EM2_G5_M1_Learn_23B_971130_Updated 05.23

A Story of Units®

5 Fractions Are Numbers LEARN ▸ Module 1 ▸ Place Value Concepts for Multiplication and Division with Whole Numbers

Student

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

Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®.

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Printed in the USA B-Print 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-64497-113-0

A Story of Units®

Fractions Are Numbers ▸ 5 LEARN

Module

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

EUREKA MATH2

5 ▸ M1

Contents Place Value Concepts for Multiplication and Division with Whole Numbers Topic A Place Value Understanding for Whole Numbers Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Relate adjacent place value units by using place value understanding.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Multiply and divide by 10, 100, and 1,000 and

identify patterns in the products and quotients.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Use exponents to multiply and divide by powers of 10.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Estimate products and quotients by using powers of 10 and their multiples.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Convert measurements and describe relationships between metric units.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Solve multi-step word problems by using metric measurement conversion.

Topic B Multiplication of Whole Numbers Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Multiply by using familiar methods.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Multiply two- and three-digit numbers by two-digit numbers by using the distributive property.

2

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Multiply two- and three-digit numbers by two-digit numbers by using the standard algorithm.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Multiply three- and four-digit numbers by three-digit numbers by using the standard algorithm.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Multiply two multi-digit numbers by using the standard algorithm.

Topic C Division of Whole Numbers Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Divide two- and three-digit numbers by multiples of 10.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Divide two-digit numbers by two-digit numbers in problems that result in one-digit quotients.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Divide three-digit numbers by two-digit numbers in problems that result in one-digit quotients.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Divide three-digit numbers by two-digit numbers in problems that result in two-digit quotients.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Divide four-digit numbers by two-digit numbers.

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EUREKA MATH2 5 ▸ M1

Topic D Multi-Step Problems with Whole Numbers Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Write, interpret, and compare numerical expressions.

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Create and solve real-world problems for given numerical expressions.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Solve multi-step word problems involving multiplication and division.

Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Solve multi-step word problems involving the four operations.

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 178

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3

(1,000,000)

millions

Expanded Form:

Standard Form:

(100,000)

hundred thousands

(10,000)

ten thousands

(1,000)

thousands

(100)

hundreds

(10)

tens

(1)

ones

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1 ▸ Place Value Chart to Millions

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5

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

.

For this counting collection, I am partners with .

We are counting

.

We think they have a value of This is how we organized and counted the collection:

We counted

altogether.

An equation that describes how we counted is: .

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?

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7

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

Use the place value chart to complete the statement and equation.

1.

millions

hundred ten thousands hundreds thousands thousands

tens

ones

×10

3 ten thousands is 10 times as much as 3​ 0,000 = 10 × 2.

millions

.

​

hundred ten thousands hundreds thousands thousands

tens

ones

×10

is 10 times as much as

= 10 ×

​

.

​

Use the place value chart to complete the equation.

3.

millions

hundred ten thousands hundreds thousands thousands

tens

ones

÷10

6​ 0,000 ÷ 10 =

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​

9

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 1

4.

millions

hundred ten thousands hundreds thousands thousands

tens

ones

÷10

÷ 10 =

​

​

5. Complete each statement by drawing a line to the correct value.

9,000 ÷ 10 =

9,000

9 millions ÷ 10 =

9 millions

The 9 in 3,429,015 represents

9 hundred thousands

.

is 10 times as much as 9 hundred thousands.

9 hundred thousands is 10 times as much as

10

PROBLEM SET

.

9 ten thousands

900

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

Use the place value chart to complete problems 6–12. millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

7

4

4

5

3

8

5

6. ​​7,445,385 = ​(7,000,000)​+ ​(400,000)​+ ​(

)​ + ​(

7. The 7 in 7,445,385 represents ​

.​

)​ + ​(

)​ + (

)​ ​+ (

8. 4 hundred thousands is 10 times as much as ​

9. ​400,000 = 10 ×

10. ​

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​ .

​

÷ 10 = 40,000​

11. 5 thousands is

12. 5 ​ ,000 =

​)​

times as much as 5 ones.

× 5​

PROBLEM SET

11

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 1

13. Consider the number shown.

​8 7 7, 4 8 7​ a. Complete the equation to represent the number in expanded form. ​877,487 = (

)+(

)+(

)+(

)+(

)+(

)​

b. Draw a box around the digit that represents 10 times as much as the underlined digit. c. Complete the equations to show the relationships between the boxed and underlined digits.

= 10 × ÷ 10 = ​

​

d. Explain how the digit in the hundred thousands place is related to the digit in the tens place.

14. Kayla and Blake both write a number.

Kayla’s Number

Blake’s Number

2,308,467

713,548

a. Kayla says, “The 3 in my number is 10 times as much as the 3 in Blake’s number.” Do you agree with Kayla? Explain.

b. Write a division equation to relate the 8 in Kayla’s number to the 8 in Blake’s number.

12

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 1

Name

Date

1

a. Write a division equation that relates the 2 on the left to the 2 on the right.

b. Use the words times as much to compare the 5 on the left to the 5 on the right.

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13

(1,000,000)

millions

(100,000)

hundred thousands

(10,000)

ten thousands

(1,000)

thousands

(100)

hundreds

(10)

tens

(1)

ones

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 2 ▸ Place Value Chart to Millions

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15

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 2

Name

2

Date

1. 5 × 10 =

2. 5 × 100 =

3. 5 × 1,000 =

4. 50 × 10 =

5. 50 × 100 =

=

6. 50 × 1,000 =

=

7. 48 × 30 =

=

=

8. 48 × 300 =

=

=

9. 48 × 3,000 = Copyright © Great Minds PBC

=

= 17

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 2

10. 270,000 ÷ 10 =

11. 270,000 ÷ 100 =

=

12. 270,000 ÷ 1,000 =

=

13. 270,000 ÷ 30 =

=

=

14. 270,000 ÷ 300 =

=

=

15. 270,000 ÷ 3,000 =

18

LESSON

=

=

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 2

Name

Date

2

1. Complete the statement.

The 8 in 58,701 represents

times as much as the 8 in 5,870.

2. Write a multiplication equation to relate the 7 in 58,701 to the 7 in 587,019.

3. Write a division equation to show the relationship between the value of the 5 in 587,019 and the value of the 5 in 5,870.

Multiply.

4. 62 × 1 ten =

62 × 10 =

5. 62 × 1 hundred =

62 × 100 =

6. 62 × 1 thousand =

62 × 1,000 =

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19

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 2

Divide.

7. 73,000 ÷ 10 =

8. 73,000 ÷ 100 =

9. 73,000 ÷ 1,000 =

Multiply or divide.

10. 47 ×

= 4,700

12. 300 × 1,000 =

14.

20

11. 860 ÷ 10 =

13. 25,700 ÷ 100 =

= 4,630 × 1,000

PROBLEM SET

15. 932,000 ÷

= 932

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 2

Complete the equations and expressions.

16. 12 × 30 =

17. 12 × 300 =

12 × 3 ×

12 × 3 ×

12 × 3 ×

20. 360 ÷ 90 =

21. 3,500 ÷ 70 =

19. 240 ÷ 80 =

240 ÷

÷8

360 ÷

18. 12 × 3,000 =

÷9

3,500 ÷

÷7

Multiply or divide.

22. 25 × 300 =

23. 450 ÷ 50 =

24. 15 × 400 =

25. 7,200 ÷ 80 =

26. 45 × 2,000 =

27. 4,800 ÷ 60 =

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PROBLEM SET

21

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 2

28. Toby finds the product of 3,240 and 1,000.

3,240 x 1,000 = 324,000 Use the number of zeros in the product to explain why Toby’s answer is not correct.

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

29. A banker has a total of $54,200, all in one hundred-dollar bills. How many one hundred-dollar bills does the banker have?

22

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 2

Name

Date

2

Find each product.

1. 80 × 10 = 2. 80 × 100 = 3. 80 × 1,000 =

Find each quotient.

4. 340,000 ÷ 10 = 5. 340,000 ÷ 100 = 6. 340,000 ÷ 1,000 =

7. How does the value the 6 represents in 3,604 compare to the value the 6 represents in the product of 3,604 and 1,000? Explain how you know without multiplying.

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23

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1,000 =

100 =

Equation

(1,000,000)

millions

(1,000,000)

millions

(100,000)

(100,000)

(10,000)

(1,000)

(1,000)

(100)

(100)

hundred ten thousands hundreds thousands thousands

(10,000)

hundred ten thousands hundreds thousands thousands

Representation

tens

(10)

(10)

tens

(1)

ones

(1)

ones

Exponential Form

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 3 ▸ Powers of 10 Chart

25

26

100,000 =

10,000 =

Equation

(1,000,000)

millions

(1,000,000)

millions

(100,000)

(100)

(100,000)

(10,000)

(1,000)

(100)

hundred ten thousands hundreds thousands thousands

(10,000)

(1,000)

hundred ten thousands hundreds thousands thousands

Representation

tens

(10)

tens

(10)

(1)

ones

(1)

ones

Exponential Form

5 ▸ M1 ▸ TA ▸ Lesson 3 ▸ Powers of 10 Chart EUREKA MATH2

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10 =

1,000,000 =

Equation

(1,000,000)

millions

(1,000,000)

millions

(100,000)

(100)

(100,000)

(10,000)

(1,000)

(100)

hundred ten thousands hundreds thousands thousands

(10,000)

(1,000)

hundred ten thousands hundreds thousands thousands

Representation

tens

(10)

tens

(10)

(1)

ones

(1)

ones

Exponential Form

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 3 ▸ Powers of 10 Chart

27

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 3

Name

Date

3

Multiply.

1. 10,000 × 100 = 2. 1,000 × 103 =

Multiply.

3. 7 × 102 = 4. 300 × 103 =

Divide.

5. 10,000 ÷ 102 = 6. 1,000,000 ÷ 103 =

Divide.

7. 9,000 ÷ 103 = 8. 360,000 ÷ 104 =

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29

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 3

Name

3

Date

Complete the table to represent each number in three different forms. The first one is done for you.

Standard Form

Multiplication Expression Using Only 10 as a Factor

Exponential Form

1.

100

10 × 10

102

2.

1,000

3.

10,000

103

10 × 10 × 10 × 10 × 10

4.

106

5.

Write each product or quotient in exponential form.

6. 100 × 100 =

7. 10,000 ÷ 10 =

8. 100 × 104 =

9. 100,000 ÷ 102 =

10. Consider the expression shown.

1,000 × 103 How does the exponent help you think about shifting the digits in the first factor to find the product?

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31

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 3

11. Use words and equations to explain how 105 is different from 10 × 5.

Rewrite each expression by using an exponent. Then find the product or quotient and write it in standard form.

12.

ten thousands thousands hundreds

tens

ones

× 10

3 × 10 × 10 × 10 × 10 = 3 × =

× 10 × 10 × 10

13.

ten thousands thousands hundreds

tens

ones

7,000 ÷ 10 ÷ 10 ÷ 10 = 7,000 ÷ =

÷ 10 ÷ 10 ÷ 10

32

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 3

Find each product or quotient and write it in standard form.

14. 8 × 104 =

15. 500,000 ÷ 105 =

16. 39,000 ÷ 102 =

17. 400 × 103 =

18. 620 × 104 =

19. 9,180,000 ÷ 103 =

20. Explain how you found the quotient in problem 16.

21. Yuna finds 300 × 103. Explain Yuna’s strategy.

Yuna’s Way

300 × 103 = 3 × 10 × 10 × 103 = 3 × 105

= 300,000

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PROBLEM SET

33

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 3

Name

Date

3

Multiply or divide. Then write each product or quotient in exponential form.

1. 10 × 10 × 10 × 10 = 2. 10 × 1,000 = 3. 100 × 10 4 = 4. 100,000 ÷ 10 2 =

Multiply or divide. Then write each product or quotient in standard form.

5. 4 × 10 5 = 6. 200 × 10 4 = 7. 70,000 ÷ 10 4 = 8. 340,000 ÷ 10 3 =

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35

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 4

Name

Date

4

Estimate each product. Show your thinking.

1. 7,114 × 20

2. 1,009 × 51

3. 92 × 396,285

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37

5 ▸ M1 ▸ TA ▸ Lesson 4

EUREKA MATH2

4. Which number is the best estimate of 976 × 52?

A. 4,500 B. 45,000 C. 50,000 D. 500,000

Estimate each quotient. Show your thinking.

5. 129 ÷ 4

6. 35,471 ÷ 9

7. 426 ÷ 64

38

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 4

8. Miss Baker buys 327 hats for students at her school. Each hat costs $18. About how much do the hats cost in total? Show your thinking.

9. A runner climbs 1,276 stairs in 11 minutes. Estimate the number of stairs the runner climbs in 1 minute. Show your thinking.

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LESSON

39

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 4

Name

4

Date

Estimate each product. Show your thinking.

1. 48 × 6

2. 247 × 9

3. 4 × 7,081

4. 32 × 18

5. 673 × 54

6. 1,235 × 43

7. Scott started to make an estimate for 718 × 41 but did not finish. a. Complete the equations to finish Scott’s estimate. ​700 × 40 = 7 ×

×4×

​

= × 10 ​ ​ = ​ ​ b. Is Scott’s estimate greater or less than the actual product of 718 and 41? Explain how you know without calculating the actual product.

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41

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 4

8. Kelly and Adesh each write an expression to show how to estimate 1,846 × 7.

Kelly’s Way

2,000 × 7

Adesh’s Way

2,000 × 10

Whose estimate is closer to the actual product? Explain your answer.

Estimate each quotient. Show your thinking.

9. 163 ÷ 4

10. 2,631 ÷ 3

11. 342 ÷ 54

12. 647 ÷ 72

13. 1,921 ÷ 91

14. 4,609 ÷ 59

42

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 4

15. Tim makes a mistake when he estimates 3,714 ÷ 94. What mistake does Tim make?

3,714 ÷ 94 ≈ 3,600 ÷ 90 = 400

16. The table shows the cost of tickets for a concert.

Adult Ticket

Child Ticket

$27

$18

a. There are 8,309 adults at the concert. About how much was spent on adult tickets?

b. The total amount spent on children’s tickets was $6,288. About how many children are at the concert?

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PROBLEM SET

43

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 4

Name

Date

4

A large helicopter can carry 25,000 pounds. The average weight of a car is 4,110 pounds. If there is enough space, about how many cars can the helicopter carry at one time? Explain how you know.

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45

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 5

Name

Date

5

Convert.

1. 456 kL =

L

2. 6,985 g =

3.

mg

cm = 308 m

4. The label on a water bottle shows the capacity of the bottle is 50 centiliters.

What is the capacity of the bottle in milliliters?

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47

5 ▸ M1 ▸ TA ▸ Lesson 5

EUREKA MATH2

5. The label on a bag of rice reads 2 kg 300 g. The label on a bag of beans reads 2,300 mg.

Which bag is heavier?

48

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 5

Name

5

Date

Convert each measurement. Write an expression to help you convert. The first one is started for you.

1.

Meters ( m)

Expression

5

5 × 10

Millimeters (mm)

2.

3

Liters ( L)

Expression

9

9 × 10

13

24

207

410

480

700

Convert.

Centiliters (cL)

2

3. 800 m =

cm

4.

mL = 1,500 cL

5. 760 g =

mg

6.

L = 320 kL

7. Consider the expressions.

600 × 100 mL

600 × 103 mL

6 × 102 × 1,000 mL

a. Circle the expression that does not represent how to convert 600 liters to milliliters. b. Explain your choice.

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49

EUREKA MATH2

5 ▸ M1 ▸ TA ▸ Lesson 5

Convert.

8. 6 L 34 cL =

10.

cL

mm = 87 m 61 mm

9.

mg = 60 g 52 mg

11. 8 kg 1,245 mg =

mg

12. Riley runs 11 kilometers. What is the distance Riley runs in meters?

13. Mr. Sharma’s dog weighs 21 kg 96 g. What is the weight of Mr. Sharma’s dog in grams?

50

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 5

Name

Date

5

Convert each measurement.

1. 4 km =

m

2. 9,430 cL =

3. 108 kg =

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mL

g

51

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 6

Name

Date

6

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

1. Sasha has 6 meters 40 centimeters of ribbon. She plans to divide the ribbon equally to wrap 8 gifts that are the same size. How many centimeters of ribbon should Sasha cut for each gift?

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

2. A family takes a road trip from New York City to Seattle, and they stop in Chicago on the way.

The distance from New York City to Chicago is 1,963 kilometers less than the distance from Chicago to Seattle. The distance from Chicago to Seattle is 3,288 kilometers. If the family travels the same route to Seattle and back, how many total meters do they travel?

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53

EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 6

Name

Date

6

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

1. Mr. Perez pours water into 8 beakers. He pours 750 milliliters of water into each beaker. a. About how many milliliters of water are in the beakers altogether?

b. Exactly how many milliliters of water are in the beakers altogether?

c. How do you know your answer in part (b) is reasonable?

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55

5 ▸ M1 ▸ TA ▸ Lesson 6

EUREKA MATH2

2. A newborn lion cub weighs 1 kg 736 g. The lion cub weighs 8 times as much as a newborn puppy. a. Convert the weight of the lion cub to grams.

b. About how many grams does the puppy weigh?

c. Exactly how many grams does the puppy weigh?

d. How do you know your answer in part (c) is reasonable?

56

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 6

3. Leo uses oil and vinegar to make a bottle of salad dressing. He uses 12 centiliters of vinegar.

He uses 3 times as much oil as vinegar. How many milliliters of salad dressing does Leo make?

4. Eddie has a blue ribbon that is 4 m 23 cm long and a green ribbon that is 756 cm long. He cuts each ribbon into pieces that are 9 cm long. How many more pieces of green ribbon than blue ribbon does Eddie have?

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PROBLEM SET

57

5 ▸ M1 ▸ TA ▸ Lesson 6

EUREKA MATH2

5. A farmer puts apples into 36 crates. Each crate has 25 kilograms of apples in it. She sells 486,235 grams of apples. How many grams of apples does she have left?

58

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TA ▸ Lesson 6

Name

Date

6

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

Lacy needs 650 centimeters of ribbon for a project. She already has 2 m 596 mm of ribbon. How many more millimeters of ribbon does Lacy need?

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59

EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 7

Name

Date

7

1. Write the following number in as many ways as you can.

28,741

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

2. On a typical day, a grade 5 student takes 24,165 breaths in one day. How many breaths will you and 5 friends take in one day?

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61

5 ▸ M1 ▸ TB ▸ Lesson 7

EUREKA MATH2

Multiply. Show or explain your work.

3. 4 times as much as 32,157

62

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 7

Name

Date

7

Multiply. Show or explain your strategy.

1. 4 times as much as 362

2. 7 times as long as 3,098 kilometers

3. 6 × 12,345

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4. 9 × 21,876

63

5 ▸ M1 ▸ TB ▸ Lesson 7

EUREKA MATH2

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

5. Mrs. Chan takes 13,564 steps each day for 4 days. How many total steps does she take in those 4 days?

6. An airplane weighs 40,823 kilograms. What is the total weight of 7 of these airplanes?

64

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 7

Name

Date

7

Multiply. Show or explain your strategy.

73,613 × 5

8

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65

EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 8

Name

Date

8

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

1. There are 122 cities competing in a math relay race. Each city sends 41 grade 5 students to compete. How many students compete?

2. 24 × 40 =

3. 22 × 41 =

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67

5 ▸ M1 ▸ TB ▸ Lesson 8

EUREKA MATH2

4. 21 × 343 =

5. 32 × 201 =

68

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 8

Name

8

Date

Complete the area model. Then multiply by showing two partial products.

1. 23 × 30

30 3

×

20

+

3 2

0 3

3 2

1 3

2. 23 × 31

31 3

×

20

+

3. 23 × 331

331

3

3

×

20

+

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3 2

1 3

69

EUREKA MATH2

5 ▸ M1 ▸ TB ▸ Lesson 8

Draw an area model to find two partial products. Then multiply by showing two partial products.

4. 34 × 121

Estimate the product. Then multiply.

5. 31 × 33 ≈

×

7. 32 × 231 ≈

×

=

×

8. 43 × 201 ≈

×

=

=

70

6. 12 × 413 ≈

PROBLEM SET

=

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 8

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

9. A toy giraffe is 403 millimeters tall. A real giraffe is 12 times as tall as the toy giraffe. How tall is the real giraffe?

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PROBLEM SET

71

EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 8

Name

Date

8

Consider the expression shown.

31 × 213 a. Complete the area model.

b. Multiply by showing two partial products.

× +

c. Complete the equation.

31 × 213 =

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73

EUREKA MATH2 5 ▸ M1 ▸ Sprint ▸ Multiply by Multiples of 10, 100, 1,000, and 10,000

Sprint Write the product.

1.

1 × 20 =

2.

2 × 600 =

3.

3 × 9,000 =

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75

EUREKA MATH2

5 ▸ M1 ▸ Sprint ▸ Multiply by Multiples of 10, 100, 1,000, and 10,000

A

Number Correct:

Write the product.

1.

1 × 10 =

23.

5,000 × 7 =

2.

1 × 30 =

24.

6,000 × 8 =

3.

2 × 30 =

25.

7,000 × 9 =

4.

3 × 30 =

26.

1 × 10,000 =

5.

30 × 3 =

27.

2 × 20,000 =

6.

40 × 4 =

28.

3 × 30,000 =

7.

50 × 5 =

29.

40,000 × 4 =

8.

1 × 100 =

30.

50,000 × 5 =

9.

2 × 200 =

31.

60,000 × 6 =

10.

3 × 400 =

32.

7 × 70,000 =

11.

300 × 4 =

33.

8 × 80,000 =

12.

200 × 5 =

34.

9 × 90,000 =

13.

200 × 6 =

35.

2 × 90 =

14.

7 × 300 =

36.

3 × 90 =

15.

8 × 400 =

37.

6 × 10,000 =

16.

9 × 500 =

38.

20,000 × 5 =

17.

1 × 1,000 =

39.

7 × 60,000 =

18.

2 × 2,000 =

40.

50,000 × 4 =

19.

3 × 2,000 =

41.

5 × 60,000 =

20.

2,000 × 4 =

42.

70,000 × 8 =

21.

3,000 × 5 =

43.

8 × 50,000 =

22.

4,000 × 6 =

44.

90,000 × 8 =

76

Copyright © Great Minds PBC

EUREKA MATH2

5 ▸ M1 ▸ Sprint ▸ Multiply by Multiples of 10, 100, 1,000, and 10,000

B

Number Correct: Improvement:

Write the product.

1.

1 × 10 =

23.

4,000 × 7 =

2.

1 × 20 =

24.

5,000 × 8 =

3.

2 × 20 =

25.

6,000 × 9 =

4.

3 × 20 =

26.

1 × 10,000 =

5.

20 × 3 =

27.

2 × 10,000 =

6.

30 × 4 =

28.

3 × 20,000 =

7.

40 × 5 =

29.

30,000 × 4 =

8.

1 × 100 =

30.

40,000 × 5 =

9.

2 × 200 =

31.

50,000 × 6 =

10.

3 × 400 =

32.

7 × 60,000 =

11.

300 × 4 =

33.

8 × 70,000 =

12.

200 × 5 =

34.

9 × 80,000 =

13.

200 × 6 =

35.

2 × 80 =

14.

7 × 200 =

36.

3 × 80 =

15.

8 × 300 =

37.

5 × 10,000 =

16.

9 × 400 =

38.

5 × 20,000 =

17.

1 × 1,000 =

39.

60,000 × 7 =

18.

2 × 2,000 =

40.

4 × 50,000 =

19.

3 × 2,000 =

41.

60,000 × 5 =

20.

2,000 × 4 =

42.

8 × 70,000 =

21.

2,000 × 5 =

43.

50,000 × 8 =

22.

3,000 × 6 =

44.

8 × 90,000 =

78

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 9

Name

9

Date

1. Mr. Perez paints the gymnasium wall. The wall is 24 feet wide and 33 feet long. How many square feet does Mr. Perez paint?

×

3

3

2

4

2. 28 × 63 =

×

+

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79

5 ▸ M1 ▸ TB ▸ Lesson 9

EUREKA MATH2

3. Flatback turtles lay 52 eggs in a nest. How many turtle eggs would there be in 427 nests?

80

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 9

Name

9

Date

Complete the area model. Then multiply by using the standard algorithm.

1. 24 × 35

30

5

4

×

20

3

5

2

4

3

2

6

4

1

+

2. 41 × 326

300 1

20

6 ×

40 +

Copyright © Great Minds PBC

81

EUREKA MATH2

5 ▸ M1 ▸ TB ▸ Lesson 9

Draw an area model to find the partial products. Then multiply by using the standard algorithm.

3. 47 × 32

×

+

4. 25 × 638

×

+

82

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 9

5. 38 × 529 ≈

6. 63 × 804 ≈

Estimate the product. Then multiply.

×

=

×

=

7. Julie makes a mistake when she uses the distributive property to find 83 × 624. Look at her work.

83 × 624 = 80 × 600 + 80 × 20 + 80 × 4 = 48,000 × 1,600 + 320 = 49,920

a. What mistake did Julie make?

b. Find the product.

83 × 624 =

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PROBLEM SET

83

5 ▸ M1 ▸ TB ▸ Lesson 9

EUREKA MATH2

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

8. A school bus travels 508 kilometers each week. How many kilometers does the school bus travel in 36 weeks?

84

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 9

Name

Date

9

Consider the expression shown.

446 × 81 a. Draw an area model to find the partial products.

b. Multiply by using the standard algorithm.

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85

EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 10

Name

Date

10

1. Lisa tiles a rectangular floor that is 204 inches long and 123 inches wide. How many square inches of tile does Lisa use?

2. The population of Waverly, Pennsylvania, is 604 people. The population of Scranton, Pennsylvania, is 127 times as much as the population of Waverly. What is the population of Scranton?

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87

5 ▸ M1 ▸ TB ▸ Lesson 10

EUREKA MATH2

3. 1,429 × 312

88

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 10

Name

10

Date

Complete the area model and find the sum of the partial products. Then multiply by using the standard algorithm. Compare your answers in each part to check that the product is correct.

1. 251 × 432

400

a.

1

30

2

b.

×

50

4

3

2

2

5

1

200

+

Draw an area model to find the partial products and find their sum. Then multiply by using the standard algorithm. Compare your answers in each part to check that the product is correct.

2. 342 × 1,627 a.

b.

×

+

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89

EUREKA MATH2

5 ▸ M1 ▸ TB ▸ Lesson 10

Estimate the product. Then multiply.

3. 689 × 824 ≈

×

=

4. 518 × 706 ≈

×

=

5. 537 × 3,296 ≈

=

×

6. 758 × 4,093 ≈

×

=

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

7. Sana drinks from a bottle that holds 946 milliliters of water. She fills the bottle and drinks all the water in it twice each day. a. How many milliliters of water does Sana drink each day?

b. How many milliliters of water does Sana drink in 365 days?

90

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 10

Name

Date

10

Multiply.

704 × 236

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91

EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 11

Name

11

Date

Estimate the product. Then multiply by using the standard algorithm.

1. 382 × 547 ≈

2. 473 × 905 ≈

×

=

×

=

3. 638 × 5,291 ≈

=

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×

4. 7,418 × 594 ≈

×

=

93

EUREKA MATH2

5 ▸ M1 ▸ TB ▸ Lesson 11

5. Blake wants to find 312 × 675. Look at Blake’s work.

Blake’s Way

×

67 5 312 1 1

1 350 67 5 2 1 + 21 01 21 5 4,0 5 0

a. Is Blake’s answer reasonable? How do you know?

b. What mistakes did Blake make?

Multiply.

6. 651 × 823

94

PROBLEM SET

7. 508 × 977

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EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 11

8. 467 times as much as 2,083

9. 6,254 × 379

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

10. A cow weighs 712 kilograms. A blue whale is 255 times as heavy as the cow. How many kilograms does the blue whale weigh?

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PROBLEM SET

95

EUREKA MATH2 5 ▸ M1 ▸ TB ▸ Lesson 11

Name

Date

11

Multiply.

768 × 9,307

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97

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 12

Name

Date

12

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

1. Tyler wants to donate boxes of crayons to kindergarten classes. He has 347 boxes. He donates sets of 40 boxes to as many classes as he can. How many boxes remain?

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99

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 12

Name

12

Date

Complete the tape diagram. Then complete the vertical form and check your work.

1. 80 ÷ 20

20 80

80 20

Check:

80 =

×

2. 240 ÷ 30

30 240

240 30

Check:

240 =

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×

101

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 12

Estimate the quotient. Complete the tape diagram. Then complete the vertical form and check your work.

3. 81 ÷ 40 ≈

÷

= 40 81

81

Quotient:

40

Remainder:

Check:

81 =

4. 324 ÷ 50 ≈

÷

×

+

= 50 324

324 50

Quotient: Remainder:

Check:

324 =

102

PROBLEM SET

×

+

Copyright © Great Minds PBC

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 12

Divide. Then check your work.

5. 120 ÷ 30

6. 72 ÷ 60

4 30 120

Quotient:

Quotient:

Remainder:

Remainder:

Check:

Check:

7. 731 ÷ 80

8. 560 ÷ 70

Quotient:

Quotient:

Remainder:

Remainder:

Check:

Check:

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PROBLEM SET

103

5 ▸ M1 ▸ TC ▸ Lesson 12

EUREKA MATH2

9. A number divided by 40 has a quotient of 6 and a remainder of 15. What is the number?

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

10. A student has 174 centimeters of ribbon for making bows. Each bow is made with 20 centimeters of ribbon. The student wants to make as many bows as possible. How many bows can the student make? How many centimeters of ribbon will be left over?

104

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 12

Name

Date

12

Consider the expression shown.

655 ÷ 80 a. Draw and label a tape diagram to represent the expression.

b. Determine the quotient and remainder.

Quotient: Remainder:

c. Write an equation to check your work.

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105

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 13

Name

Date

13

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

1. Sasha is training for a competition and plans to do 96 push-ups in one day. She plans to do these push-ups in sets of 16. How many sets of push-ups will she need to do to reach her goal of 96 push-ups? Show your thinking, including an estimate and a check.

Estimate:

Divide:

Check:

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107

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 13

2. A camp plans to take its 92 students on a field trip. Each bus holds 21 students.

How many buses does the camp need for the field trip? Show your thinking.

3. There are 92 coins split into 21 piles. Each pile has the same number of coins and as many coins as possible. How many coins are in each pile?

108

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 13

Name

13

Date

Estimate the quotient. Complete the tape diagram. Then complete the vertical form and check your work.

1. 63 ÷ 21 ≈

÷

=

2

1

6

3

63 21 Check:

63 =

2. 72 ÷ 18 ≈

÷

×

=

1

8

7

2

72 18 Check:

72 =

Copyright © Great Minds PBC

×

109

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 13

Estimate the quotient. Complete the tape diagram. Then complete the vertical form and check your work.

3. 95 ÷ 31 ≈

÷

=

3

1

9

5

95 Quotient:

31

Remainder:

Check:

95 =

4. 84 ÷ 19 ≈

÷

×

+

=

1

9

8

4

84 19

Quotient: Remainder:

Check:

84 =

110

PROBLEM SET

×

+

Copyright © Great Minds PBC

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 13

Divide. Then check your work.

5. 96 ÷ 32

6. 54 ÷ 27

32 96

Quotient:

Quotient:

Remainder:

Remainder:

Check:

Check:

7. 83 ÷ 21

8. 95 ÷ 19

Quotient:

Quotient:

Remainder:

Remainder:

Check:

Check:

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PROBLEM SET

111

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 13

9. Scott wants to find 78 ÷ 42. First, he estimates the quotient. Then he uses his estimate to divide.

78 ÷ 42 ≈ 80 ÷ 40 =2 2 42 7 8 −84 a. What should Scott do next?

b. Find 78 ÷ 42.

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

10. An auditorium has 25 seats in each row. How many rows are needed to seat 92 students?

112

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 13

Name

Date

13

Divide. Then check your answer.

81 ÷ 17

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113

EUREKA MATH2 5 ▸ M1 ▸ Sprint ▸ Powers of 10

Sprint Write each power of ​10​in exponential form.

1.

100

2.

10 × 10 × 10 × 10

3.

Ten to the third power

4.

One million

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115

EUREKA MATH2

5 ▸ M1 ▸ Sprint ▸ Powers of 10

A

Number Correct:

Write each power of 1 ​ 0​in exponential form.

1.

100

23.

1,000

2.

1,000

24.

1,000,000

3.

100,000

25.

10,000

4.

10,000

26.

10 × 10

5.

1,000,000

27.

10 × 10 × 10 × 10 × 10

6.

10

28.

10

7.

10 × 10

29.

Ten to the fourth power

8.

10 × 10 × 10

30.

Ten to the sixth power

9.

10 × 10 × 10 × 10 × 10 × 10

31.

Ten to the fifth power

10.

10 × 10 × 10 × 10

32.

One thousand

11.

10 × 10 × 10 × 10 × 10

33.

One hundred thousand

12.

10

34.

One million

13.

Ten to the second power

35.

1,000

14.

Ten to the third power

36.

10,000

15.

Ten to the fifth power

37.

100 × 10

16.

Ten to the sixth power

38.

10 × 102

17.

Ten to the fourth power

39.

10 × 10,000

18.

One hundred

40.

103 × 10

19.

One thousand

41.

100 × 100

20.

One million

42.

100 × 104

21.

One hundred thousand

43.

1,000 × 100

22.

Ten thousand

44.

103 × 1,000

116

Copyright © Great Minds PBC

EUREKA MATH2

5 ▸ M1 ▸ Sprint ▸ Powers of 10

B

Number Correct: Improvement:

Write each power of 1 ​ 0​in exponential form.

1.

100

23.

100

2.

1,000

24.

100,000

3.

10,000

25.

1,000

4.

100,000

26.

10 × 10

5.

1,000,000

27.

10 × 10 × 10 × 10

6.

10

28.

10

7.

10 × 10

29.

Ten to the third power

8.

10 × 10 × 10

30.

Ten to the fifth power

9.

10 × 10 × 10 × 10 × 10

31.

Ten to the fourth power

10.

10 × 10 × 10 × 10

32.

One thousand

11.

10 × 10 × 10 × 10 × 10 × 10

33.

Ten thousand

12.

10

34.

One million

13.

Ten to the second power

35.

100

14.

Ten to the third power

36.

1,000

15.

Ten to the sixth power

37.

10 × 100

16.

Ten to the fifth power

38.

102 × 10

17.

Ten to the fourth power

39.

10,000 × 10

18.

One hundred

40.

10 × 103

19.

One thousand

41.

100 × 100

20.

One million

42.

104 × 100

21.

Ten thousand

43.

100 × 1,000

22.

One hundred thousand

44.

1,000 × 103

118

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 14

Name

Date

14

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

1. A school activity has 301 students split into 43 equal-size groups. How many students are in each group?

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119

5 ▸ M1 ▸ TC ▸ Lesson 14

EUREKA MATH2

2. Eddie has 34 days to read a 170-page book. If he reads the same number of pages each day, how many pages does he need to read each day to finish the book in 34 days?

120

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 14

3. Miss Baker needs to order 546 pencils. If each pack has 72 pencils, what is the fewest number of packs Miss Baker should order?

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LESSON

121

5 ▸ M1 ▸ TC ▸ Lesson 14

EUREKA MATH2

4. Riley has 457 centimeters of ribbon. Each costume he makes needs 55 centimeters of ribbon.

How many costumes can Riley make?

122

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 14

Name

Date

14

Estimate the quotient. Then complete the vertical form and check your work. Draw a tape diagram if it helps you divide.

1. 156 ÷ 52 ≈

÷

=

52 156

Quotient: Remainder: Check:

156 =

×

2. 136 ÷ 34 ≈

÷

=

34 136

Quotient: Remainder: Check:

136 =

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×

123

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 14

3. 139 ÷ 27 ≈

÷

=

27 139

Quotient: Remainder: Check:

139 =

×

4. 204 ÷ 48 ≈

+

÷

=

48 204

Quotient: Remainder: Check:

204 =

124

×

PROBLEM SET

+

Copyright © Great Minds PBC

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 14

Divide. Then check your work.

5. 287 ÷ 41

6. 415 ÷ 83

41 287

Quotient:

Quotient:

Remainder:

Remainder:

Check:

Check:

7. 555 ÷ 91

8. 702 ÷ 78

Quotient:

Quotient:

Remainder:

Remainder:

Check:

Check:

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PROBLEM SET

125

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 14

9. Consider the division work.

7 39 284 –273 11 a. Show another division problem with the same quotient and remainder as 284 ÷ 39.

b. Explain how you found another division problem with the same quotient and remainder as 284 ÷ 39.

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

10. Kayla’s book has 307 pages. She plans to read 45 pages each day. How many days will it take Kayla to finish reading the book?

126

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 14

Name

Date

14

There are 418 people going on a field trip. Each bus can hold 72 people. What is the least number of buses the school must use? Explain your answer.

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127

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 15

Name

15

Date

1. Determine the unknown values in the area model. Then write a multiplication equation and a division equation that the area model represents.

Area Model

60 840

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Multiplication Equation

Division Equation

5 28

×

=

÷

=

129

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 15

Name

15

Date

1. Julie started the division for 464 ÷ 29 by using the area model shown.

10

29

290

145

29

a. Complete Julie’s model. b. Use the partial quotients from part (a) to show the division for 464 ÷ 29 in vertical form.

2

9

4

6

4

c. What is 464 ÷ 29? How do you know?

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131

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 15

Divide by using an area model. Then check your work.

2. 234 ÷ 18

Check:

234 =

× 18

Estimate the partial quotients as you divide. Then check your work.

3. 436 ÷ 17 Check:

436 = 1

7

4

3

× 17 +

6

Quotient: Remainder:

132

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 15

Divide. Then check your work.

4. 868 ÷ 28

28 868

Check:

21 504

Check:

Quotient: Remainder:

5. 504 ÷ 21

Quotient: Remainder:

6. 865 ÷ 43

Check:

Quotient: Remainder:

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PROBLEM SET

133

5 ▸ M1 ▸ TC ▸ Lesson 15

EUREKA MATH2

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

7. Tara uses 25 blocks to build a tower. She has 362 blocks. How many towers of 25 blocks can she build?

134

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 15

Name

Date

15

A parking lot has 567 parking spots in 27 rows. If each row has the same number of parking spots, how many parking spots are in each row?

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135

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 16

Name

Date

16

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

1. A tree farm has 15 rows of trees. Each row has the same number of trees. If there is a total of 1,635 trees, how many trees are in each row?

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

2. Lacy plans to ride her bike 2,900 miles, which is about the distance from San Francisco to New York. If she rides 68 miles each week, how many weeks will it take Lacy to ride 2,900 miles?

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137

EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 16

Name

16

Date

Estimate the partial quotients as you divide. The first estimate is started for you. Make as many estimates as you need to. Then check your work.

1. 5,985 ÷ 19

Estimates:

1

9

5, 9

8

5

÷ 20 =

Check:

5, 985 =

× 19

Quotient: Remainder:

2. 1,376 ÷ 32 Estimates:

3

2

1, 3

7

6

÷ 30 =

Check:

1,376 =

× 32

Quotient: Remainder: Copyright © Great Minds PBC

139

EUREKA MATH2

5 ▸ M1 ▸ TC ▸ Lesson 16

3. 6,081 ÷ 27

Estimates:

2

7 6, 0

8

1

÷ 30 =

Check:

6,081 =

× 27 +

Quotient: Remainder:

Divide. Then check your work.

4. 7,242 ÷ 34 Check:

Quotient: Remainder:

140

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 16

5. 3,164 ÷ 45 Check:

Quotient: Remainder:

6. 5,123 ÷ 47 Check:

Quotient: Remainder:

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PROBLEM SET

141

5 ▸ M1 ▸ TC ▸ Lesson 16

EUREKA MATH2

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

7. A warehouse has 1,250 video games to distribute evenly to 12 stores. If the warehouse distributes as many as possible, how many games does each store get? How many games are left over?

142

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TC ▸ Lesson 16

Name

Date

16

Divide. Then check your work.

7,139 ÷ 31

Quotient: Remainder:

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143

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 17

Name

17

Date

Write an expression to represent the statement. Use the tape diagram to help you.

1. 3 times the sum of 15 and 25

15 + 25

15 + 25

15 + 25

?

Draw a tape diagram and write an expression to represent the statement.

2. The difference between 72 and 48, then divide by 2

Write a statement and equation to represent the tape diagram.

3.

8

8

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8

6

6

145

EUREKA MATH2

5 ▸ M1 ▸ TD ▸ Lesson 17

Use >, =, or < to compare the expressions.

4. 22 × (18 + 31)

(18 + 31) × 34

5. (2 × 8) + (10 × 8) 6. 145 × 71

146

LESSON

(7 × 8) − (4 × 8)

(100 + 45) × (70 + 1)

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 17

Name

Date

17

Draw a tape diagram and write an expression to represent the statement.

1. Double the sum of 9 and 6

2. The difference between 67 and 43, then divide by 2

3. 3 times as much as the sum of 11 and 29

4. The sum of two 18s and three 12s

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147

EUREKA MATH2

5 ▸ M1 ▸ TD ▸ Lesson 17

Write a statement and an expression to represent the tape diagram. Then evaluate your expression.

5.

37

18

37

18

37

18

37

18

Statement: Expression: Value of expression:

6.

9

9

9

9

7

7

Statement: Expression: Value of expression:

7. Evaluate. a. 40 + (3 × 9) − 6

b. (40 + 3) × (9 − 6)

c. Why do expressions (a) and (b) have different values?

148

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 17

8. Kelly forgot to put parentheses in her equation. Write parentheses to make her equation true.

6 + 8 × 12 − 2 = 140

Use >, =, or < to compare the expressions. Explain how you can compare the expressions without evaluating them.

9. 35 × (12 + 28)

(12 + 28) × 70

Explain:

10. 225 × 81

(200 + 25) × (80 + 1)

Explain:

11. (48 × 7) − (37 × 7)

(5 × 7) + (5 × 7)

Explain:

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PROBLEM SET

149

EUREKA MATH2

5 ▸ M1 ▸ TD ▸ Lesson 17

12. Consider the statement.

5 times as much as the sum of 319 and 758 a. Adesh makes a mistake when he writes an expression to represent the statement.

What mistake does Adesh make?

(5 × 319 319)) + 758

b. Write an expression to represent the statement.

c. Evaluate the expression you wrote in part (b).

150

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 17

Name

Date

17

1. Write an expression to represent the statement. Draw a tape diagram if it helps you.

4 times as much as the sum of 3 and 12

2. Place parentheses to make the equation true.

12 × 3 + 2 − 5 = 55

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

(24 × 3) + (10 × 3)

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(47 × 3) − (15 × 3)

151

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 18

Name

Date

18

1. 2 × (15 + 20)

2.

?

9

9

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9

16

16

16

153

EUREKA MATH2

5 ▸ M1 ▸ TD ▸ Lesson 18

96

3.

33 ?

4. (24 − 6) ÷ 3

5. (9 + 4) × 3 − 6

154

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 18

Name

Date

18

1. Draw lines to match the expressions to the word problems. a. (3 + 9 − 5) × 12

Yuna buys 3 bags of oranges. There are 9 oranges in each bag. She eats 5 oranges.

Then she gives 12 oranges to her friends.

How many oranges does Yuna have now?

b. 3 × 9 − 5 − 12

Tyler has 3 pencils. He finds 9 more pencils.

Sasha has 5 times as many pencils as Tyler.

Eddie has 12 fewer pencils than Sasha.

How many pencils does Eddie have?

c. (3 + 9) × 5 − 12

Riley gets 3 books from the library on Monday and 9 more books on Tuesday. She reads and returns 5 books on Wednesday. Riley has 12 times as many books on her bookshelf as she still has from the library. How many books are on Riley’s bookshelf?

2. Write an expression that represents the tape diagram. Then write a word problem that can be represented by the tape diagram and expression.

?

12

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12

12

17

155

5 ▸ M1 ▸ TD ▸ Lesson 18

EUREKA MATH2

3. Consider the expression.

4 × (15 + 8) Write a word problem that can be represented by the given expression.

4. Consider the expression.

(26 − 8) ÷ 2 a. Write a word problem that can be represented by the given expression.

b. Solve your problem.

156

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 18

Name

Date

18

Write a word problem that can be solved by using the expression shown.

(6 + 7) × 11 − 34

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157

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 19 ▸ Multiplication and Division Tape Diagram Card Sort

Division (number of groups known)

Multiplication

96

Division (group size known)

...

6

How many 6s are in 96?

?

39

39

39

39

20 39

39

39

4

444

1,428 5

?

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...

42 groups

?

16

4

325 groups

a 5

4

...

14

? groups

5

4

?

...

12

4

972 ?

159

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 19

Name

Date

19

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

1. A florist uses 2,448 flowers to make bouquets. They put 24 flowers in each bouquet and sell the bouquets for $25 each. If the florist sells all the bouquets of flowers, how much money do they earn?

2. Miss Song buys 15 boxes of fruit snacks for the school field day. Each box holds 24 packs of fruit snacks. She gives as many packs of fruit snacks as possible to 22 classrooms so that they each get the same number. How many extra packs of fruit snacks does Miss Song have?

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161

5 ▸ M1 ▸ TD ▸ Lesson 19

EUREKA MATH2

3. A carton of eggs has 12 eggs. A box of eggs holds 12 cartons. A baker uses 5 eggs for each cake he makes. If the baker buys 3 boxes of eggs, what is the greatest number of cakes he can make?

162

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 19

Name

Date

19

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

1. Miss Baker orders 13 cases of soup for her grocery store. Each case has 48 cans of soup. She puts all the cans on the shelves so that each shelf has an equal number. If there are 16 shelves, how many cans of soup are on each shelf?

2. Mr. Sharma bakes 732 cupcakes each week for his bakery. He puts 12 cupcakes in each box and earns $14 for each box he sells. If he sells all the boxes of cupcakes, how much money does he earn?

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163

5 ▸ M1 ▸ TD ▸ Lesson 19

EUREKA MATH2

3. There are 9,675 people at a concert. An equal number of people sit in each of the 15 sections.

A ticket for a seat in section B costs $47. What is the total cost of the tickets for the seats in section B?

4. 24 students are in each classroom at Oak Street School. There are 37 classrooms. Each row in the auditorium has 45 seats. What is the fewest number of rows needed for all the students to have a seat?

164

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 19

5. A box of name tags holds 18 name tags. A case of name tags has 25 boxes. Principal Song buys 17 cases of name tags. She gives an equal number of name tags to each of 42 classrooms. If she gives out as many name tags as possible, how many extra name tags does Principal Song have?

6. A farmer’s cows produce 9,548 liters of milk in 31 days. Each cow produces 28 liters of milk a day. The farmer feeds each cow 17 kilograms of hay each day. What is the total number of kilograms of hay the cows eat each day?

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PROBLEM SET

165

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 19

Name

Date

19

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

Blake buys 6 cases of water for a picnic. Each case has 32 water bottles. Blake plans to give everyone the same number of water bottles. If there are 48 people at the picnic, how many water bottles does each person get?

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167

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 20

Name

20

Date

1. Match each mathematical expression with the real-world situation it represents.

Mathematical Expression

Real-World Situation

A. (18 × 4) + 5

Leo buys 4 pens. Blake buys 5 pens. The total cost of the pens is $18. If all the pens cost the same amount, what is the cost for 1 pen?

B. 18 ÷ (4 + 5)

At a camp, 1 group has 18 kids, and 4 groups have 5 kids each. How many kids are at the camp?

C. (18 × 4) − 5

Sana buys 4 cases of water.

Each case has 18 bottles.

If she also has 5 cans of juice, how many total drinks does she have?

D. 18 + (4 × 5)

Yuna mows 4 lawns and gets paid $18 per lawn. If Yuna spends $5, how much money does she have left over?

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169

5 ▸ M1 ▸ TD ▸ Lesson 20

EUREKA MATH2

Use the Read–Draw–Write process to solve the problem. Show your thinking.

2. Jada is saving money for a computer that costs $1,149. That is three times as much money as she has already saved. Her parents also gave her $150 for the computer. Jada earns $14 each hour at her job. How many hours does Jada need to work to earn the remaining money she needs to buy the computer?

170

LESSON

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 20

Name

Date

20

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

1. Noah delivers packages 4 days per week. He is expected to deliver 115 packages each day that he works. This week, he delivers 48 extra packages. How many packages does Noah deliver this week?

2. A motorcycle is 24 times as heavy as a bike. The motorcycle weighs 1,329 kilograms less than a car. The car weighs 1,521 kilograms. How many kilograms does the bike weigh?

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171

5 ▸ M1 ▸ TD ▸ Lesson 20

EUREKA MATH2

3. The school librarian has $9,050 to spend on new carpet and chairs for the library. The library is 42 feet long and 37 feet wide. He buys carpet that costs $4 for each square foot. How much money does the librarian have to spend on chairs?

4. A load of bricks is twice as heavy as a load of wood. The total weight of 4 loads of bricks and 4 loads of wood is 768 kilograms. What is the total weight of 17 loads of wood?

172

PROBLEM SET

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EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 20

5. A driver earns $17 each hour. He earns a total of $1,224 in 4 weeks. A gardener works twice as many hours as the driver and earns $21 each hour. How much more money does the gardener earn than the driver in 4 weeks?

6. Each fish tank at the pet store holds 662 liters of water. There are 9 tanks of goldfish and 4 tanks of angelfish. The aquarium at the zoo holds 78 times as many liters of water as all the tanks at the pet store. How many more liters of water does the aquarium hold than the fish tanks?

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PROBLEM SET

173

EUREKA MATH2 5 ▸ M1 ▸ TD ▸ Lesson 20

Name

Date

20

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

Sasha builds a fence around part of her yard. The three sides of the fence measure 88 feet, 32 feet, and 48 feet. The fence comes in pieces that are 8 feet long. Each piece costs $48. How much does the fence cost?

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EUREKA MATH2 5 ▸ M1

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.

All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History.

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 47, Brovko Serhii/Shutterstock.com; All other images are the property of Great Minds.

For a complete list of credits, visit http://eurmath.link/media-credits.

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EUREKA MATH2

Acknowledgments Kelly Alsup, Adam Baker, Agnes P. Bannigan, Reshma P Bell, Joseph T. Brennan, Dawn Burns, Amanda H. Carter, David Choukalas, Mary Christensen-Cooper, Cheri DeBusk, Lauren DelFavero, Jill Diniz, Mary Drayer, Karen Eckberg, Melissa Elias, Danielle A Esposito, Janice Fan, Scott Farrar, Krysta Gibbs, January Gordon, Torrie K. Guzzetta, Kimberly Hager, 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, 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, Michael Short, Erika Silva, Jessica Sims, Heidi Strate, Theresa Streeter, James Tanton, Cathy Terwilliger, Rafael Vélez, Jessica Vialva, Allison Witcraft, 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

178

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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 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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? Why?

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

What does this painting have to do with math?

Color and music fascinated Wassily Kandinsky, an abstract painter and trained musician in piano and cello. Some of his paintings appear to be “composed” in a way that helps us see the art as a musical composition.

In math, we compose and decompose numbers to help us become more familiar with the number system. When you look at a number, can you see the parts that make up the total?

On the cover Thirteen Rectangles, 1930 Wassily Kandinsky, Russian, 1866–1944 Oil on cardboard Musée des Beaux-Arts, Nantes, France Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY

ISBN 978-1-64497-113-0

9

781644 971130