 3_ − 2 12 5 15

____ −

____

Subtract.

__ − 2 3_ = 4. 5 15 7 28

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9 5. 15 1_ − 2 __ = 5 10

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 13

3 6. 4 __ − 3 _4 = 5 10

2 7. 3 _ − 1 _2 = 3 6

11 8. 18 2_ − 7 __ = 3 12

4 9. 6 4_ − 2 __ = 5 15

7 10. 11__ − 3 2_ = 5 20

116

PROBLEM SET

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__ = 11. 16 3_ − 7 19 7 21

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 13

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

5 feet tall. How many feet 12. A maple tree was 6 _2 feet tall when it was planted. The tree is now 13 __ 3

has the maple tree grown since it was planted?

7 kilometers on Sunday. Her goal was to jog 13. Lacy jogged 7 _2 kilometers on Saturday and 5 __ 5

10 _1 kilometers during the weekend. How many kilometers more than her goal did Lacy run? 2

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PROBLEM SET

117

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 13

Date

Subtract. Show your work. 5 − 1 1_ = 1. 3 _ 2 8

5 2. 7 __ − 5 _3 = 12 4

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 14

Name

Date

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

2 4 hours of driving. She stops to take a break after 5 _ hours. How many 1. Yuna’s car trip will take 9 _ 3

hours does Yuna still need to drive after her break?

8 = 2. 20 5_ − 14 _ 6 9

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 14

Date

Subtract.

4 − 6 _1 = 1. 9 _ 7 2

3 7 2. 8 _ − 5 __ = 10 8

2 3. 13 _ − 2 _4 = 9 6

2 4. 14 _ − 6 4_ = 7 6

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 14

7 5. 18 _ − 4 _5 = 9 8

2 6. 10 _ − 8 _6 = 7 4

1 7. 17 _ − 5 _4 = 5 9

8. 16 3_ − 9 3_ = 6 8

124

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 14

9 4 − 7 __ = 9. 15 _ 10 6

5 7 10. 11 _ − 3 __ = 12 9

11. Kelly makes a mistake when finding the difference between 16 _2 and 7 _3 . 7

21 8 3 2 3 2 16 7 - 7 4 = 9 7 − 4 = 9 28 - 28 = 8 28 − 28 = 8 28

8 8 28 1

a. What mistake does Kelly make?

b. Show Kelly a correct way to find the difference.

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PROBLEM SET

125

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TC ▸ Lesson 14

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

12. Ryan needs to read for 6 _1 hours over the weekend. He reads for 1 _3 hours on Saturday and 5

2 _1 hours on Sunday. For how much longer does Ryan need to read to reach his goal? 3

126

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M2 ▸ TC ▸ Lesson 14

Date

Subtract. Show your work. 4 − 4 _1 = 1. 7 _ 5 3

1 2. 3 _ − 1 _2 = 3 4

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127

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Interpret Division as a Fraction

Sprint Write the quotient for each expression. Use a whole number or mixed number when possible. 1.

1÷8

4÷4

5÷4

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Interpret Division as a Fraction

Number Correct:

Write the quotient for each expression. Use a whole number or mixed number when possible. 1.

1÷2

23.

6÷2

1÷3

24.

7÷2

1÷8

25.

8÷8

2÷2

26.

9÷8

2÷3

27.

15 ÷ 8

3÷3

28.

8÷4

3÷4

29.

11 ÷ 4

3 ÷ 10

30.

15 ÷ 2

3÷5

31.

24 ÷ 5

10.

5÷5

32.

17 ÷ 4

11.

6÷5

33.

20 ÷ 3

12.

7÷5

34.

13 ÷ 6

13.

9÷5

35.

30 ÷ 7

14.

2÷3

36.

27 ÷ 8

15.

4÷4

37.

49 ÷ 9

16.

5÷4

38.

29 ÷ 6

17.

7÷4

39.

47 ÷ 7

18.

4÷2

40.

53 ÷ 8

19.

5÷2

41.

67 ÷ 9

20.

10 ÷ 5

42.

59 ÷ 6

21.

11 ÷ 5

43.

63 ÷ 8

22.

13 ÷ 5

44.

71 ÷ 9

130

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ Sprint ▸ Interpret Division as a Fraction

Number Correct: Improvement:

Write the quotient for each expression. Use a whole number or mixed number when possible. 1.

1÷3

23.

15 ÷ 5

1÷4

24.

16 ÷ 5

1 ÷ 10

25.

6÷6

5÷5

26.

7÷6

5÷6

27.

11 ÷ 6

3÷3

28.

6÷3

3÷7

29.

8÷3

3 ÷ 10

30.

13 ÷ 2

3÷4

31.

23 ÷ 5

10.

4÷4

32.

15 ÷ 4

11.

5÷4

33.

19 ÷ 4

12.

2÷2

34.

19 ÷ 6

13.

3÷2

35.

31 ÷ 7

14.

4÷5

36.

37 ÷ 8

15.

10 ÷ 10

37.

50 ÷ 9

16.

11 ÷ 10

38.

17 ÷ 6

17.

13 ÷ 10

39.

48 ÷ 7

18.

10 ÷ 5

40.

51 ÷ 8

19.

11 ÷ 5

41.

68 ÷ 9

20.

13 ÷ 5

42.

53 ÷ 6

21.

4÷2

43.

61 ÷ 8

22.

5÷2

44.

70 ÷ 9

132

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 15

Name

Date

1. Miss Song records the number of miles she walks each day for a month. Her results are shown in the calendar. SUN

MON

TUE

WED

THU

FRI

SAT

2 5 miles 2 7 miles 2 1 miles 1 3 miles 2 3 miles 8 8 2 4 4 6

1 1 miles 2 1 miles 2 3 miles 1 7 miles 2 5 miles 1 1 miles 1 1 miles 2 2 4 8 8 8 4 2 3 miles 1 3 miles

2 1 miles 2 3 miles 2 7 miles 2 1 miles

2 miles 22

1 1 miles 1 1 miles 1 1 miles 2 5 miles 2 7 miles 2 8 4 8 8 27

2 miles

2 1 miles 2

2 1 miles 2 3 miles 1 7 miles 2 1 miles a. How many miles did Miss Song walk on the first Monday of the month?

b. What is the longest distance Miss Song walked?

c. What is the shortest distance Miss Song walked?

d. On which day did Miss Song walk 1 4 miles?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 15

e. How many days did Miss Song walk at least 1 4 miles?

Did Miss Song usually walk more or less than 1 4 miles?

g. Use the data in the calendar to create a line plot.

• 1/--------------------• 0

h. What is the most frequent distance Miss Song walked?

How many miles did Miss Song walk on the third Saturday of the month?

What is the difference, in miles, between the longest and the shortest distances Miss Song walked?

k. How many days did Miss Song walk less than 2 miles?

134

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 15

Name

Date

1. Adesh gathers maple tree seeds for a science project. He measures the length of each seed to the nearest eighth inch. Adesh records the data in a table. Lengths of Maple Tree Seeds (inches)

2 1_

1 3_

1 7_

2 3_

1 3_

2 1_

1 7_

1 5_

8 8

4 8

8 4

a. Create a line plot to represent Adesh’s data.

b. Explain how you determined the interval length for your line plot.

c. What is the most frequent maple tree seed length?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 15

d. How many maple tree seeds are less than 2 _1 inches long? 8

e. What is the total length of the maple tree seeds that are 1 _3 inches long? 4

What is the difference between the lengths of the longest and the shortest maple tree seeds?

g. Adesh says that most of the maple tree seeds are 1 _3 to 2 _1 inches long. Do you agree with Adesh? Why?

h. Adesh’s sister finds another maple tree seed. She measures the seed and finds that it is

_1 inch longer than Adesh’s shortest seed. What is the length of the maple tree seed Adesh’s 2

sister finds?

136

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 15

Name

Date

Eddie tracks how far he walks each day for 10 days. The distances shown are in miles. Day

Distance (miles)

1 1_ 4

2 3_

1 1_

2 1_

2 _1

2 1_

1 2

_ 7 8

1. Create a line plot for the data shown in the table. Title and label the line plot. Then plot the data.

2. Eddie says he usually walks at least 1 mile each day. Is that a correct statement? Why?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

Name

Date

1. Mr. Sharma weighs each pumpkin he sells at his pumpkin farm. He records the data on a line plot. Weights of Pumpkins Sold

•

× × ×

× ×

I 1111 I 0

× ×

•

Weight (pounds)

a. How many pumpkins did Mr. Sharma sell?

b. What is the weight of the heaviest pumpkin?

c. What is the most frequent weight of the pumpkins sold?

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

d. What is the total weight of the two lightest pumpkins?

e. How many pumpkins weigh at least 12 _ pounds? 1 4

Eddie bought the two heaviest pumpkins. Jada bought the lightest pumpkin. What is the difference in weight between Jada’s pumpkin and the total weight of Eddie’s pumpkins?

g. Julie bought two pumpkins that have a total weight of 25 pounds. Based on the data on the line plot, what could be the weights of Julie’s pumpkins?

140

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

2. An animal clinic measures the weights of 10 kittens. The weights are recorded in the table.

Kitten Weight (pounds)

"" "" "" "" "" 1

1 3_

2 1_

1 3_

2 1_

1 7_

2 1_

1 _5

2 1_

1 5_

a. Use the data values in the table that are not crossed off to complete the line plot. Weights of Kittens

× 0

1 1

× ×

1 1 3 1 5 3 7 1 1 3 1 5 3 7 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 8 4 8 2 8 4 8 8 4 8 2 8 4 8 Weight (pounds)

b. Write three questions that can be answered by using the line plot.

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LESSON

141

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

3. Mrs. Chan’s class measures the lengths of 10 pencils. The lengths are recorded in the table.

Pencil Length (inches)

"" "" "" "" "" 1

5 3_

6 1_

5 3_

5 1_

6 7_

6 1_

5 3_

5 _1

5 5_

a. Use the data values in the table that are not crossed off to complete the line plot. Lengths of Pencils

× 0

5 5

× ×

1 1 3 1 5 3 7 1 1 3 1 5 3 7 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 8 4 8 2 8 4 8 8 4 8 2 8 4 8 Length (inches)

b. Write three questions that can be answered by using the line plot.

142

LESSON

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

4. Tyler records the amount of time he spends reading each week for 10 weeks. The data values are recorded in the table.

Week Time (hours)

"" "" "" "" "" 1

2 3_

2 1_

3 3_

3 1_

2 7_

2 1_

2 _1

2 1_

3 1_

a. Use the data values in the table that are not crossed off to complete the line plot. Tyler’s Weekly Reading

× 0

2 2

× ×

1 1 3 1 5 3 7 1 1 3 1 5 3 7 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 8 4 8 2 8 4 8 8 4 8 2 8 4 8 Time (hours)

b. Write three questions that can be answered by using the line plot.

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143

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

Name

Date

1. Sasha measures the amount of water in several containers, labeled A through J. She records the data in a table. a. Sasha starts to create a line plot to represent the data. Use the data values in the table that are not crossed off to complete the line plot.

Container

6 7_

5 3_

5 1_

6 1_

6 5_

6 3_

6 7_

5 5_

_ 65

Amounts of Water in Sasha’s Containers

×× I

× I

1 1 3 1 5 3 7 1 1 3 1 5 3 7 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 8 4 8 2 8 4 8 8 4 8 2 8 4 8

Amount Amou nt of Wa Wate terr (c (cup ups) s)

b. How many containers have at least 6 _5 cups of water? 8

c. Find the difference in the amount of water between the containers with the least and greatest amounts of water.

d. Sasha says the most frequent amount of water in a container is 6 _5 cups. Do you agree? Why? 8

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Amount of Water (cups) 8

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

e. What is the total amount of water in the 3 containers that have the least amount of water?

2. Mr. Evans weighs each watermelon he sells at his fruit stand. The line plot shows the weights of the watermelons.

Weights of Watermelons Sold

× 1 8

1 4

3 8

1 2

× 5 8

× 3 4

10 10 10 10 10 10 10 10

× ×

× × × × ×

7 1 1 3 1 5 3 7 11 11 11 11 11 11 11 11 12 8 8 4 8 2 8 4 8

Weight (pounds)

a. How many watermelons did Mr. Evans sell? How do you know?

b. What is the most frequent weight of the watermelons sold?

146

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

c. What is the total weight of the 2 heaviest watermelons?

d. What is the difference in weight between the heaviest and lightest watermelons?

e. Mr. Evans tells his customers that most of the watermelons he sold today weigh at least

11 _3 pounds. Do you agree with Mr. Evans? Why? 8

Mr. Evans sells 2 watermelons that have a total weight of 23 pounds. Based on the data on the line plot, what could be the weight of each watermelon?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 16

Name

Date

Sana measures the lengths of one type of insect for a class project. She begins to organize the data on a line plot but is unable to finish her work.

1 2 3 ~ ~ ~

Insect

1 1_

Length (inches)

1 3_

1 5_

1 3_

1 1_

1 7_

1 5_

1 1_

a. Use the data values in the table that are not crossed off to complete Sana’s line plot. Insect Length

I 0

× ×

/,-1 --------------------+-----+-I-> 1

1 8

1 4

3 8

1 2

5 8

3 4

7 8

Length Le ngth (i (inche nches) s)

b. How much longer, in inches, is the longest insect than the shortest insect?

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EUREKA MATH2 Tennessee Edition

Liquid (cups)

1 8

1 4

3 8

1 2

Liquid in Measuring Cups

5 8

3 4

7 8

5 ▸ M2 ▸ TD ▸ Lesson 17 ▸ Liquid Line Plot

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EUREKA MATH2 Tennessee Edition

5 ▸ M2 ▸ TD ▸ Lesson 17

Name

Date

1. The line plot shows the weights of rice in 6 containers. Weights of Rice in Containers

× 0

1 8

1 4

× ×

3 8

1 2

5 8

3 4

7 8

I • 1

Weight (pounds)

a. Each model represents 1 and is partitioned into eighths. Shade the models to show how many pounds of rice are in each container.

1 pound 8

3 pounds 8

1 pound 2

3 pounds 4

7 pounds 8

b. How many eighths are shaded altogether?

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5 ▸ M2 ▸ TD ▸ Lesson 17

c. Each model represents 1 and is partitioned into eighths. Shade the models to show how the rice can be redistributed equally among the 6 containers.

d. How many pounds of rice are in each container now?

e. Complete the line plot to represent the weight of rice in each container when the rice is redistributed equally among the containers. Weights of Rice in Containers

•

I 0

1 8

1 4

3 8

1 2

5 8

3 4

7 8

I • 1

Weight (pounds)

154

How does redistributing the pounds of rice equally among the containers change the most frequent weight?

PROBLEM SET

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5 ▸ M2 ▸ TD ▸ Lesson 17

2. The line plot shows the amount of water in 8 bottles. Amount of Water in Bottles

× ×

× × ×

• l!t-1 --------------1-• 1 1 3 1 5 3 7 0

Amount of Water (cups)

a. Decompose the amount of water in each bottle into a whole number and a fraction with eighths. Then find the total number of cups of water in the bottles

1 8

1 4

1 2

3 4

7 8

I\ I\ I\ I\ I\ I\ I\ I\

b. How can you redistribute the water equally among the 8 bottles? Draw a model to help you, if needed.

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PROBLEM SET

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5 ▸ M2 ▸ TD ▸ Lesson 17

c. Complete the line plot to represent the amount of water in each bottle when the water is redistributed equally among the bottles.

Amount of Water in Bottles

1 8

1 4

3 8

1 2

5 8

3 4

7 8

Amount of Water (cups)

d. How does redistributing the cups of water equally among the bottles change the most frequent amount of water?

156

PROBLEM SET

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5 ▸ M2 ▸ TD ▸ Lesson 17

Name

Date

The line plot shows the number of cups of sand in 8 different containers collected by a scientist.

Amount of Sand

2 2

1 1 3 1 5 3 7 2 2 2 2 2 2 8 4 8 2 8 4 8

× 3 3

× ×

1 1 3 1 5 3 7 1 1 3 1 3 3 3 3 3 3 4 4 4 4 4 8 4 8 2 8 4 8 8 4 8 2

Amount (cups)

The sand is redistributed equally among the 8 containers for a test. How many cups of sand are in each container after redistribution?

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5 ▸ M2

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 3, Photology1971/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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5 ▸ M2

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

160

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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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L1uuKA?. MATH 2~

TENNESSEE

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

ISBN 978-1-63898-515-0

GREAT MINDS 9

781638 985150