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A Story of Units®

4 Fractional Units Module 1 ▸ Place Value Concepts for Addition and Subtraction

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A Story of Units®

Fractional Units ▸ 4 APPLY

Module

1 2 3 4 5 6

Place Value Concepts for Addition and Subtraction

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

Foundations for Fraction Operations

Place Value Concepts for Decimal Fractions

Angle Measurements and Plane Figures

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

Published by Great Minds PBC. greatminds.org © 2021 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 B-Print 1 2 3 4 5 6 7 8 9 10 XXX 27 26 25 24 23 ISBN 978-1-64497-654-8

EUREKA MATH2 4 ▸ M1

Contents Place Value Concepts for Addition and Subtraction Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Multiplication as Multiplicative Comparison Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Interpret multiplication as multiplicative comparison.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Write numbers to 1,000,000 in standard form and word form.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Compare numbers within 1,000,000 using >, =, and <.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Solve multiplicative comparison problems with unknowns in various positions.

Topic C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Describe relationships between measurements by using multiplicative comparison.

Name numbers by using place value understanding.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Represent the composition of larger units of money by using multiplicative comparison.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Find 1, 10, and 100 thousand more than and

Topic B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Place Value and Comparison within

1,000,000

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Organize, count, and represent a collection of objects.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Demonstrate that a digit represents 10 times

the value of what it represents in the place to its right.

Rounding Multi-Digit Whole Numbers

less than a given number.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Round to the nearest thousand.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Round to the nearest ten thousand and hundred thousand.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Round multi-digit numbers to any place.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Apply estimation to real-world situations by using rounding.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Write numbers to 1,000,000 in unit form and expanded form by using place value structure.

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4 ▸ M1

EUREKA MATH2

Topic D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Topic E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Multi-Digit Whole Number Addition and Subtraction

Metric Measurement Conversion Tables

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Add by using the standard algorithm.

Express metric measurements of length in terms of smaller units.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Solve multi-step addition word problems by using the standard algorithm.

Lesson 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Express metric measurements of mass and liquid volume in terms of smaller units.

Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Subtract by using the standard algorithm, decomposing larger units once.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 151

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Subtract by using the standard algorithm, decomposing larger units up to 3 times.

Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Subtract by using the standard algorithm, decomposing larger units multiple times.

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Solve two-step word problems by using addition and subtraction.

Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Solve multi-step word problems by using addition and subtraction.

2

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Module 1 Topic A

FAMILY MATH Multiplication as Multiplicative Comparison Dear Family, Key Term

In previous grades, your student learned to compare numbers times as many and use addition or subtraction to describe how many more or how many less. Now, your student uses their prior knowledge of multiplication and division to compare numbers and describe their relationship as times as many. Your student explores a variety of patterns and models such as blocks, tape diagrams, and money, to explain what it means to say times as many. They find an unknown quantity when two quantities are compared by writing multiplication and division equations.

dollars

dimes

pennies

10¢

Figure E

Figure F

12 8

8

9

10

11

13

14

15

16 15 14 13 12 11 10 9

8

8

3

3

4

4

10

10

5

6

6

7

7

9

9 5

7

7

11 12

12

0CM 1

2

2

11 0CM 1

6

6

Amy’s Tower

Gabe’s Tower

Amy’s tower is 3 times as tall as Gabe’s tower.

15 = 3 × 5

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There are ​10​times as many cents in a dime as there are in 1 ​ ​ penny.

16

There are ​4​times as many hexagons in figure F as there are in figure E.

Measurement

Comparison

weight liquid volume capacity height length width distance

times as heavy times as much times as much times as tall times as long times as wide times as far

The comparison phrase times as many can be adjusted to match different contexts.

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EUREKA MATH2

At-Home Activity Use Comparison Language Help your student practice describing multiplication and division equations by using times as many language. You may find it useful to use the comparison language provided in the chart of measurements.

4

•

Use two different-size containers that can hold water, such as a small measuring cup and a large water glass. Have your student fill the larger container by using water from the smaller container. Discuss the amount of liquid each container holds. Help your student by asking a question such as, “What can we say about how much more liquid the larger container holds?” Then say, “We can say that the larger container holds about ____ times as much liquid as the smaller container.” Repeat with other different-size containers like a pot and a bowl, or a pitcher and a cup.

•

Get two dry spaghetti noodles. Break off a small piece, about ​1​inch, of the first noodle.

Leave the second noodle whole. Use the piece of noodle to measure the whole noodle from one end to the other by moving the piece along the whole noodle with no gaps or overlaps. Then compare the length of the piece to the whole noodle by using times as long language. Use a comparison statement such as, “The whole noodle is about ____ times as long as the piece of noodle.” Encourage your student to describe about how many times as long one noodle is than the other.

•

Consider starting conversations with your student such as, “I noticed it took you ​ 2​minutes to brush your teeth and 1​ 0​minutes to eat your breakfast. How many times as long did it take you to eat your breakfast than it did to brush your teeth?”

FA M I LY M AT H ▸ Module 1 ▸ Topic A

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

Complete the statement and equation to match the tape diagram.

1.

8

48​is ​

6

​times as many as ​8​.

48

​= ​

6

​× 8​

48

I see ​1​ unit of 8 ​ ​and ​6​units of ​8​.

8

8 8

8

8

8

8

8

48 I can add to see that the total of ​6​ units of ​ 8​is ​4 8​.

The tape diagram shows that ​4 8​ is ​6​ times as many as ​8​.

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EUREKA MATH2

4 ▸ M1 ▸ TA ▸ Lesson 1

2. Pablo eats ​7​grapes. Luke eats 3 ​ ​times as many grapes as Pablo. How many grapes does Luke eat?

3 × 7 = 21 Luke eats 2 ​ 1​ grapes.

I can draw a tape diagram to represent the problem.

I draw ​1​unit of 7​ ​for Pablo.

I draw ​3​units of 7​ ​for Luke because he eats ​ 3 times as many grapes as Pablo.

7

Pablo Luke ?

I can multiply to find the total number of grapes Luke eats.

6

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1

REMEMBER Add or subtract.

3. ​714 − 235 = ​ 479 ​​​

I can write the problem vertically.

714 - 235

I start by making my units ready to subtract.

I can rename 1​ ​ten as 1​ 0​ones. I add the ​1 0​ ones to 4 ​ ​ ones.

0 14

714 - 235

I also have to rename the hundreds, 1​ ​hundred as ​1 0​ tens.

714 - 235

10 6 0 14

714 - 235 479

Now I am ready to subtract.

4. 252 + 388 = ​ 640

10 6 0 14

To find ​252 + 388​, I can decompose each number into hundreds, tens, and ones.

252 200 50 2

+

388 300 80 8

I add like units. ​200 + 300 = 500 50 + 80 = 130 2 + 8 = 10​ Then I add. ​500 + 130 + 10 = 640​

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P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

Complete the statement and equation to match the tape diagram.

1.

36 is

9

times as many as 9.

= 9

9

9

×9

9

36 2.

42 is

6

times as many as 6.

=

×6

42 Draw a tape diagram to represent the statement. Then complete the equation.

3. 21 is 3 times as many as 7.

21 =

×7

4. Adam reads 6 pages in his book. Gabe reads 4 times as many pages in his book as Adam. How many pages does Gabe read?

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4 ▸ M1 ▸ TA ▸ Lesson 1

EUREKA MATH2

REMEMBER 5. Add or subtract. a. 613 – 164 =

b. 497 + 213 =

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P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 2

Name

2

Date

Use the tape diagram to complete the statement and equations.

1.

​ 63​is ​​

7

9

​times as many as 7 ​ ​.

​ 63 ÷ 7 = ​ 9 ​​

63 =

63

7

...

9

×7

? times as many

I need to find how many units of 7​ ​equals ​63​.

The value of the unknown is ​9​because 6 ​ 3 ÷ 7 = 9.

This tells me ​7​is repeated 9 ​ ​times. I can find the unknown with multiplication too. ​63 = 9 × 7​ 7

7

7

7

7

7

7

7

7

63

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EUREKA MATH2

4 ▸ M1 ▸ TA ▸ Lesson 2

Draw a tape diagram to represent the statement.

Then write an equation to find the unknown and complete the statement.

2. 32​is 4 ​ ​times as many as ​

?

8

​ ​.

32 ​32 ÷ 4 = 8​

I know the unknown unit is repeated ​4​times to equal 3 ​ 2​.

I draw a unit with a question mark because I do not know what number is being repeated.

Then I draw a second tape to show the single unit repeated ​4​times. The total is ​32​.

The value of the unknown is ​8​because 3 ​ 2 ÷ 4 = 8​ .

This tells me 8 ​ ​is repeated ​4​ times. ?

8

8

8

8

32

12

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 2

REMEMBER 3. Which shape has an area of 1 ​ 0​square units? represents 1 ​ ​square unit.

Circle the correct answer.

A.

Same-size square tiles are placed side by side with no gaps to measure area.

The area is equal to the number of square units.

B.

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Shape B is covered with 1​ 0​same-size square tiles.

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 2

Name

2

Date

Use the tape diagram to complete the statement and equations.

1.

?

​56 ​is ​7​times as many as ​56 ÷ 7 =

​ 56 = 7 ×

56 2.

4

​24​ is

​times as many as 4​ ​.

2​ 4 ÷ 4 =

​​​

24 4

​ .

24 =

...

×4

? times as many Draw a tape diagram to represent each statement.

Then write an equation to find the unknown and complete the statement.

​ times 3. ​18​ is as many as ​6​.

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4.

​​​is 5​ ​ times as many as ​3​.

5. ​36​is 4 ​ ​ times as many as ​

​ .

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4 ▸ M1 ▸ TA ▸ Lesson 2

EUREKA MATH2

REMEMBER 6. Which rectangles have an area of 8 ​ ​square units? represents 1 ​ ​square unit.

Circle the two correct answers.

A.

B.

C.

D.

16

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 3

Name

3

Date

Record each measurement. Then complete the statement and the equation.

1.

The paintbrush is ​4​times as heavy as the toothbrush.

40

30

​ 40

0 50 g

10

20

grams

40

30

0 50 g

40

10

​g = 4 ×

10 ​ g​

20

​ 10

​ grams

I see that the paintbrush weighs 4 ​ 0​grams. The toothbrush weighs 10 grams.

The paintbrush weighs more than the toothbrush.

I can also say that the paintbrush is heavier than the toothbrush.

I recognize the relationship between the weight of the paintbrush and the weight of the toothbrush.

I can write a multiplication equation to describe the relationship.

I say “times as heavy” when weight is measured.

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EUREKA MATH2

4 ▸ M1 ▸ TA ▸ Lesson 3

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

2. While playing softball, Robin’s team drinks 8 ​ ​liters of water, and Carla’s team drinks 2 ​ 4​ liters of water. How many times as much water does Carla’s team drink as Robin’s team?

​24 ÷ 8 = 3​ Carla’s team drinks 3 ​ ​times as much water as Robin’s team.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram. I draw one tape and label it 8 to represent the 8 liters of water that Robin’s team drinks.

I draw another tape and label it 24 to represent the 24 liters of water that Carla’s team drinks.

8

24 8

...

? times as much I need to find how many eights are in ​24​. I divide ​24​by ​8​to get 3 ​ ​.

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P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 3

REMEMBER 3. Find the area of the shape. Each

Area:

represents 1 ​ ​square inch.

​10​ square inches

I can count each square as 1 square inch.

The shape is made up of 10 squares, so it has an area of 10 square inches.

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1 2 3 4 5 6 7 8 9 10

P R ACT I C E PA R T N E R

19

EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 3

Name

3

Date

Record each measurement. Then complete the statement and the equation.

1.

40

30

0 50 g

10

40

20

30

​grams 2.

0 CM 1

0 50 g

The plum is 6 ​ ​times as 10

​g = 6 × ​

20

​

2

3

4

5

6

7

8

11

12

6

7

5

6

7

The glue ​ 3​times 0 CM 1stick2 is 4 4 as5

6

as 7 the 8 eraser.

12

11

10

​ cm = 4 ×

​ cm

8

​​centimeters 8

9

4

centimeters

9

3

11 2

10

0 CM 1

5

9

4

10

3

9

2

​ g​

​​grams

​ 0 CM 1

as the cherry.

10

11

12 12

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

3. Deepa and David pick lemons. David picks ​ 3 ​times as many lemons as Deepa. David picks 2 ​ 7​lemons. How many lemons does Deepa pick?

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4. Amy has a yellow dog and a brown dog.

The yellow dog weighs 2 ​ 8​pounds, and the brown dog weighs ​7 ​pounds. How many times as heavy is the yellow dog as the brown dog?

21

EUREKA MATH2

4 ▸ M1 ▸ TA ▸ Lesson 3

REMEMBER 5. Find the area of the shape. Each

represents 1 ​ ​square inch.

Area:

22

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 4

Name

4

Date

Complete the chart to show how to make a new unit. Then complete the statement and equations.

1. dollars

dimes

×

​1​dime is worth ​ 10

1​ dime = ​ 10 ​10¢ = ​ 10

​× ​

pennies

10

times as much as 1 ​ ​ penny .

​× 1 ​penny ​​ 1

​¢ ​

I know that with pennies and dimes ​1 0​of the smaller unit has the same value as ​1​of the larger unit.

When I have ​1 0​pennies, I can make 1​ ​ dime.

So ​1​dime has the same value as ​1 0​ pennies.

=

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23

EUREKA MATH2

4 ▸ M1 ▸ TA ▸ Lesson 4

2. Oka says that because 1 ​ ​dollar is worth 1 ​ 0​times as much as 1 ​ ​dime, 4 ​ ​dollars must be worth ​ 10​times as much as 4​ ​dimes. Do you agree with Oka? Why?

​ 0 = 10 × 4​.

Yes, I agree with Oka because ​10 = 10 × 1​and 4

​1​dollar is worth as much as ​1 0​ dimes.

So ​4​dollars are worth as much as ​4 0​ dimes.

=

24

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 4

REMEMBER 3. A rectangular patio has a width of 5 ​ ​feet and a length of 9 ​ ​ feet.

What is the area of the patio?

The patio is in the shape of a rectangle.

I can multiply the length and width of the patio to find its area.

9 ft

5 ft ​5 × 9 = 45​ The area of the patio is 4 ​ 5​square feet.

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P R ACT I C E PA R T N E R

25

EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 4

Name

4

Date

Complete the chart to show how to make a new unit. Then complete the statement and equations.

1.

dollars

dimes

2.

pennies

×

​10¢ = 10 ×

​ ​ ¢​

dimes

pennies

×

​1​dime is worth 1 ​ 0​times as much as 1 ​​ ​1 dime = 10 × 1

dollars

.

​1​dollar is worth 1 ​ 0​times as much as 1 ​​

.

​1 dollar = 10 × 1 ​$1 = 10 ×

​¢​

​ 0​times as much as 1 ​ ​penny, 6 ​ ​dimes must be worth ​ 3. Mia says that because 1 ​ ​dime is worth 1 10​times as much as 6​ ​pennies. Do you agree with Mia? Why?

4. David says that because ​1​dollar is worth 1 ​ 0​times as much as 1 ​ ​dime, 5 ​ ​dollars must be worth ​ 5​times as much as 5​ ​dimes. Do you agree with David? Why?

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EUREKA MATH2

4 ▸ M1 ▸ TA ▸ Lesson 4

REMEMBER 5. A rectangular garden has a length of 7 ​ ​feet and a width of 6 ​ ​ feet.

What is the area of the garden?

6 ft

7 ft

28

P R ACT I C E

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Module 1 Topic B

FAMILY MATH Place Value and Comparison within 1​ ,000,000​ Dear Family,

Key Terms

In previous grades, your student learned about place value hundred thousand for numbers up to 1 ​ ,000​. Using that knowledge, your student million explores counting with large sums of money as a context for understanding large numbers. They learn to read, write, and ten thousand compare numbers up to ​1,000,000​. They also connect recent 10 times as much learning about times as much to realize that a digit represents ​ 10​times the value of the same digit in the place to its right.

A strong sense of place value understanding helps your student add, subtract, multiply, and divide with large numbers later this year.

millions 1,000,000

hundred thousands 100,000

ten thousands 10,000

thousands 1,000

hundreds 100

tens 10

ones 1

A place value chart organizes numbers and shows the relationships between place value units.

56,348 50,000 + 6,000 + 300 + 40 + 8 fifty-six thousand, three hundred forty-eight

thousands

hundreds

tens

ones

× 10

56 thousands 3 hundreds 4 tens 8 ones Writing numbers in various forms, such as in standard form, expanded form, word form, and unit form, enables flexible thinking.

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​10​times as much as 3 ​ ​tens is 3 ​ ​ hundreds.

​10 × 30 = 300​ ​3​hundreds is 1 ​ 0​times as much as 3 ​ ​ tens. ​300 = 10 × 30​

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4 ▸ M1 ▸ TB

EUREKA MATH2

At-Home Activities Comparing Money Encourage your student to practice multiplying and dividing by 1 ​ 0​by using pennies, dimes, and dollars. Ask your student how many cents are in a penny (​1¢​), a dime (​10¢​), and a dollar (​100¢​).

Talk about how many pennies equal the value of a dime and how many dimes equal the value of a dollar. Ask your student to say a multiplication sentence for each relationship such as, “10 times 1 cent is 10 cents, and 10 times 10 cents is 100 cents.” Then ask questions about larger amounts.

•

“How many cents is ​7​dimes worth?” (​70​ cents)

•

​ ​dimes?” (​7​dollars or 70 dimes) “What is ​10​times as much as 7

•

​ 0​times as much as how many cents?” (​7​ cents) “​70​cents is 1

•

​ 00​cents. How many cents is 1 ​ 0​times as much as 7 ​ ​ dollars?” “​7​dollars is worth 7 (​7,000​ cents)

Comparing Large Numbers Write two large numbers, such as 3 ​ 8,720​and 3 ​ 6,954​. Ask your student to say which number is greater and which number is less and explain how they know. Encourage your student to draw a place value chart to help them. For an added challenge, ask your student to write a number greater than one of the numbers, write a number less than the other number, and write a number whose value is between both numbers.

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FA M I LY M AT H ▸ Module 1 ▸ Topic B

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 5

Name

5

Date

Use the place value disks to help you complete the equation.

1.

10,000 10,000

1

10,000 10,000 100,000

​ hundred thousand = 10 ten thousands​

10,000 10,000 10,000 10,000

Ten thousand is a place value unit composed of 1​ 0​ thousands.

10,000 10,000

Hundred thousand is a place value unit composed of 1​ 0​ten thousands.

I know I can bundle ​1 0​of a smaller unit to make 1​ ​of the next larger unit.

There are ​1 0​ten thousands. I look at a place value chart.

I find ten thousands. The next larger unit is hundred thousands.

Next Larger Unit

millions 1,000,000

hundred ten thousands thousands thousands 100,000 10,000 1,000

hundreds 100

tens 10

ones 1

I can bundle and rename ​1 0​ten thousands as ​1​hundred thousand.

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31

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 5

Use the place value disks to help you complete the equation.

2.

100,000 100,000

100,000 100,000

1 1,000,000

100,000 100,000

​ million = 10 hundred thousands​

100,000 100,000

100,000 100,000

Million is a place value unit composed of ​1 0​hundred thousands.

I know I can bundle ​1 0​of a smaller unit to make ​1​of the next larger unit.

There are ​1 0​hundred thousands. I look at a place value chart.

I find hundred thousands. The next larger unit is millions.

Next Larger Unit

millions 1,000,000

hundred ten thousands thousands thousands 100,000 10,000 1,000

hundreds 100

tens 10

ones 1

I can bundle and rename ​1 0​hundred thousands as ​1​ million.

32

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 5

REMEMBER 3. Shade the rectangle to break it into 2 ​ ​smaller rectangles.

Then complete the equations to find the total area of the large rectangle.

Each square represents 1 ​ ​square unit.

5×

13

=5×(

10

+

= (5 ×

10

) + (5 ×

=

+

15

50

3

) 3

)

​ = 65 ​ Area: ​ 65 square units ​

I can use the break apart and distribute strategy to find the area.

I decompose 1​ 3​ into ​1 0​ and ​3​.

I shade a ​5 by 10​rectangle and label the side lengths of the shaded and unshaded parts of the large rectangle.

10

3

5

I find the area by multiplying each part of 13 by ​5​ and then adding the products.

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P R ACT I C E PA R T N E R

33

EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 5

Name

5

Date

Use the place value disks to help you complete the equation.

1.

1,000

2.

1,000

1,000

1,000

1,000

1,000

1,000

100

1,000

1,000

100

1,000

1,000

100

100

100

100

100

100

100 100

10,000

​ thousand = 10 hundreds​ 3.

10,000 10,000

1 4.

100,000 100,000

10,000 10,000 100,000

​1

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= 10 thousands​

100,000 100,000

10,000 10,000

1,000,000

100,000 100,000

10,000 10,000

100,000 100,000

10,000 10,000

100,000 100,000

= 10 ten thousands​

​1

= 10 hundred thousands​

35

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 5

REMEMBER 5. Shade the rectangle to break it into 2 ​ ​smaller rectangles.

Then complete the equations to find the total area of the large rectangle.

Each square represents 1 ​ ​square unit.

​3 × ​

​ = 3 × ​(​​​

​ + ​

= ​(​​3 × ​

​​)​​ + ​(​​3 × ​

= Area:

36

P R ACT I C E

​ + ​

​​)​​ ​​)​​

​​​

​

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 6

Name

6

Date

Use the place value chart to complete the statements and equations.

1.

thousands

hundreds

×

tens

ones

10

​10​times as much as 2 ​ ​tens is 2 ​ ​ hundreds .

1​ 0 × 20 = ​ 200 ​ ​ 0​times as much as ​2​hundreds is 1 2​ ​ tens . ​200 = 10 ×

20

I need to find ​1 0​ times as much as ​2​ tens.

When I multiply by ​1 0​, the units shift one place to the left on the place value chart.

Now there are ​2​ units in the hundreds place. So ​1 0​ times as much as ​2​ tens is ​2​ hundreds.

When I divide by ​1 0​, the units shift one place to the right on the place value chart.

Now there are ​3​units in the hundreds place.

So ​3,000​divided by ​1 0​ is equal to 3 ​ 00​.

Use the place value chart to complete the equation.

2.

ten thousands

thousands

hundreds

tens

ones

÷ 10

3,000 ÷ 10 = ​ 300 Copyright © Great Minds PBC

37

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 6

REMEMBER 3. Find the area of the shape. Show your strategy.

2 in 7 in

3 in

3 in 2 in

6 in ​6 × 7 = 42​

3​ × 3 = 9​ 4​ 2 − 9 = 33​ Area: 33 square inches ​​

I can find the areas of the large and small rectangles.

Then I can subtract the area of the smaller rectangle from the area of the larger rectangle.

To find the area of the smaller rectangle, I need to know the lengths of the sides. The opposite sides of rectangles have the same lengths.

I know the large rectangle is ​7​ inches by ​6​ inches.

I know the small rectangle is ​3​ inches by ​3​ inches.

6 in 2 in

3 in

7 in 3 in

2 in

38

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 6

Name

6

Date

Use the place value chart to complete the statements and equations. tens

ones

2.

thousands hundreds

.

​

6​ ​hundreds is 1​ 0​times as much as 6​ ​ ​600 = 10 ×

ones

×

×1 ​10​times as much as 6 ​ ​tens is 6 ​​

1​ 0 × 60 = ​

tens

10

thousands hundreds

0

1.

1​ 0​times as much as 4​ ​ hundreds is 4 ​​ .

1​ 0 × 400 =

.

​

​

4​ ​thousands is 1​ 0​times as much . as 4 ​​ ​4,000 = 10 ×

​

Use the place value chart to complete the equation.

3.

ten thousands

thousands

hundreds

tens

ones

900 ÷ 10 = ​

​

÷ 10

4.

ten thousands

thousands

hundreds

tens

ones

7,000 ÷ 10 =

​

÷ 10

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39

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 6

REMEMBER 5. Find the area of the shape. Show your strategy.

3 in

3 in 4 in

6 in

9 in

Area:

40

P R ACT I C E

​​

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 7

Name

7

Date

Count the number of place value disks in each column of the chart.

Write the number at the bottom of each column.

Then fill in the blanks to write the unit form of the number represented in the chart.

1.

1,000

100

1

100,000

100

1

100,000

100

100,000

1,000,000

100 100

​

1

3

0

1

​​million

3

​hundred thousands

5

​​hundreds

0

​​​tens

1

2

0

5

0

2

​ten thousands

1

​​thousand

​​​ones

I count the number of disks in each column.

There is ​1​millions disk, so I write ​1​at the bottom of the first column.

I write the other numbers of disks at the bottom of each column.

I express the number shown in the chart in unit form.

Unit form helps me know how many of each place value unit are in a number. It helps me use the correct names for each digit.

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41

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 7

Fill in the blanks to write the number in expanded form in two ways.

Standard Form 2. ​105,340​

Expanded Form

100,000 ​​ +

5,000

​​(​ ​​1 × ​ 100,000 ​​​)​​ + ​(​​​

​ + ​ 5

300

​​ + ​

​​ × 1, 000​)​​ + ​(​​​

40 3

​​​ ​ × 100​)​​ + ​(​​4 ×

10

)​​​​

I can write a number in expanded form by using addition. I write the value of each digit.

There is ​1​hundred thousand. I write ​ 100,000​.

There are ​5​thousands. I write ​5,000​.

There are ​3​hundreds. I write 3 ​ 00​.

There are ​4​tens. I write ​4 0​.

I do not need to include ​0​ ten thousands or ​0​ones because they do not change the value of the number.

42

P R ACT I C E PA R T N E R

I can also write a number in expanded form by using multiplication and addition.

The value of each digit is ­represented by using multiplication. The ­parentheses help to show each place value unit.

I think about the place value units and complete each expression.

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 7

REMEMBER 3. Luke’s rectangular living room floor is ​8​feet wide and ​10​feet long. He puts a rectangular rug that ​ ​feet long on the floor. is ​3​feet wide and 6 What is the area of the floor that is not covered by the rug?

10 ft

6 ft 8 ft

Area:

62 square feet

3 ft

​

I can find the areas of the floor and the rug. Then I can subtract the area of the rug from the area of the floor.

Area of the Living Room Floor

Area of the Rug

8 × 10 = 80

3 × 6 = 18

80 − 18 = 62​ The area of the floor not covered by the rug is ​62​square feet.

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P R ACT I C E PA R T N E R

43

EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 7

Name

7

Date

Count the number of place value disks in each column of the chart.

Write the number at the bottom of each column.

Then fill in the blanks to write the unit form of the number represented in the chart.

1.

​

10,000

1,000

100

10

1

10,000

1,000

100 1

10

1

1,000

100 1

100 1

10

1

1,000

100 1

100 1

10

1,000

100 1

100 1

​ten thousands ​

thousands ​

hundreds ​

tens ​

ones

Use the numbers on the place value chart to complete the expanded form.

2.

millions

hundred ten thousands thousands thousands

4

Expanded form: ​

6

​ ​+

hundreds

tens

ones

3

1

0

5

​​ ​+

​​ + ​

​​ + ​

​

Fill in the blanks to write the number in expanded form in two ways.

Standard Form

Expanded Form

3. ​ 42,910​

​​(​ ​​4 × Copyright © Great Minds PBC

​ + 2,000 + ​

​ + ​

​​​ )​​ + ​( ​​​​

​ × 1, 000)​​ + ​(​​​​

​ × 100​)​​ + ​(​​1 × ​​

)​​​​ 45

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 7

REMEMBER 4. Robin’s rectangular bedroom floor is ​7​feet wide and ​9​feet long. She puts a rectangular rug that is​ 4​feet wide and 5​ ​feet long on the floor.

What is the area of the floor that is not covered by the rug?

7 ft

4 ft

9 ft

Area:

46

P R ACT I C E

5 ft

​

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 8

Name

8

Date

Express the following number in standard form by using commas.

1. 3141592​

3,141,592 ​ I know that the place value chart is organized into groups of three place value units. Those groups are called periods. A comma separates the digits between each period.

I start to the right of the digit in the ones place and count ​three​places to the left.

3 1 41,5 9 2 I write a comma between ​1​ thousand and ​5​ hundreds.

Then I count t ​ hree​more places to the left of the first comma.

I write a comma between ​3​ ­millions and ​1​ hundred thousand.

3,1 41,5 9 2

Fill in the blank to make a true number sentence.

2. 4 ​ 0,000 + 2,000 + 60 + 7 =

42,067 ​

I can use a place value chart. millions 1,000,000

hundred thousands 100,000

ten thousands 10,000

thousands 1,000

hundreds 100

tens 10

ones 1

4

2

0

6

7

I see there are 4 ​ ​ten thousands, ​2​ thousands, 6​ ​tens, and ​7​ones.

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47

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 8

Complete the table.

3.

Standard Form

Unit Form

Word Form

2​ 0,534​

​2​ten thousands 5 ​ ​ hundreds ​ 3​tens 4​ ​ ones

Twenty thousand, five hundred thirty-four

I read the number in unit form and show it in a place value chart. millions 1,000,000

48

P R ACT I C E PA R T N E R

hundred thousands 100,000

ten thousands 10,000

thousands 1,000

hundreds 100

tens 10

ones 1

2

0

5

3

4

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 8

REMEMBER 4. Liz collects leaves in her backyard. The tally chart shows the number of leaves she collects in each color. Use the data in the tally chart to draw a scaled picture graph.

In a scaled picture graph, each symbol represents more than ​1​object or observation.

Liz’s Leaf Collection Number of Leaves

Color

I make a table from the data in the tally chart.

Green

Green Yellow 2

Yellow

4

Red 6

Brown Orange 2

8

I create a scale. I think it is reasonable for a circle to represent ​2​leaves because each number is a multiple of ​2 ​.

Red

I give the graph a title. I label the left side of my graph with the colors of the leaves.

I write the key I will use below the graph.

Brown Orange

Liz’s Leaf Collection Green Yellow Color

Now I can draw circles to represent the data.

Red Brown Orange

Each

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represents

2

leaves.

I draw circles to represent the data.

As I draw circles for each color, I count by twos until I represent the correct number of leaves because each circle represents 2 leaves.

P R ACT I C E PA R T N E R

49

EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 8

Name

8

Date

Express the following numbers in standard form by using commas.

1. ​9560​

​​​

2. 3 ​ 6805​

​​​

3. ​308223​

​​​

4. 3 ​ 4651047​

​

Fill in the blank to make a true number sentence.

5. ​10,000 + 5,000 + 300 + 8 = ​ 6. 4 ​ 00,000 + ​

​

​ + 900 + 20 + 6 = 430,926​

7. ​42 thousands + 8 hundreds + 4 ones =

​

Complete the table.

Standard Form

Unit Form

8.

​5​thousands 2 ​ ​hundreds 8 ​ ​ ones

9.

​3​ten thousands 5 ​ ​ hundreds ​ 8​tens 2​ ​ ones

10.

​4​ten thousands 2 ​ ​ hundreds ​ 9​tens 7​ ​ ones

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Word Form

51

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 8

REMEMBER 11. Mr. Davis surveys his students about their pets. The tally chart shows the results of the survey.

Use the data in the table to draw a scaled picture graph.

Students’ Pets Pet

Number of Students

Dog Cat Fish Rabbit Horse

Each 52

P R ACT I C E

represents

.

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 9

Name

9

Date

Represent each number with digits on the place value chart. Then circle the greater number.

1.

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

5

2

1

6

4

5

521,645

5

3

4

9

0

4

534,904

I write the digits of each number in the correct places in the place value chart.

I see that each number has a digit in the hundred thousands place. Both numbers have ​5​ hundred thousands. millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

5

2

1

6

4

5

5

3

4

9

0

4

I look at the next smallest place value unit, the ten thousands. millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

5

2

1

6

4

5

5

3

4

9

0

4

​ 2​ ten thousands is less than ​53​ ten thousands, so ​521,645​ is less 5 than ​534,904​.

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53

EUREKA MATH2

4 ▸ M1 ▸ TB ▸ Lesson 9

​ ​to compare the numbers.

Use ​>​, ​=​, or < 2. ​5,622

<

5 thousands 8 hundreds 7 tens 5 ones​

To compare ​5,622​ and ​5​ thousands ​8​ hundreds ​7​ tens 5 ​ ​ ones, I first write them in the same form.

I can think about both numbers in unit form. ​5​thousands ​6​hundreds ​2​ tens ​2​ ones ​5​ thousands ​8​ hundreds ​7​ tens ​5​ ones Both numbers have 5 ​ ​thousands. The first number has ​6​ hundreds, and the second number has ​8​ hundreds. ​ hundreds < 8 hundreds​, 6 so ​5,622 < 5 thousands 8 hundreds 7 tens 5 ones​.

Arrange the numbers from least to greatest.

3. 1 ​ 1,554​

9​ ,232​ 8​ ,240​ 9​ ,338​

​ 8,240

​ , ​

9,232

​ , ​

9,338

​ , ​ 11,554 ​

I can write the numbers in a place value chart and compare the digits. ten thousands

thousands

hundreds

tens

ones

1

1,

5

5

4

9,

2

3

2

8,

2

4

0

9,

3

3

8

​ ,240​ has the smallest number of thousands, ​8​ thousands, so it is the 8 smallest number.

1​ 1,554​has the largest number of thousands, ​11​thousands, so it is the largest number. ​9,232​ and ​9,338​ both have ​9​ thousands, so I compare the hundreds place. ​9,232​ has ​2​hundreds, and ​9,338​ has 3 ​ ​hundreds. So, 9 ​ ,232 < 9,338​.

From least to greatest, the numbers are ​8,240​, ​9,232​, ​9,338​, and ​1 1,554​.

54

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 9

REMEMBER 4. Measure the lengths of the lollipops to the nearest quarter inch. Record the data in the table.

Create a line plot to represent your data.

Lengths of Lollipops (inches)

2​ ​1_​ 2

​2 ​1_​ 4

​3 ​3_​ 4

2​ ​

​2​

​3​

I measure each lollipop. I line up the end of my ruler with the end of the lollipop. I measure to the nearest quarter inch.

2​ ​ _1 ​​ 2

1 ​3 ​ _ ​​ 4

1

0

×

2

24

1

× × 1

22

3

24

×

×

3

34

Length (inches)

1

3

4

2 34 inches

Lengths of Lollipops

× ×

2

I organize my data in the table.

× 1

32

3

34

4

I look at the data in the table to help me decide the scale on the line plot.

I write a title for the line plot, and I write a label to show that the numbers represent lengths in inches.

The smallest measurement is ​2​ inches, and the largest measurement is 3​​ _3​​inches. I make intervals of ​​ _1 ​​ inch 4

on the line plot.

4

I make an X above the line plot for each piece of data.

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P R ACT I C E PA R T N E R

55

EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 9

Name

9

Date

Represent each number with digits on the place value chart. Then circle the greater number.

1.

hundred thousands

millions

ten thousands

thousands

hundreds

tens

ones

2,530 2,399

2.

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

73,253 74,019

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

3. ​5,408

3,981​

5. ​90,000 + 5,000 + 400 + 20 + 1 7. ​520,600

95,421​

five hundred forty thousand​

4. ​1,327

1,331​

6. 6 ​ ,118

6 thousands 2 hundreds 4 ones​

8. ​9 thousands 5 tens 7 ones

9,057​

Arrange the numbers from least to greatest.

9. 6 ​ ,803​

7​ ,446​ 7​ ,890​ 6​ ,996​ ​

10. 2 ​ 08,115​

1​ 85,302​ 2​ 00,460​ 1​ 81,327​ ​

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​ , ​​

​ , ​

​ ,

​​ ​, ​

​ , ​

​ , ​

​

57

4 ▸ M1 ▸ TB ▸ Lesson 9

EUREKA MATH2

REMEMBER 11. Cut out the ruler. Measure the lengths of the crackers to the nearest quarter inch. Record the data in the table. Create a line plot to represent your data.

58

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TB ▸ Lesson 9

Lengths of Crackers (inches)

0

inch

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1

2

1

24

2

1

22

3

24

3

3

1

1

34

32

4

3

34

4

5

6

P R ACT I C E

59

Module 1 Topic C

FAMILY MATH Rounding Multi-Digit Whole Numbers Dear Family,

Your student is learning to round numbers to the nearest thousand, ten thousand, and hundred thousand. First, they name numbers in unit form based on the place value to which they are rounding. Then they use the vertical number line to show their understanding. Labeling the number line with two benchmark numbers and the number that is halfway between the two benchmark numbers can help your student to identify the closest benchmark. Your student also decides when it may be helpful to round to the nearest or next benchmark. They understand that some situations require an estimate greater than the actual amount, such as when estimating a cost.

thousands hundreds

6

2

tens

ones

7

5

6 thousands 2 hundreds 7 tens 5 ones 62 hundreds 7 tens 5 ones 627 tens 5 ones 6,275 ones ​6,275​ written in different ways.

190,000 = 19 ten thousands 186,045 185,000 = 18 ten thousands 5 thousands 180,000 = 18 ten thousands 186,045 ≈ 190,000

​186,045​rounded to the nearest ten thousand on the vertical number line.

Liz has $70. She wants to buy a book bag that costs $34, a book that costs $19, and a calculator that costs $24.

Liz rounds to the nearest ten.

Liz rounds to the next ten.

30 + 20 + 20 = 70

40 + 20 + 30 = 90

To make sure she has enough money, Liz decides to use the estimate that rounds to the next ten instead of the nearest ten.

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61

EUREKA MATH2

4 ▸ M1 ▸ TC

At-Home Activities Rounding Numbers Get six pieces of paper. Label the first piece with the first digit from your phone number, the second piece with the second digit from your phone number, and so on until all pieces of paper have been used. Mix up the papers and place facedown in a row. Then have your student turn ​ ​-digit number. Invite your student to help you round the over all 6 ​ ​pieces of paper to form a 6 number to the nearest thousand, ten thousand, and hundred thousand. Have them explain their reasoning as they round. Repeat with a different ​6​-digit number.

Estimate Costs Practice using estimation by planning an imaginary shopping trip. Let your student choose the reason for the trip and the items to purchase. For example, your student may decide they are shopping for a party or a gift. Use a store flyer or a store’s online website and ask your student to help you think about how much money is needed to buy some items. Decide on a budget, such as $ ​ 100​. Make a shopping list and label items with whole-dollar amounts. Begin with ​2​items, rounding to the nearest ten dollars. Ask questions to discuss the estimates.

62

•

“What is the total cost when we estimate by rounding each price to the nearest ten dollars?”

•

“Do we have enough money to buy the items if we use that estimate?”

•

“Is there another way to estimate the total to make sure we have enough money?”

FA M I LY M AT H ▸ Module 1 ▸ Topic C

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 10

Name

10

Date

1. Represent ​2,137​on the place value chart to match the given unit form. ​ 3​tens 7 ​ ​ ones ​2​thousands 1 thousands

hundreds

tens

ones

I draw to represent 2​ ​in the thousands column, ​ 13​in the tens column, and ​7​in the ones column. ​2​ thousands 1​ 3​tens 7​ ​ones is the same as ​2,137​.

2. Rename ​1,584​in different ways.

1

thousand

5

hundreds

8

tens

4

ones

15

hundreds

8

tens

4

ones

​ 158 ​ tens

4

ones

1,584 ones I can use a place value chart to rename ​1 ,584​ in different ways.

I can rename ​1​ thousand as ​1 0​ hundreds. So ​1 ,584​ can be renamed as ​1 5​ hundreds ​8​ tens ​4​ ones.

I can use place value to rename ​1 ,584​ in other ways too.

thousands hundreds

1

thousands hundreds

1

5

thousands hundreds

1

5

thousands hundreds

1 Copyright © Great Minds PBC

5

5

tens

ones

8

4

tens

ones

8

4

tens

ones

8

4

tens

ones

8

4 63

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 10

Write the answer for each question.

3. How many thousands are in the thousands place in 2 ​ 4,308​?

4. How many thousands are in 2 ​ 4,308​?

24

4

thousands

thousands

I write ​24,308​ in a place value chart. There are ​4​ thousands in the thousands place. ten thousands thousands hundreds

2

4

3

tens

ones

0

8

I can rename ​24,308​ as ​24​ thousands, ​3​ hundreds, ​0​ tens, and ​8​ ones. ten thousands thousands hundreds

2

4

3

tens

ones

0

8

So there are ​24​ thousands in ​24,308​.

REMEMBER 5. Fill in the blanks to make the equations true. ​42 ÷

7

= 6​

6. Complete the equations to find 4 ​ 2 ÷ 6​.

​4​ 2 ÷ 6 = ​(​​30 ÷ 6​)​​ + ​(​​ 12 = ​(​​ 5 ​)​​ + ​(​​ 2 = 7 ​

÷ 6​)​​ ​)​​

I can use a related multiplication equation with an unknown factor. ​ × 6 = 42​

I can use a number bond to break apart ​42​ into smaller parts. Then I can divide by ​6​ by using facts I know.

I skip-count by ​6​ to get to the total, ​42​.

42 ÷ 6 = (30 ÷ 6) + (12 ÷ 6)

I skip-counted by ​6​ seven times.

So, 7​ × 6 = 42​and ​42 ÷ 7 = 6​.

30 12

​6​, ​1 2​, ​1 8​,​ ​​24​, ​30​ , ​36​, ​42​

I divide each part by ​6​ and add the quotients to find ​42 ÷ 6​.

64

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 10

Name

10

Date

1. Represent ​1,524​on each place value chart to match the given unit form. a. ​1​thousand 5 ​ ​hundreds 2 ​ ​tens 4 ​ ​ ones thousands

hundreds

tens

ones

hundreds

tens

ones

b. ​15​hundreds 2 ​ ​tens 4 ​ ​ ones thousands

2. Rename ​6,219​in different ways. thousands ​

​hundreds ​

​ten ​

​ ones

​

​hundreds ​

​ten ​

​ ones

​

​tens ​

​ ones

​

​ ones

Write the answer for each question.

3. How many thousands are in the thousands place in 4 ​ 9,225​?

4. How many thousands are in 4 ​ 9,225​? ​ Copyright © Great Minds PBC

thousands

​ thousands 65

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 10

REMEMBER 5. Fill in the blanks to make the equations true. ​30 ÷ ​

= 5​ × 9 = 45​

6. Complete the equations to find 5 ​ 4 ÷ 6​.

​5​ 4 ÷ 6 = ​(​​30 ÷ 6​)​​ + ​(​​ = ​(​​ =

66

P R ACT I C E

​)​​ + ​(​​

÷ 6​)​​ ​)​​

​

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 11

Name

11

Date

Draw or cross out disks on the chart to match the statement. Complete the statement.

1.

100,000

10,000

1,000

100

10

100,000

10,000

1,000

100

10

100,000

10,000

1,000

100

100,000

1,000

1,000

100

100,000

1,000

1,000

100

1

​1​ten thousand less than 5 ​ 37,521​ is 527,521 .

I see ​3​ten thousands disks.

To find ​1​ ten thousand less than ​537,521​, I can cross out ​1​ ten thousands disk.

Now I see ​2​ ten thousands disks.

So ​537,521 − 10,000 = 527,521​.

Complete the statement and equation.

2. 1 ​ ,000​more than 2 ​ 2,175​ is ​22,175 + 1,000 =

23,175

23,175 . ​

There are ​2 2​ thousands in ​2 2,175​. ​1​ thousand more than ​2 2​ thousands is ​23​ thousands. ​2 2 thousands + 1 thousand = 23 thousands​ So ​1 ,000​more than ​2 2,175​​ ​is​ ​​23,175​.

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67

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 11

Use the rule to complete the number pattern.

3. Rule: Subtract 1 ​ 0,000​ ​83,504​

73,504

63,504​​

43,504

53,504​​

There are ​8​ten thousands in 8 ​ 3,504​ . I subtract ​ 1​ten thousand to find the next number in the pattern. ​8 ten thousands − 1 ten thousand = 7 ten thousands​ The next number in the pattern is ​73,504​.

I repeat this rule to complete the pattern.

REMEMBER 4. Ivan plots a point on a number line to show what time he starts fishing.

Each interval represents ​5​ minutes. start 4:00 p.m.

a. What time does Ivan start fishing? ​4 : 15​ p.m. b. Ivan catches a fish at ​4 : 40​ p.m.

Plot and label this time on the number line.

5:00 p.m.

4:40 p.m.

I know that each interval represents ​5​ minutes.

I start at ​4 : 00​ p.m. I skip-count by fives until I arrive at the point. Ivan starts fishing at ​4 : 15​ p.m.

5

I skip-count by fives until I reach ​4 0​. I plot a point at the tick mark that represents ​4 0​. Then I label the time on the number line.

4:00 p.m.

P R ACT I C E PA R T N E R

start

4:00 p.m.

5

68

10 15

10 15 20 25 30 35 40 start

4:40 p.m.

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 11

Name

11

Date

Draw or cross out disks on the chart to match the statement. Complete the statement.

1.

100,000

10,000

1,000

100

100,000

10,000

1,000

100

1

100,000

10,000

1,000

100

1

100,000

10,000

1,000

10,000

10

1

1

10,000

​ 1​hundred thousand less than 4​ 64,314​is

.

Complete each statement and equation. ​ 4,528​ is 2. ​10,000​more than 7

7​ 4,528 + 10,000 =

is 1 ​ ,000​less than 3 ​ 26,420​.

3.

. ​

​

= 326,420 − 1,000​

Use the rule to complete the number pattern.

4. Rule: Add ​100,000​ ​205,699​

​​

​​

​​

​​

5. Rule: Subtract 1 ​ ,000​ ​42,891​

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​​

69

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 11

REMEMBER 6. Eva plots a point on a number line to show what time math class begins.

Each interval represents ​5​ minutes.

11:00 a.m.

12:00 p.m.

a. What time does math class begin? b. Eva has lunch at ​11 : 55​a.m. Plot and label this time on the number line.

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P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 12

Name

12

Date

Round to the nearest thousand. Draw a number line to show your thinking.

1. 2 ​ 05,787 ≈ ​ 206,000

206,000 = 206 thousands 205,787 205,500 = 205 thousands 5 hundreds

The symbol ​≈​means about. ​205,787 ≈ 206,000​ ​205,787​is about ​206,000​.

205,000 = 205 thousands

There are ​205​thousands in 2​ 05,787​. ​1​ more thousand is ​206​ thousands. I draw and label the bottom and top tick marks. ​205​ thousands 5 ​ ​hundreds is halfway between ​ 205​thousands and ​206​thousands. I draw and label the tick mark that represents halfway between 2​ 05,000​and ​206,000​. ​205,787​is greater than ​205,500​. I plot 2​ 05,787​ between ​205,500​ and ​206,000​.

2​ 05,787​ is greater than ​205,500​, which means it is more than halfway between ​205,000​​ ​ and​ ​​ 206,000​. That tells me that 2​ 05,787​is closer to 2​ 06,000​than to 2​ 05,000​.

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71

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 12

2. There are 1 ​ 4,366​people at an amusement park. To the nearest thousand, about how many people are at the amusement park? ​14,366 ≈ 14,000​

There are about 1 ​ 4,000​people at the amusement park.

I can draw a number line to round ​ 14,366​to the nearest thousand.

1​ 4,366​ is less than halfway between ​ 14,000​and ​1 5,000​. That means ​14,366​ is closer to ​14,000​ than to ​1 5,000​.

15,000 = 15 thousands 14,500 = 14 thousands 5 hundreds 14,366 14,000 = 14 thousands

72

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 12

REMEMBER 3. Carla reads from 6 ​ : 02​p.m. to ​6 : 14​p.m. She takes 7 ​ ​minutes to fill out a worksheet. How many total minutes does it take Carla to read and fill out her worksheet?

It takes Carla 1 ​ 9​minutes to read and fill out her worksheet.

I think about a time that is easy for me to count on to.

I choose ​6 : 10​p.m. because 1​ 0​is a benchmark number.

I use the arrow way to count on from ​6 : 02​ to ​6 : 10​.

There are ​8​minutes from ​6 : 02​ to ​6 : 10​.

Then I count on from ​6 : 10​to ​6 : 14​. There are ​4 ​minutes from ​6 : 10​ to 6 ​ : 14​.

6:02

+8

6:10

+4

6:14

I add 8 ​ ​and ​4​to get ​1 2​. Carla reads for ​1 2 ​minutes.

Finally, I add the minutes she reads and the minutes she takes to fill out her worksheet. ​1 2 + 7 = 19​

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P R ACT I C E PA R T N E R

73

EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 12

Name

12

Date

Round to the nearest thousand. Show your thinking on the number line.

1. 3 ​ ,800 ≈ ​​

2. ​18,155 ≈

​

​

Round to the nearest thousand. Draw a number line to show your thinking.

3. 4 ​ 7,706 ≈

​

4. 1 ​ 04,621 ≈

​

5. There are ​17,129​books in a library. To the nearest thousand, about how many books are in the library?

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75

4 ▸ M1 ▸ TC ▸ Lesson 12

EUREKA MATH2

REMEMBER 6. Amy watches a video for science class from ​1 : 13​p.m. to ​1 : 24​p.m. She answers questions about the video for 4 ​ ​minutes. How many total minutes does Amy spend watching the video and answering questions?

76

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 13

Name

Date

13

Round to the nearest ten thousand. Show your thinking on the number line.

1. 8 ​ 4,211 ≈

80,000 ​

90,000 = 9 ten thousands

85,000 = 8 ten thousands 5 thousands 84,211

80,000 = 8 ten thousands

There are ​8​ten thousands in ​84,211​. ​1​ more ten thousand is ​9​ ten thousands.

I label the bottom and top tick marks. ​8​ ten thousands ​5​ thousands is halfway between ​8​ ten thousands and ​9​ ten thousands. I label the tick mark that represents halfway between the ten thousands. ​84,211​ is less than ​85,000​. I plot ​84,211​ between ​8 0,000​ and ​85,000​.

Because ​84,211​ is less than ​85,000,​it is less than halfway between ​8 0,000​ and ​ 90,000​. That tells me that 8 ​ 4,211​is closer to ​8 0,000​ than to ​9 0,000​.

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77

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 13

2. Rocky Mountain National Park covers an area of ​265,769​ acres. To the nearest hundred thousand, about how many acres does the park cover?

2​ 65,769 ≈ 300,000​

The park covers about 3 ​ 00,000​ acres.

I can draw a number line to round ​265,769​ to the nearest hundred thousand.

2​ 65,769​ is more than halfway between ​200,000​ and ​300,000​. That means ​265,769​ is closer to ​300,000​ than to ​200,000​.

78

P R ACT I C E PA R T N E R

300,000 = 3 hundred thousands 265,769 250,000 = 2 hundred thousands 5 ten thousands 200,000 = 2 hundred thousands

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 13

REMEMBER 3. Eva walks the perimeter of her backyard. Her backyard is in the shape of a regular pentagon.

She walks a total of ​45​ yards. What is the length of each side of her backyard?

? yd

Each side of her backyard is 9 ​ ​ yards.

I need to find the length of each side of Eva’s backyard.

I know that a pentagon has ​5​sides. I also know that all side lengths in a regular pentagon are equal in length.

So Eva walks ​45​ yards around ​5​sides of equal length.

I can divide to determine the length of each side. ​45 ÷ 5 = 9​

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P R ACT I C E PA R T N E R

79

EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 13

Name

13

Date

Round to the nearest ten thousand. Show your thinking on the number line.

1. 3 ​ 2,144 ≈

​

2. ​508,223 ≈

​

Round to the nearest hundred thousand. Use the number line to show your thinking.

3. ​521,309 ≈

​

4. ​791,547 ≈

​

5. ​​612,338​people visited the Westfield Zoo last year. About how many people visited the zoo?

Round to the nearest ten thousand.

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81

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 13

REMEMBER 6. Mr. Lopez designs a dog kennel in the shape of a regular octagon. He uses 5 ​ 6​feet of fencing around the perimeter of the kennel. What is the length of each side of the kennel?

? ft

82

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 14

Name

14

Date

Round the number to the given place. Show your thinking on the number line.

1. 38,357 a. Nearest thousand

b. Nearest ten thousand

39,000 = 39 thousands

40,000 = 4 ten thousands

38,500 = 38 thousands 5 hundreds 38,357

35,000 = 3 ten thousands 5 thousands

38,000 = 38 thousands

30,000 = 3 ten thousands

​38,357 ≈ ​ 38,000

38,357

​38,357 ≈

40,000

​38,357​is less than ​38,500​, which means it is less than halfway between ​38,000​ and ​39,000​.

​38,357​is greater than ​35,000​, which means it is more than halfway between ​30,000​ and ​4 0,000​.

So ​38,357​is closer to ​38,000​than to ​ 39,000​.

So ​38,357​is closer to ​4 0,000​than to ​ 30,000​.

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83

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 14

Round the number to the given place.

2. 783,455 Nearest hundred thousand

800,000

Nearest ten thousand

780,000

​

Nearest thousand

783,000

​

​783,455​is greater than ​750,000​, which means it is more than halfway between ​7 00,000​ and ​8 00,000​. So it is closer to ​8 00,000​than to ​7 00,000​.

To the nearest hundred thousand, ​783,455 ≈ 800,000​.

I can use similar thinking to round to the nearest ten thousand and nearest thousand.

84

P R ACT I C E PA R T N E R

800,000 783,455 750,000 700,000

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 14

REMEMBER 3. Draw and shade ​2​different rectangles that each have an area of 3 ​ 6​square units. Show how to find the area and perimeter of each rectangle.

Equation to find area: 3 × 12 = 36 ​ Area: ​ 36

​square units

Equation to find perimeter:

(2 × 3)​ + ​(2 × 12)​ = 6 + 24 = 30 Perimeter:

30

units

Equation to find area: Area:

36

4 × 9 = 36 ​

square units

Equation to find perimeter:

(2 × 4)​ + ​(2 × 9)​ = 8 + 18 = 26 Perimeter:

26

units

I can write expressions to represent the side lengths for rectangles with an area of ​36​ square units.

The expressions are ​1 × 36​, ​2 × 18​, ​3 × 12​, ​4 × 9​, and ​6 × 6​.

For the first rectangle, I choose to draw a rectangle with side lengths of ​3​units and ​1 2​ units.

I multiply the width times the length to find the area.

Opposite side lengths of rectangles are equal, so I multiply the width by ​2​and the length by ​2 ​. Then I add the products to find the perimeter. The perimeter is ​30​ units.

For the second rectangle, I choose to draw a rectangle with side lengths of 4 ​ ​units and ​9​ units.

The rectangles have the same number of square units; they are just arranged differently. So the rectangles have the same area, but their perimeters are different.

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P R ACT I C E PA R T N E R

85

EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 14

Name

14

Date

Round the number to the given place. Show your thinking on the number line.

1. ​77,129​ a. Nearest thousand

b. Nearest ten thousand

​77,129 ≈

​77,129 ≈

Round the numbers to the given place.

2. ​81,266​

Nearest hundred thousand ​

3. ​388,205​

Nearest hundred thousand

Nearest ten thousand

Nearest ten thousand

Nearest thousand

Nearest thousand

4. ​58,862​

5. ​526,325​

Nearest hundred thousand

Nearest hundred thousand

Nearest ten thousand

Nearest ten thousand

Nearest thousand

Nearest thousand

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​

​

87

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 14

REMEMBER 6. Draw and shade ​2​different rectangles that each have an area of 2 ​ 0​square units. Show how to find the area and perimeter of each rectangle.

Equation to find area: ​ Area:

​​​ square units

Equation to find perimeter:

​

​ Perimeter:

units

Equation to find area:​ Area:​ ​

​

square units

Equation to find perimeter:

Perimeter:

88

P R ACT I C E

​​units

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 15

Name

Date

15

1. Jayla earns ​5,615​points in Level 3 of a video game. Jayla and Ray estimate the number of points by rounding the number.

Jayla rounds to the nearest thousand, and Ray rounds to the nearest hundred.

Is Jayla’s estimate or Ray’s estimate more accurate? Explain.

Jayla rounds 5,615 to 6,000. Ray rounds 5,615 to 5,600. Jayla’s estimate is 385 more than 5,615.

Ray’s estimate is more accurate because it is only 15 less than 5,615.

I draw a number line to round 5,615 to the nearest thousand.

6,000

5,615 is greater than 5,500, which means it is more than halfway between 5,000 and 6,000.

5,615 5,500

So it is closer to 6,000 than to 5,000.

To the nearest thousand, 5,615 ≈ 6,000.

5,000

Next, I draw a number line to round ​5,615​ to the nearest hundred.

5,700

​ ,615​is less than ​5,650​, which means it 5 is less than halfway between ​5,600​and ​5,700​.

5,650

So it is closer to 5 ​ ,600​than to 5 ​ ,700​.

To the nearest hundred, ​5,615 ≈ 5,600​.

5,615 5,600

I compare the estimates to the actual number of points.

Jayla’s estimate of ​6,000​is 3 ​ 85​points more than the actual number.

Ray’s estimate of ​5,600​is ​1 5​points less than the actual number.

Because Ray’s estimate is closer to the actual number, his estimate is more accurate.

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89

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 15

​ 68​the first week and $ ​ 77​the second week.

2. Zara wants to save $ ​ 250​to buy a guitar. She saves $ Should Zara round to the nearest hundred or to the nearest ten to estimate how much she still needs to save? Explain.

Round to the nearest hundred

6​ 8 ≈ 100​

Round to the nearest ten

1​ 00 + 100 = 200​

7​ 0 + 80 = 150​

​77 ≈ 100​

2​ 50 − 200 = 50​

6​ 8 ≈ 70​

​77 ≈ 80​

​250 − 150 = 100​

Zara should round to the nearest ten so that her estimates are closer to the actual amounts. ​ 200​ If she rounds to the nearest hundred, she will get $ ​ 200​for an estimate of her total savings. $ is much higher than the actual amount she saved, so she might think she only needs to save ​ 100​ more. about $ ​ 50​more when she really needs to save about $

Rounded to the nearest hundred, Zara’s savings are $ ​ 68 ≈ $100​ and ​$77 ≈ $100​.

So she would estimate that she has saved about ​$200​so far.

100 68 50

100 77 50

This means she would still need to save about ​$50​.

0

0

Rounded to the nearest ten, Zara’s savings are $ ​ 68 ≈ $70​ and ​$77 ≈ $80​.

70

80

So she would estimate that she has saved about ​$150​so far.

65

77 75

60

70

This means she would still need to save about ​$100​.

68

The actual amount saved is ​$68 + $77 = $145.​Rounding to the nearest ten results in estimates that are closer to the actual values than rounding to the nearest hundred.

So Zara should round to the nearest ten.

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P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 15

REMEMBER 3. Gabe draws a quadrilateral that has 2 ​ ​pairs of parallel sides, 4 ​ ​sides of equal length, and ​ 4​right angles. Which shape does Gabe draw? Circle all the shapes that can name Gabe’s quadrilateral.

A. Square B. Rectangle C. Trapezoid D. Parallelogram E. Rhombus

I know each shape listed is a quadrilateral. I can think about other attributes of each shape. square • 2 pairs of parallel sides • 4 sides of equal length • 4 right angles

rectangle

trapezoid

• 2 pairs of • At least parallel 1 pair of sides parallel • Opposite sides sides of equal length • 4 right angles

parallelogram

rhombus

• 2 pairs of • 2 pairs of parallel parallel sides sides • Opposite • 4 sides of sides of equal equal length length

Gabe’s quadrilateral has ​2​pairs of parallel sides.

A square, rectangle, parallelogram, and a rhombus always have ​2​pairs of parallel sides. A trapezoid has at least 1​ ​pair of parallel sides, which means it can have 1​ ​or more pairs of parallel sides.

Gabe’s quadrilateral has ​4​sides of equal length.

A square and a rhombus always have 4 sides of equal length. A trapezoid, parallelogram, and rectangle can have 4 sides equal in length.

Gabe’s quadrilateral also has ​4​right angles. A square and a rectangle always have 4 right angles. A trapezoid, parallelogram, and rhombus can have 4 right angles.

Gabe’s quadrilateral is a square. Rectangle, trapezoid, parallelogram, and rhombus also name the shape because all of them can be a square. square • 2 pairs of parallel sides • 4 sides of equal length • 4 right angles

rectangle

trapezoid

• 2 pairs of • At least parallel 1 pair of sides parallel • Opposite sides sides of equal length • 4 right angles

parallelogram

rhombus

• 2 pairs of • 2 pairs of parallel parallel sides sides • Opposite • 4 sides of sides of equal equal length length

That means that square, rectangle, trapezoid, parallelogram, and rhombus can all name Gabe’s quadrilateral.

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P R ACT I C E PA R T N E R

91

EUREKA MATH2

4 ▸ M1 ▸ TC ▸ Lesson 15

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

4. Ivan measures a string that is 5 ​ ​times as long as Gabe’s string. Ivan’s string is 3 ​ 5​inches long.

How long is Gabe’s string?

3​ 5 ÷ 5 = 7​ Gabe’s string is 7 ​ ​inches long.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram with 1​ ​unit to represent the length of Gabe’s string. I label it with a question mark because it is the unknown.

I draw another tape with ​5​units to represent that Ivan’s string is 5 ​ ​times as long as Gabe’s string. Ivan’s string is ​35​inches long, so I label the ​5​units with a total of 3 ​ 5​. ?

Gabe Ivan 35 I need to find the length of Gabe’s string.

I see that I can divide 35 by 5 to find the size of 1 unit.

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P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TC ▸ Lesson 15

Name

Date

15

1. A principal needs to order 1 ​ ,437​T-shirts for students at her school. She rounds to the nearest hundred to estimate the number of T-shirts to order. Will there be enough T-shirts for all the students? Explain.

2. Ivan’s family drives ​2,213​miles on a vacation. Ivan rounds this number to the nearest thousand.

His sister rounds to the nearest hundred. Whose estimate is more accurate? Explain.

3. Liz’s class will win a prize if they sell ​500​magnets. They sell 6 ​ 2​magnets in the first month and ​ 93​in the second month. Liz wants to estimate the number of magnets they still need to sell.

Should she round to the nearest hundred or to the nearest ten? Explain.

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93

4 ▸ M1 ▸ TC ▸ Lesson 15

EUREKA MATH2

REMEMBER 4. Liz draws a quadrilateral that has 2 ​ ​pairs of parallel sides, 4 ​ ​sides of equal length, and no right angles. Which shape does Liz draw? Circle all the shapes that can name Liz’s quadrilateral.

A. Square B. Rectangle C. Rhombus D. Trapezoid E. Parallelogram Use the Read–Draw–Write process to solve the problem.

5. Carla reads 2 ​ ​times as many pages as Casey. Carla reads 1 ​ 8​pages. How many pages does Casey read?

94

P R ACT I C E

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Module 1 Topic D

FAMILY MATH Multi-Digit Whole Number Addition and Subtraction Dear Family,

Your student is learning to add and subtract numbers within 1,000,000 by using the standard algorithm. They begin by using concrete place value disks and drawings on the place value chart. The place value chart helps your student make sense of when they must rename units when adding or subtracting. Your student uses rounding to estimate to check whether their answer is reasonable. They also solve word problems by using the Read–Draw–Write process to practice adding and subtracting. They use tape diagrams to represent and make sense of the problems and write equations with a letter for the unknown. millions

hundred thousands

ten thousands

thousands

2 0 0, 0 0 0 + 5 0, 0 0 0 2 5 0, 0 0 0

hundreds

tens

ones

1 8 2, 4 1 9 + 5 3, 6 7 0 1 1 2 3 6, 0 8 9

The place value chart shows renaming 10 hundreds as 1 thousand and 10 ten thousands as 1 hundred thousand.

Rounding and estimating before adding shows that the answer of 236,089 is reasonable.

Town A has 13,546 residents.

Town B has 2,243 more residents than Town A. Town C has 1,230 fewer residents than Town B. What is the total number of residents in all three towns?

13,546 Town A 2,243 Town B

r ?

Town C 1 5, 7 8 9 – 1, 2 3 0 1 4, 5 5 9

r = 43,894 The total number of residents is 43,894.

Town C ?

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Town B 1 3, 5 4 6 + 2, 2 4 3 1 5, 7 8 9

Total Residents 1 3, 5 4 6 1 5, 7 8 9 + 1 4, 5 5 9 1 1 1 2 4 3, 8 9 4

1,230

95

4 ▸ M1 ▸ TD

EUREKA MATH2

At-Home Activity Large Number Fun Explore adding and subtracting with large numbers related to topics that your student finds interesting. Encourage rounding, estimating, determining reasonableness, and checking subtraction problems with addition. Consider using the following example topics.

96

•

Gather information such as the number of average visitors per year at your student’s favorite amusement parks or other attractions. You can also create your own information such as Adventure Park had 745,691 visitors this year and Discovery Park had 667,345 visitors. Ask your student questions such as, “How many more people visited Adventure Park than Discovery Park this year?”

•

Gather information about the weights of large animals. For example, a crocodile weighs 1,098 pounds, an elephant weighs 10,648 pounds, a shark weighs 2,562 pounds, and a bear weighs 1,332 pounds. Ask your student questions such as, “What is the combined weight of the shark and bear?”

FA M I LY M AT H ▸ Module 1 ▸ Topic D

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 16

Name

16

Date

Add by using the standard algorithm.

1.

+

3,

8

4

7

2,

7

9

2

1

1

3

9

6,

6

I add the ones. ​7 ones + 2 ones = 9 ones​. I write a ​9​in the ones column below the line.

+

3,

8

4

7

2,

7

9

2 9

Then I add the tens. ​4 tens + 9 tens = 13 tens​. I rename ​ 13​tens as ​1​hundred ​3​tens. I write a ​1​on the line in the hundreds column and a ​3​in the tens column below the line.

+

3,

8

4

7

2,

7

9

2

3

9

1

Next, I add the hundreds. ​8 hundreds + 7 hundreds + 1 hundred = 16 hundreds​. I rename 1​ 6​hundreds as ​1​ thousand ​6​hundreds. I write a 1​ ​on the line in the thousands column and a ​6​in the hundreds column below the line.

+

3,

8

4

7

2,

7

9

2

6

3

9

1

1

Last, I add the thousands. 3 ­thousands + 2 thousands + 1 thousand = 6 thousands​. I write a ​6​ in the thousands column below the line.

+

3,

8

4

7

2,

7

9

2

6

3

9

1

6,

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1

97

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 16

2. ​53,492 + 423,973 + 4,310​

4

4

9

2

2

3,

9

7

3

4,

3

1

0

1,

7

7

5

1

8

1

1

ill io n hu s nd r te ed t n th hou ou sa th s ou an nds ds sa hu nd nd s r te eds ns on es

+

3,

m

4

5

First, I write the numbers in vertical form.

I line up the numbers by place value units.

4

5

3,

4

9

2

2

3,

9

7

3

4,

3

1

0

+

Then I add like place value units. I rename a sum when there are ​1 0​or more of a place value unit.

I see there is only one​number in the hundred thousands place to add, so I write the ​4​in the hundred thousands column below the line.

4 + 4

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5

3,

4

9

2

2

3,

9

7

3

4,

3

1

0

7

7

5

1

8

1

1,

1

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 16

Use the Read–Draw–Write process to solve the problem. ​ 8,183.​ 3. Smithfield has a population of 6 ​ 5,225​. Flatwood has a population of 2 What is the total population of the two​cities? ​65,225 + 28,183 = 93,408​ The total population of the two cities is 9 ​ 3,408.​

I read the problem. I read again.

As I r­ eread, I think about what I can draw.

I draw and label parts in the tape diagram to represent the populations of Smithfield and Flatwood.

I do not know the total population of the two​cities. I can use the letter p ​ ​to represent the total population.

65,225

28,183 p

I can write an equation to represent the problem, 6​ 5,225 + 28,183 = p​.

I can add by using the standard algorithm.

65, 2 2 5 2 8,1 8 3

+ 1

1

93,4 0 8

p = 93,408

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P R ACT I C E PA R T N E R

99

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 16

REMEMBER 4. Use the picture to write a word problem that can be represented by the expression ​2 × 7.​

Carla picks 2 ​ ​rows of carrots. Each row has 7 ​ ​carrots. How many carrots does Carla pick?

I look at the picture.

I see 2​ ​rows of carrots. Each row has 7​ ​ carrots.

7

7 The expression ​2 × 7​represents how to find the total number of ­carrots in the picture.

I can find how many carrots there are in all. I write a word problem that asks about the total number of carrots.

100

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 16

Name

16

Date

Add by using the standard algorithm.

1.

+

4,

7

1

5

3,

8

2

6

4. ​409,416 + 62,762​

2.

+

8,

1

3

4

2,

5

3

7

5. ​225 + 364 + 137​

3.

1 +

3,

4

5

9

2,

4

8

3

6. ​4,231 + 3,598 + 1,824​

+ +

+

Use the Read–Draw–Write process to solve the problem. ​ ,568​points this season​.

7. A basketball team scored ​5,104​points last season and 5 How many total points did the team score in the t​ wo years?

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101

4 ▸ M1 ▸ TD ▸ Lesson 16

EUREKA MATH2

REMEMBER 8. Use the picture to write a word problem that can be represented by the expression ​4 × 7​.

102

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 17

Name

17

Date

Use the Read–Draw–Write process to solve the problem. ​ 60​miles longer than the 1. The Appalachian Trail is ​2,193​miles long. The Pacific Crest Trail is 4 Appalachian Trail. The Continental Divide Trail is 3 ​ ,100​miles long. What is the total length of the three trails? Is your answer reasonable? Explain.

2​ ,200 + ​(2,200 + 500)​ + 3,100 = 8,000​ 2​ ,193 + ​(2,193 + 460)​ + 3,100 = 7,946​ ​ ,946​ miles.

The total length of the ​three t​ rails is 7 Yes, my answer is reasonable. I estimated the answer by rounding each number to the nearest hundred before adding. My estimate was ​8,000​miles. When I added the actual amounts, ​ ,000.​ my answer was 7 ​ ,946​miles. I know that ​7,946​is very close to 8

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent the problem. I know the Appalachian Trail is 2​ ,193​miles long. I know the Pacific Crest Trail is ​460​miles longer than the Appalachian Trail. I know the Continental Divide Trail is ​3,100​miles long. I do not know the total length of all t ​ hree trails.

I can use the letter ​d​to represent the total length of all t ​ hree trails.

Appalachian Trail

2,193

Pacific Crest Trail

2,193

Continental Divide Trail

3,100

460

d

I am trying to find the total length of the t ​ hree trails. I can write an equation to represent the problem, 2​ ,193 + ​(2,193 + 460)​ + 3,100 = d​.

Before I solve the problem, I can estimate the answer by rounding each number to the nearest hundred. ​2,200 + ​(2,200 + 500)​ + 3,100 = 8,000​. My estimate is ​8,000​ miles.

When I add the actual amounts, my answer is ​7,946​ miles. ​7,946​is very close to 8 ​ ,000​, so my answer is reasonable.

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103

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 17

REMEMBER 2. Write the pattern and complete the table.

Pattern: ​ Multiply the input by 9 ​ Input

​2​

​3​

​5​

​7​

​8​

1​ 0​

Output

​18​

​27​

​45​

​63​

​72​

​90​

I look for a pattern in the table.

When the input number is 2​ ​, the output number is 1​ 8​. I know that 2​ × 9 = 18​.

I think the pattern is multiply by ​9​. I can check other input and output numbers to see if I am correct.

I know that ​5 × 9 = 45​.

I know that ​8 × 9 = 72​.

The pattern is multiply by ​9​ .

I can multiply each input number by ​9​to complete the table.

3. Miss Diaz paints _ ​​​ ​1 ​​​​of a wall.

2

Partition and shade the rectangle to show how much of the wall Miss Diaz paints.

1 2

1 2

I know Miss Diaz paints ​ _​1 ​​of a 2 wall. The fractional unit is halves, so I draw 1​ ​line to partition the rectangle into 2​ ​equal parts.

I shade ​1​part, or ​1​half, to show how much of the wall Miss Diaz paints.

104

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 17

Name

Date

17

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

1. An apple orchard has Honeycrisp trees and McIntosh trees. The orchard has 1 ​ ,603​ Honeycrisp trees. It has 3 ​ 27​more McIntosh trees than Honeycrisp trees. a. About how many apple trees does the orchard have?

b. Exactly how many apple trees does the orchard have?

c. Is your answer reasonable? Compare your estimate from part (a) to your answer from part (b).

Explain your reasoning.

​ 1,527​more on Saturday than on Friday.

2. A restaurant made $ ​ 5,987​on Friday. It made $ On Sunday, the restaurant made $ ​ 2,641​. How much money did the restaurant make in the ​three ​ days? Is your answer reasonable? Explain.

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105

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 17

REMEMBER 3. Write the pattern and complete the table. ​

Pattern: Input

​2​

Output

​10​

​3​

​5​ ​25​

​7​

​8​

​10​

​40​

4. Mr. Endo decorates _ ​​ 1 ​of a bulletin board with blue paper.

8

Partition and shade the rectangle to show how much of the bulletin board is decorated with blue paper.

106

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 18

Name

Date

18

Subtract by using the standard algorithm.

1.

–

4

12

5,

2

8

3

2,

7

4

1

2,

5

4

2

I look at the numbers in each place value to see whether I am ready to subtract.

I start with the ones place. I am ready to subtract the ones because 3 ​ ​ones is more than ​1​ one.

I am also ready to subtract the tens because ​8​tens is more than ​4​ tens.

I am not ready to subtract the hundreds because 2​ ​hundreds is not more than ​7​hundreds. I need to rename ​1​thousand as ​1 0​hundreds. Now there are 1​ 2​hundreds because ​ 2 hundreds + 10 hundreds = ​12​ hundreds​.

I am ready to subtract the hundreds because ​1 2​hundreds is more than ​7​ hundreds.

I am also ready to subtract the thousands because ​4​thousands is more than ​2​ thousands.

Now I am ready to subtract like place value units. ​3 ones - 1 one = 2 ones​ ​8 tens - 4 tens = 4 tens​ ​1 2 hundreds - 7 hundreds = 5 hundreds​ ​4 thousands - 2 thousands = 2 thousands​ I record the subtraction below each place value unit.

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107

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 18

REMEMBER 2. Amy eats ​_ ​​​ 1 ​​​​of a small cake. Pablo eats _​​ ​​1 ​​​​of a large cake.

4

8

Pablo’s Cake

Amy’s Cake

a. Shade the circles to represent the amount of cake that Amy eats and the amount of cake Pablo eats.

​​​ ​1 ​​​​is always greater b. Pablo says that his piece of cake is bigger than Amy’s so that means that _ than ​_ ​​​ 1 ​​​ ​. Do you agree with Pablo? Why?

8

4

No, I do not agree with Pablo because the cakes are not the same size. You have to start with the same-size wholes when comparing fractions.

I shade ​1​equal part in the circle that represents Amy’s cake to show ​ _ ​​​1 ​​​ ​.

4

I shade ​1​equal part in the circle that represents Pablo’s cake to show _ ​​​​ 1 ​​​ ​.

8

I see that Pablo’s piece of cake is bigger. However, I know that when I compare fractions, the wholes must be the same size.

108

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 18

3. Write an equation to represent that 3 ​ 2​is 4 ​ ​times as much as 8 ​ ​. ​32 = 4 × 8​

I think about the statement 3 ​ 2​ is ​4​ times as much as ​8​.

I can draw a tape diagram to represent 1​ ​unit of 8 ​ .​ Then I draw ​4​units of 8 ​ ​because the statement is ​4​ times as much as ​8​.

I know the total of ​4​units of ​8​is 3 ​ 2​, so I label the total 3 ​ 2​.

8 8

8

8

8

32 I write an equation to represent the tape diagram.

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P R ACT I C E PA R T N E R

109

EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 18

Name

18

Date

Subtract by using the standard algorithm.

1.

3.

2.

–

9,

7

4

5

6,

5

2

1

–

7,

8

1

4

2,

4

3

4

5. 22,679 − 17,452

4.

8, –

6

5

3

4

6

2

–

–

1

6,

7

5

3

1

2,

4

3

6

6. 634,513 − 394,202

–

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

7. A florist sells 17,926 flowers. 7,583 of these flowers are roses. The rest of the flowers are lilies.

How many lilies are sold?

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111

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 18

REMEMBER 8. Ivan eats ​​ _1 ​​ of a small pie. Oka eats _ ​​ 1 ​​ of a large pie.

3

6

Oka’s Pie

Ivan’s Pie

a. Shade the circles to represent the amount of pie that Ivan eats and the amount of pie Oka eats.

b. Oka says that her piece of pie is bigger than Ivan’s so that means that _ ​​ 1 ​​ is always greater 6 than ​​ _1 ​​ . Do you agree with Oka? Why? 3

9. Write an equation to represent that 27 is 3 times as much as 9.

112

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 19

Name

Date

19

Subtract by using the standard algorithm.

1.

I look at the numbers in each place value to see whether I am ready to subtract.

10

–

I am ready to subtract the ones because ​3​ones is more than ​1​ one.

6

0

10

4

7,

1

0

3

2

0,

4

9

1

2

6,

6

1

2

I am not ready to subtract the tens because 0​tens is not more than ​9​tens. I need to ­rename​ 1​hundred as ​1 0​tens. Now there are ​1 0​tens because ​0 tens + 10 tens = 10 tens​.

I am ready to subtract the tens because ​1 0​tens is more than ​9​ tens.

I notice that I am also not ready to subtract the hundreds. I need to rename ​1​thousand as ​1 0​hundreds. Now there are ​1 0​hundreds because ​ 0 hundreds + 10 hundreds = 10 hundreds​.

I am ready to subtract the hundreds because ​ 10​hundreds is more than ​4​hundreds.

I am also ready to subtract the thousands and ten thousands.

Now I am ready to subtract like place value units. ​3 ones − 1 one = 2 ones​ ​1 0 tens − 9 tens = 1 ten​ ​1 0 hundreds − 4 hundreds = 6 hundreds​ ​6 thousands − 0 thousands = 6 thousands​ ​ ten thousands − 2 ten thousands = 4 2 ten thousands​ I record the subtraction below each place value unit.

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113

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 19

2. Use the Read–Draw–Write process to solve the problem. ​ 4,028​miles. He flew from New York City Mr. Davis is a pilot. He flew a total distance of 1 to London and then from London to Sydney. The distance from New York City to London is ​ 3,470​ miles.

How far did Mr. Davis fly from London to Sydney?

1​ 4,028 − 3,470 = 10,558​ Mr. Davis flew ​10,558​miles from London to Sydney.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram and label ​14,028​to represent the total distance Mr. Davis flew. I partition a part and label ​ 3,470​to represent the distance from New York City to London. I do not know the distance from London to Sydney.

I can use the letter ​d​to represent this amount.

3,470

d 14,028

I can write an equation to represent the problem. ​14,028 − 3,470 = d​ I rewrite the problem in vertical form and subtract.

9 3 1012

1 4,028 – 3,47 0 1 0,558 ​d = 10,558

114

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 19

REMEMBER 3. Partition the rectangle into 2 ​ ​equal parts. Shade 1 ​ ​ part.

What fraction of the rectangle is shaded?

1 _ ​​ ​​ 2

I draw 1​​line to partition the rectangle into 2​ ​equal parts.

Then I shade 1​ ​ part.

There are 2​ ​equal parts, which means the fractional unit is halves. One half is shaded, so I can write the fraction _​​​​ 1 ​​ ​.

2

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

1​ 8 = 3 × 6​

I can think about ​1 8 = 3 × 6​ as ​3​times as much as ​6​ or ​6​times as much as 3 ​​ .

a. Draw ​2​tape diagrams to represent the equation.

6

3

6

6

6

3

18 b. Complete both statements.

​18 is ​

3

​times as much as 6 ​ .​

18​​ is ​

6

times as much as 3 ​ .​

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3

3

3 18

3

3

To represent 3 ​ ​times as much as ​6​, I draw 1​ ​unit of 6​ ​. Then I draw 3 ​ ​units of ​6​ because ​ 18​is ​3​times as much as 6 ​ ​.

I label the product ​1 8​.

To represent 6​ ​times as much as ​3​, I draw 1​ ​unit of ​3​. Then I draw 6​ ​units of 3 ​ ​ because ​ 18​is ​6​times as much as ​3​.

I label the product ​1 8​.

P R ACT I C E PA R T N E R

115

EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 19

Name

19

Date

Subtract by using the standard algorithm.

1.

3. 714,918 − 391,986

2.

–

5,

6

0

5

3,

8

3

2

–

1

6,

2

7

4

1

3,

5

8

8

–

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

4. Pablo has ​4,620​football and baseball cards in total. He has​ 1,486​football cards.

How many baseball cards does Pablo have?

5. The sum of two numbers is ​17,426​. One number is 8 ​ ,731​. What is the other number?

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117

4 ▸ M1 ▸ TD ▸ Lesson 19

EUREKA MATH2

REMEMBER 6. Partition the rectangle into 4 ​ ​equal parts. Shade 1 ​ ​ part.

What fraction of the rectangle is shaded?

7. Use the equation to complete parts (a) and (b). ​28 = 7 × 4​ a. Draw ​2​tape diagrams to represent the equation.

b. Complete both statements.

118

​28​is ​

times as much as 7 ​ ​.

2​ 8​ is

​​times as much as ​4​.

P R ACT I C E

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 20

Name

Date

20

Subtract by using the standard algorithm.

1. 6 ​ 50,000 − 31,387​

6 – 6

9

9

9

4

10

10

10

10

5

0,

0

0

0

3

1,

3

8

7

1

8,

6

1

3

I can rewrite the problem in vertical form.

Then I get ready to subtract by renaming place value units when I do not have enough to subtract.

I rename ​650,000​as ​6​hundred thousands, ​4​ten thousands, 9 ​ ​ thousands, ​9​ hundreds, ​9​tens, and ​1 0​ ones.

Now I am ready to subtract like place value units. ​1 0 ones − 7 ones = 3 ones​ ​9 tens − 8 tens = 1 ten​ ​9 hundreds − 3 hundreds = 6 hundreds​ ​9 thousands − 1 thousand = 8 thousands​ ​4 ten thousands − 3 ten thousands = 1 ten thousand​ ​ hundred thousands − 0 hundred thousands = 6 6 hundred thousands​ I record the subtraction below each place value unit.

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119

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 20

Use the Read–Draw–Write process to solve the problem. ​ 60,430​gallons of water. It currently has 4 2. An Olympic-size swimming pool can hold 6 ​ 18,795​ gallons of water in it. How many more gallons of water are needed to fill the pool? ​660,430 − 418,795 = 241,635​ Carla needs 2 ​ 41,635​more gallons of water to fill the pool.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram and label the total as 6​ 60,430 to represent the amount of water the pool can hold.

I partition a part and label it as ​418,795​to represent the amount of water the pool currently has in it. I do not know how many more gallons of water are needed to fill the pool. I can use the letter g​to represent this amount.

418,795

g

660,430 I can write an equation to represent the problem. ​6 60,430 – 418,795 = g​ I rewrite the problem in vertical form and subtract.

9 1312 5 10 3 2 10

6 6 0,430 – 4 1 8,7 95 2 4 1, 635

​g = 241,635

120

P R ACT I C E PA R T N E R

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 20

REMEMBER 3. Use an inch ruler to draw a quadrilateral so that exactly 1 ​ ​pair of sides has the same length.

Label the equal side lengths.

Sample:

3 in

3 in

I know that a quadrilateral has ​4​ sides.

I start by using my inch ruler to draw the top side. I choose to make the top side 3 inches long.

2

3

1

Then I use my ruler to draw the left side.

I also make the left side 3 inches long.

1

2 3

Next, I use my ruler to make sure the other 2 sides of my quadrilateral are different lengths and neither side is 3 inches long.

Last, I label the sides that have the same length.

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3 in

3 in

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121

EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 20

Name

20

Date

Subtract by using the standard algorithm.

1.

2.

1 –

1

4,

4

3

6

7

5,

7

8

7

2 –

5

2,

2

1

7

8

3,

8

4

6

3. 900,000 − 886,071

–

​​Use the Read–Draw–Write process to solve each problem. ​ 82,149​plain bagels.

4. A bagel shop sells 1 ​ 76,663​blueberry bagels and 1 How many more plain bagels than blueberry bagels does the shop sell?

5. Liz has driven her car ​71,435​miles. She needs to have her car serviced at 1 ​ 00,000​ miles.

How many more miles can Liz drive before her car needs to be serviced?

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123

4 ▸ M1 ▸ TD ▸ Lesson 20

EUREKA MATH2

REMEMBER 6. Use an inch ruler to draw a quadrilateral so that all sides have different lengths. Label each side.

124

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 21

Name

21

Date

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

1. A music festival had 2 ​ 2,485​attendees on Friday. It had 2 ​ 8,327​attendees on Saturday. After Sunday, the music festival had a total of 7 ​ 2,558​ attendees. a. Estimate the number of attendees the music festival had on Sunday. Round each value to the nearest thousand. ​22,000 + 28,000 = 50,000​ ​73,000 − 50,000 = 23,000 The music festival had about ​23,000​attendees on Sunday. b. Find the number of attendees the music festival had on Sunday. ​22,485 + 28,327 = 50,812​ ​72,558 − 50,812 = 21,746 The music festival had ​21,746​attendees on Sunday. c. Is your answer reasonable? Use your estimate from part (a) to explain.

Yes, my answer of ​21,746​attendees is reasonable.​21,746​attendees rounded to the nearest ​ 3,000​. thousand is 2 ​ 2,000​, which is close to my estimate of 2

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram and partition it into three parts, one part for each day of the festival. I label the total as 72,558 because that is the total number of attendees. I label one part as 22,485 to represent Friday’s attendees. I label another part as 28,327 to represent Saturday’s attendees.

I do not know the number of attendees on Sunday. I can use the letter ​a​to r­ epresent this amount.

22,485 28,327 72,558 Copyright © Great Minds PBC

a

I need to find the number of attendees on Sunday.

My tape diagram helps me see that I need to add the numbers of attendees on Friday and Saturday.

Then I can subtract that total from ​72,558​to find the number of attendees on Sunday.

I round each value to the nearest thousand.

2​ 2,485 ≈ 22,000​ ​28,327 ≈ 28,000​ ​7 2,558 ≈ 73,000​

My estimate for a is ​23,000​.

The actual answer for ​a​is ​2 1,746​.

The actual amount is close to my estimate of 2​ 3,000​ attendees.

125

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 21

2. Aberdeen has a population of 2 ​ 93,097​. It has 5 ​ 9,812​more people than Monroe. What is the total population of the two cities? Make an estimate before finding the answer. Is your answer reasonable? Explain. ​290,000 − 60,000 = 230,000​

2​ 90,000 + 230,000 = 520,000​ 2​ 93,097 − 59,812 = 233,285​ 2​ 93,097 + 233,285 = 526,382​ The total population of both cities is ​526,382​. The answer is reasonable because my estimate is ​ 520,000​, which is close to 5​ 26,382​.

I read the problem. I read again.

I need to find the total population of the two cities.

As I reread, I think about what I can draw.

My tape diagram helps me see that I need to subtract 5 ​ 9,812​ from ​293,097​to find the population of Monroe. Then I can add to find the total population of the 2​ ​ cities.

I draw a tape diagram. I draw and label one tape as 293,097 to represent the population of Aberdeen. I draw a shorter tape to represent the population of Monroe. I label the difference between the two cities as ​59,812​.

I round each value to the nearest ten ­thousand. ​293,097 ≈ 290,000​ ​59,812 ≈ 60,000​ My estimate for ​p​is ​520,000​.

The actual answer for ​p​is ​526,382​.

I do not know the population of Monroe. I also do not know the ­total population of the two cities. I use the letter ​p​ to represent this amount.

Aberdeen

The actual total population is ​526,382​ people, which is close to my estimate of 5 ​ 20,000​.

293,097 p

Monroe

?

59,812

126

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 21

REMEMBER 3. 5,572 ​The value of the underlined 5 ​ ​ is

10

​times as much as the value of the circled 5​ .​

I can use a place value chart to compare the values of the d ­ igits. ten thousands

thousands

hundreds

tens

ones

× 10

The underlined 5 ​ ​is in the thousands place. It has a value of ​5,000.​ The circled ​5​is in the hundreds place. It has a value of 5 ​ 00​. ​5​thousands is 1​ 0​times as much as 5 ​ ​ hundreds. ​5,000 = 10 × 500

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P R ACT I C E PA R T N E R

127

EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 21

Name

Date

21

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

1. A book company sold 3 ​ 42,380​copies of a book in the first week. The company sold 3 ​ 61,419​ ​ 23,468​copies of the book. copies in the second week. After 3 ​ ​weeks, the book company had sold 9 a. Estimate the number of copies of the book the company sold in the third week. Round each value to the nearest ten thousand.

b. Find the number of copies of the book the company sold in the third week.

c. Is your answer reasonable? Use your estimate from part (a) to explain.

​ 8,654​more seats than a baseball stadium. How 2. A soccer stadium has ​93,810​seats. It has 2 many total seats do the baseball and soccer stadiums have? Make an estimate before finding the answer. Is your answer reasonable? Explain.

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129

EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 21

REMEMBER 3. ​2, ​9 ​9 3 ​ The value of the underlined 9 ​ ​ is

130

P R ACT I C E

​​times as much as the value of the circled 9 ​ ​.

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 22

Name

22

Date

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

1. A book company has 1 ​ 2,532​mystery books.

It has ​1,982​fewer fantasy books than mystery books.

It has ​1,432​more science fiction books than mystery books.

How many total mystery, fantasy, and science fiction books does the book company have? ​12,532 − 1,982 = 10,550​ ​12,532 + 1,432 = 13,964​ ​12,532 + 10,550 + 13,964 = 37,046​ The book company has ​37,046​ total mystery, fantasy, and science fiction books.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram. I draw and label one tape as 12,532 to represent the mystery books.

Mystery

12,532

Fantasy

?

c 1,982

Science Fiction

I draw a second tape that is shorter than the mystery books to represent the fantasy books and label the difference 1,982.

12,532

1,432

?

I draw a third tape that is longer than the mystery books to represent the science ­fiction books and label the difference 1,432.

I need to find the total number of books the book company has.

I can use the letter ​c​ to represent the unknown total number of books.

First, I subtract ​1 ,982​from ​1 2,532​to find the number of fantasy books. It is ​1 0,550​.

Next, I add ​1 2,532​and ​1 ,432​to find the number of science fiction books. It is ​1 3,964​.

Last, I add the number of mystery, fantasy, and science fiction books together to find ​c​.

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4 ▸ M1 ▸ TD ▸ Lesson 22

REMEMBER 2. Compare the numbers by using > ​ ​, ​=​, or < ​ ​. Explain how you know. ​700,000 + 20,000 + 1,000 + 300 + 4

>

​ 718,529 ​

​ ​hundred thousands.

I write the first number in standard form, 7 ​ 21,304​. Both numbers have 7 The first number has 2 ​ ​in the ten thousands place. The second number has ​ 1​in the ten thousands place. I know that 2​ ​ten thousands is greater than 1​ ​ten thousand, so ​ 721,304 > 718,529​.

I write the first number in standard form, ​7 21,304​.

I can use a place value chart to record ​7 21,304​and ​7 18,529​. hundred ten thousands hundreds thousands thousands

tens

ones

7

2

1

3

0

4

7

1

8

5

2

9

Both numbers have 7​ ​hundred thousands, so I look at the unit to the right, ten thousands. ​7 21,304​has a ​2​in the ten thousands place. ​7 18,529​has a 1​ ​in the ten thousands place. ​2​ten thousands, or 2​ 0,000​, is greater than ​1​ten thousand, or ​1 0,000​.

So ​7 21,304 > 718,529​.

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EUREKA MATH2 4 ▸ M1 ▸ TD ▸ Lesson 22

Name

Date

22

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

1. Mia is an entomologist. She records the number of ants, beetles, and termites in part of a forest.

She records 1 ​ 2,861​ ants.

She records ​4,859​fewer beetles than ants.

She records ​5,589​fewer termites than beetles.

How many total insects does Mia record?

2. The Maplewood School District has ​6,705​first grade students and 6​ ,441​second grade students.

The school district has 1 ​ ,304​more third graders than first graders.

It has​ 1,577​more fourth graders than second graders.

What is the total number of first through fourth graders in the district?

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EUREKA MATH2

4 ▸ M1 ▸ TD ▸ Lesson 22

REMEMBER 3. Compare the numbers by using > ​ ,​ ​=​, or < ​ ​. Explain how you know. ​300,000 + 10,000 + 400 + 20 + 5 ​

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309,887 ​

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Module 1 Topic E

FAMILY MATH Metric Measurement Conversion Tables Dear Family,

Key Terms

Your student is learning to convert from larger metric units to convert smaller metric units. They work with units that measure length kilometer (centimeters, meters, and kilometers), mass (grams and kilograms), and liquid volume (milliliters and liters). Measurements are mixed units sometimes given as mixed units, such as 1 kilometer 300 meters.

Mixed units have more than 1 unit. For example, the number 1,300 can be written with mixed units as 1 thousand 3 hundreds. Your student uses what they know about whole number place value units to rename mixed measurement units. Then they add and subtract measurements to solve word problems.

(1 km) 1,000 m

100 m

10 m

1m

× 1,000

Kilometers

Meters

1

1,000

2

2,000

3

3,000

4

4,000

The relationship between

1 kilometer and 1,000 meters 1 kilometer is 1,000 times as long as 1 meter. is used to convert 2, 3, and 1 km = 1,000 × 1 m 2,250 mL + 1 4Lkilometers 750 mL to meters.

1 kilometer = 1,000 meters 1 L 750 mL = 1,750 mL

Metric units have a similar relationship to place value units.

2,250 mL + 1 L 750 mL 1 L 750 mL = 1,750 mL

2,250 + 1,750 1 1 4,000 Mrs. Smith has 4,000 mL. 2,250 mL

1 L 750 mL

2,250 + 1,750 1 1 4,000 Mrs. Smith has 4,000 mL.

d

11 LL750 750mL mLis a mixed measurement unit. Converting to milliliters before adding is one strategy for adding mixed measurement units.

2,250 mL

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4 ▸ M1 ▸ TE

EUREKA MATH2

At-Home Activities Metric Units Use real-world examples to practice converting metric units. For example, think of a familiar route, such as the distance from home to school. Find the distance of that route in whole number kilometers. If you don’t know the distance in kilometers then estimate. 1 kilometer is about the 6 ​​miles. Then have your student convert kilometers to meters and centimeters. same as ​​ __ 10

How Much Taller?

Help your student practice subtracting mixed units by measuring the heights of members of your family. Use a meter stick or a tape measure with metric units to measure in meters and centimeters. Another option is to use an online conversion tool to convert known heights in feet and inches into meters and centimeters. Then have your student use subtraction to see how much taller one family member is than another.

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FA M I LY M AT H ▸ Module 1 ▸ Topic E

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EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 23

Name

Complete the conversion table.

1.

23

Date

Kilometers

Meters

​9​

​9,000​

A kilometer (​km​) is a unit for measuring distance or length.

I know there are ​1 ,000​ meters in ​1​kilometer.

(1 km) 100 m 1,000 m

10 m

1m

× 1,000 I know that ​1​ kilometer is ​1 ,000​ times as long as ​1​ meter.

I can multiply the number of kilometers by ​1 ,000​ to find the equivalent number of meters. ​9 × 1,000 m = 9,000 m​ There are ​9,000​ meters in ​9​kilometers.

Convert.

2. ​ 17,086

m = 17 km 86 m​

Convert means to express a measurement in terms of a different, related measurement unit.

I look at the measurement that is given, 1​7 km 86 m​. This is a mixed unit because it has more than ​1​unit. It has units of kilometers and meters.

I can multiply the number of kilometers by ​1 ,000​ to convert to meters. ​17 × 1,000 m = 17,000 m​ ​17​ kilometers is ​17,000​ meters. ​8 6​ more meters is ​17,086​ meters. ​17,000 m + 86 m = 17,086 m​

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EUREKA MATH2

4 ▸ M1 ▸ TE ▸ Lesson 23

Subtract.

I can rename both measurements as centimeters because when they are written in mixed units, there are not enough centimeters in the first number to subtract ​7 6 cm​. To convert meters to centimeters, I multiply the number of meters by ​1 00​.

3. 9 ​ m 63 cm − 5 m 76 cm = 387 cm ​

​9 m 63 cm = 900 cm + 63 cm = 963 cm​ ​5 m 76 cm = 500 cm + 76 cm = 576 cm​ Now I subtract to find the answer. ​963 cm − 576 cm = 387 cm​

15 8 5 13

963 - 576 387

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

4. Ray kicks a field goal that is 1 ​ 6​meters ​45​centimeters long. Casey kicks a field goal that is ​ 21​meters 6 ​ 7​centimeters long. What is the total length of both field goals? ​16 m 45 cm + 21 m 67 cm = 3,812 cm​ The total length of both field goals is 3 ​ ,812​ centimeters.

I read the problem. I read again.

As I reread, I think about what I can draw.

16 m 45 cm 21 m 67 cm

I draw a tape diagram. I partition the d tape diagram into two parts. One part represents the length Ray kicks. The other part represents the length Casey kicks. I make Casey’s part longer because he kicked farther. I label each part.

I use the letter d to represent the total length, which is unknown.

I see that I can add the two lengths together to find the total length of both field goals.

The lengths are in mixed units. I rename both measurements as centimeters and then add.

16 m 45 cm = 1,645 cm 21 m 67 cm = 2,167 cm So d = 3,812.

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1, 6 4 5 + 2,11 167 3,8 1 2 Copyright © Great Minds PBC

EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 23

REMEMBER 5. Measure the length of each pencil to the nearest quarter inch. Then use the data to complete the line plot.

Pencil Lengths Pencil Lengths

0 0

1 4 1 4

1 2 1 2

× × × ×

× × × ×

×

3 4 3 4

1

14

1

× 1

× × × × × × 1

3

12

14

1 1 3 14 12 14 Length (inches)

2 2

1

1

24

3

22

1 24

24

1 22

3 24

3 3

Length (inches)

I use a ruler to measure the length of each pencil to the nearest quarter inch.

I line up one end of the pencil with the edge of the ruler because it represents 0 inches. The ruler shows tick marks by fourths, or quarter inches.

1

2

3

4

5

6

The other end of the pencil lines up with the mark for 1 ​​ __1 ​​ inches on the ruler.

2

The length of this pencil is 1 ​​ __1 ​​ inches. I draw an X above 1 ​​ __1 ​​ on the line plot.

2

2

I measure the rest of the pencils. For each length, I make an X above the same​ number on the line plot.

There are 8 pencils, so there are 8 Xs on my line plot.

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139

EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 23

Name

23

Date

Complete the conversion tables.

1.

Meters

2.

Centimeters

Kilometers

​4​

​3​

​7​

6​ ​

Meters

Convert.

3. ​

cm = 235 m​

4. 8 ​ km 205 m =

m​

Add or subtract.

5. 6 ​ m 42 cm − 18 cm = 6. ​8 m 72 cm + 2 m 43 cm =

​ ​

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

7. There are two rock walls to choose from at a park. Ray climbs the wall that is 4 ​ ​ meters ​ 26​centimeters tall. Ivan climbs the wall that is 3​ 35​centimeters tall. How much taller is Ray’s wall than Ivan’s wall?

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141

EUREKA MATH2

4 ▸ M1 ▸ TE ▸ Lesson 23

REMEMBER 8. Cut out the ruler. Measure the length of each fish to the nearest quarter inch. Then use the data to complete the line plot.

Fish Lengths

0

1 4

1 2

3 4

1

1

14

1

12

3

14

2

1

24

1

22

3

24

3

Length (inches)

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EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 23

inch

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1

2

3

4

5

6

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EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 24

Name

24

Date

Complete the conversion tables.

1.

Kilograms

Grams

6

​6,000​

2.

Liters

Milliliters

2

​2,000​

I know ​1​kilogram is 1​ ,000​times as heavy as ​1​ gram.

I know ​1​ liter is ​1 ,000​times as much as ​1​ milliliter.

I can multiply the number of kilograms by 1​ ,000​to find the equivalent number of grams.

I can multiply the number of liters by ​1 ,000​to find the equivalent number of milliliters.

​6 × 1,000 g = 6,000 g​

​2 × 1,000 mL = 2,000 mL​

There are ​6,000​grams in ​6​ kilograms.

There are ​2,000​milliliters in ​2​ liters.

Convert.

3. ​ 63,213

g = 63 kg 213 g​

I know that ​1​ kilogram is equal to ​1 ,000​ grams.

I can multiply the number of kilograms by ​ 1,000​to convert to grams. ​63 × 1,000 g = 63,000 g​ ​2 13​ more grams is ​63,213​ grams. ​63,000 g + 213 g = 63,213 g​

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145

EUREKA MATH2

4 ▸ M1 ▸ TE ▸ Lesson 24

Subtract.

4. 9 ​ L 421 mL − 3 L 410 mL = 6 L 11 mL ​

I can subtract like units because there are enough milliliters in the first number to subtract ​410​ milliliters. ​9 L − 3 L = 6 L​ ​421 mL − 410 mL = 11 mL​ The answer is ​6 L 11 mL​.

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

5. Mia has a brown horse and a white horse. The brown horse eats 4​ 7 kg 456 g​of hay each week. The white horse eats 3​ 3 kg 743 g​ of hay each week. How much total hay do the horses eat each week? ​47 kg 456 g = 47,456 g​ ​33 kg 743 g = 33,743 g​ ​47,456 g + 33,743 g = 81,199 g ​ The horses eat a total of 8 ​ 1,199 ​grams of hay each week.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram. I partition the tape diagram into two parts. One part is longer than the other and represents the amount of hay the brown horse eats. The other part represents the amount of hay the white horse eats. I label each part.

I use the letter h to represent the total amount both horses eat, which is what I need to find.

47 kg 456 g

33 kg 743 g

I see that I can add the two amounts of hay together.

The weights are in mixed units. I can rename both weights as grams and then add. ​47 kg 456 g = 47,456 g​ ​33 kg 743 g = 33,743 g​ So ​h = 81,199​.

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h

4 7,4 5 6 + 31 3,1 7 43 8 1, 1 9 9 Copyright © Great Minds PBC

EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 24

REMEMBER 6. Partition the interval from 0 ​ ​to 1 ​ ​into halves. Plot the fraction on the number line.

1_ ​​ 2

0 2

1 2

2 2

0

1

To partition the interval from ​0​ to ​1​ into halves, I know I need ​2​ equal parts. I draw ​1​ tick mark evenly spaced between ​0​ and ​1​. Now the interval from ​0​ to ​1​ is partitioned into ​2​ equal parts, or halves.

I count by halves from ​0​ halves to ​1​ half. I plot __​​ 1 ​​ on the number line.

2

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

7. Gabe has a page of 4 ​ 0​stickers in rows.

There are ​5​stickers in each row.

How many rows of stickers are there? ​40 ÷ 5 = 8​ There are 8 ​ ​rows of stickers.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram and label ​4 0​ to represent the total number of stickers.

I know there are ​5​stickers in each row.

I draw one part and label it 5. I do not know how many rows of ​5​ stickers there are. I label the unknown.

40 5

...

? rows I see that I can divide to find the number of rows.

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P R ACT I C E PA R T N E R

147

EUREKA MATH2 4 ▸ M1 ▸ TE ▸ Lesson 24

Name

24

Date

Complete the conversion tables.

1.

Kilograms

2.

Grams

Liters

4

6

​17​

​13​

Milliliters

Convert.

3. ​51 kg 128 g =

g​

4. ​8 L 16 mL =

mL​

Add or subtract.

5. 9 ​ L 421 mL − 3 L 410 mL =

​

6. ​14 kg 641 g + 3 kg 407 g =

​

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

7. A baseball team drinks 1 ​ 8 L 932 mL ​of sports drink at their game. A football team drinks ​ 26 L 498 mL​of sports drink at their game. How much more sports drink does the football team drink than the baseball team?

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149

EUREKA MATH2

4 ▸ M1 ▸ TE ▸ Lesson 24

REMEMBER 8. Partition the interval from 0 ​ ​to 1 ​ ​into thirds. Plot the fraction on the number line.

1_ ​​ 3

0 3

3 3

0

1

Use the Read–Draw–Write process to solve the problem. Use a letter to represent the unknown.

9. Carla plants 3 ​ 0​tulips in equal rows. She plants 6 ​ ​tulips in each row.

How many rows of tulips does Carla plant?

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EUREKA MATH2 4 ▸ M1

Acknowledgments Kelly Alsup, Lisa Babcock, Adam Baker, Reshma P. Bell, Joseph T. Brennan, Leah Childers, Mary Christensen-Cooper, Jill Diniz, Janice Fan, Scott Farrar, Krysta Gibbs, Torrie K. Guzzetta, Kimberly Hager, Eddie Hampton, Andrea Hart, Rachel Hylton, Travis Jones, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Ashley Meyer, Bruce Myers, Marya Myers, Victoria Peacock, Maximilian Peiler-Burrows, Marlene Pineda, Elizabeth Re, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Tara Stewart, Mary Swanson, James Tanton, Julia Tessler, Jillian Utley, Saffron VanGalder, Rafael Velez, Jackie Wolford, Jim Wright, Jill Zintsmaster Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

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

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151

MATH IS EVERYWHERE Do you want to compare how fast you and your friends can run?

Or estimate how many bees are in a hive?

Or calculate your batting average?

Math lies behind so many of life’s wonders, puzzles, and plans.

From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars.

Fueled by your curiosity to understand the world, math will propel you down any path you choose.

Ready to get started?

Module 1 Place Value Concepts for Addition and Subtraction Module 2 Place Value Concepts for Multiplication and Division Module 3 Multiplication and Division of Multi-Digit Numbers Module 4 Foundations for Fraction Operations Module 5 Place Value Concepts for Decimal Fractions Module 6 Angle Measurements and Plane Figures

What does this painting have to do with math?

American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square?

On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/ Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

ISBN 978-1-64497-654-8

9

781644 976548