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A Story of Units®

3 Units of Any Number Module 1 ▸ Multiplication and Division with Units of 2, 3, 4, 5, and 10

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A Story of Units®

Units of Any Number ▸ 3 APPLY

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Module

1

Multiplication and Division with Units of 2, 3, 4, 5, and 10

2

Place Value Concepts Through Metric Measurement

3

Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

4

Multiplication and Area

5

Fractions as Numbers

6

Geometry, Measurement, and Data

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 978-1-64497-648-7

EUREKA MATH2 3 ▸ M1

Contents Multiplication and Division with Units of 2, 3, 4, 5, and 10 Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Topic C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Conceptual Understanding of Multiplication

Properties of Multiplication

Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Organize, count, and represent a collection of objects.

Demonstrate the commutative property of multiplication using a unit of 2 and the array model.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Interpret equal groups as multiplication.

Demonstrate the commutative property of multiplication using a unit of 4 and the array model.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Relate multiplication to the array model.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Interpret the meaning of factors as number of groups or number in each group.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Represent and solve multiplication word problems by using drawings and equations.

Topic B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Conceptual Understanding of Division Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Explore measurement and partitive division by modeling concretely and drawing.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Model measurement and partitive division by drawing equal groups.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Model measurement and partitive division by drawing arrays.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Represent and solve division word problems using drawings and equations.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Demonstrate the distributive property using a unit of 4.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Demonstrate the commutative property of multiplication using a unit of 3 and the array model.

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Demonstrate the distributive property using units of 2, 3, 4, 5, and 10.

Topic D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Two Interpretations of Division Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Model division as an unknown factor problem.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Model the quotient as the number of groups using units of 2, 3, 4, 5, and 10.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Model the quotient as the size of each group using units of 2, 3, 4, 5, and 10.

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Represent and solve measurement and partitive division word problems.

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1

3 ▸ M1

EUREKA MATH2

Topic E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Application of Multiplication and Division Concepts Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Use the distributive property to break apart multiplication problems into known facts.

Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Use the distributive property to break apart division problems into known facts.

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Compose and decompose arrays to create expressions with three factors.

Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Represent and solve two-step word problems using the properties of multiplication.

Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Represent and solve two-step word problems using drawings and equations.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . 143

2

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Module 1 Topic A

FAMILY MATH Conceptual Understanding of Multiplication Dear Family,

Key Terms and Symbols

Your student is making sense of multiplication by connecting it to addition. Instead of repeatedly adding the same number, they recognize that multiplying can be more efficient. They create representations of multiplication in equal groups or arrays by using cubes or drawing pictures. Then they write multiplication equations to match. For now, the factors ​ ,​ 4 ​ ,​ 5 ​ ​, and 1 ​ 0​as your student builds their are limited to 2 ​ ,​ 3 understanding of multiplication.

factor multiplication multiplication symbol ​​×​​ multiply product

Draw an array to show 4 rows of 3.

Number in each group: 3

3 + 3 + 3 + 3 = 12 Number of groups: 4

4 threes = 12 4 × 3 = 12

4 × 3 = 12 factor

factor

product

At-Home Activities How Can You Make Equal Groups?

Gather groups of everyday objects from around your home such as toy cars, crackers, or beads.

Together with your student, arrange the objects into equal groups or arrays. Ask them to write or say a multiplication equation to represent the groups of objects. Encourage skip-counting to figure out the product.

Equal Groups and Arrays at the Grocery Store Look for items packaged in equal groups and arrays, such as eggs, hamburger buns, or toilet paper. Discuss with your student the number of groups and the number in each group for each situation. Then have them use multiplication to find the total in each package.

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3

EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 1

1

Name

1. Count the pencils.

10

10

Pencils

10

Pencils

Pencils

How many pencils are there in total?

32

I see each box holds 1​ 0​ pencils.

I count by tens. Then I count on 2 more.

10

10

10

Pencils

Pencils

Pencils

10

20

30

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32

5

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 1

2. Group the strawberries to help you count. Circle strawberries to show your groups.

I can circle groups of 1​ 0​. a. How many strawberries are there in total?

35

I know ​3​tens is 3 ​ 0​ and there are ​5​ more.

b. Describe another way you can group the strawberries.

​30 + 5 = 35

The strawberries can be circled in ​7​groups of 5 ​ .​

I can also circle groups of 5.

5 10 15 20 25 30 35 I skip-count by fives until all the groups have been counted.

6

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

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 1

REMEMBER 3. Draw the missing hand on the clock to show the time.

quarter to 5

I know that quarters are ​4​equal parts of a whole.

Quarter to is when the minute hand is three quarters of the way around the clock. At quarter to, the minute hand points at 9.

Quarter to

Quarter past

At quarter to 5, the hour hand is almost to the 5.

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

7

EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 1

1

Name

1. Count the crayons.

10

Crayons

10

Crayons

10

Crayons

10

Crayons

10

Crayons

How many crayons are there in total?

2. Group the dots to help you count. Circle dots to show your groups.

a. How many dots are there in total? b. Describe another way you can group the dots.

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9

3 ▸ M1 ▸ TA ▸ Lesson 1

EUREKA MATH2

REMEMBER 3. Draw the missing hand on the clock to show the time.

quarter past​ ​9

10

P R ACT I C E

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 2

2

Name

1. Use the equal groups for parts (a) and (b).

3

6

​​​ ,

9

,

12

,

15 ​​​

,

a. Skip-count by 3 ​ .​

If I need practice skip-counting by 3 ​ ​, I can whisper-count by ones and say every third number aloud. For example, I whisper “​1 ​, ​2 ​” and say “​3​” aloud.

I whisper “​4​, ​5​” and say “​6​” aloud.

I write each number that I say aloud.

1

4

2

3

7

5

6

8

9

b. Fill in the blanks to show the total number of apples.

3

+

3

+

3

​5​groups of three is

15

5​ ​threes is ​5 × 3 =

15 15

​​

​+

3

​+

3

=

15

The multiplication symbol (​​×​)​​​​ is used to show multiplication. ​​

.

​5 × 3 = 15​

​​ .

Multiplication is another way to represent repeated addition when the groups are the same size.

Instead of adding lots of numbers, we can multiply. ​​​ 5

Number of groups

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× ​​

3

Number in each group

= ​ ​​

15

​

Total

11

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 2

REMEMBER 2.

Read David has 3 ​ 7​ dollars. ​ ​five-dollar bills, and 1 ​ ​one-dollar bill.

Carla has ​2​ten-dollar bills, 3 Who has more money?

Draw

I read the problem. I read again.

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

I draw rectangles to represent each type of bill and label their values.

10

5

5

10

5

1

Then I add the values of the bills to find how much money Carla has.

I am trying to find who has more money.

I know David has ​37​ dollars and Carla has ​ 36​dollars.

Write

Sample:

​$20 + $15 + $1 = $36​ David has more money than Carla. ​37​ dollars is more than ​36​ dollars.

12

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

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 2

2

Name

1. Use the equal groups for parts (a) and (b).

a. Skip-count by ​5​.

,

​​ ,

,

​​

b. Fill in the blanks to show the total number of fingers.

+

​+

+

​=

​​groups of five is

.

​4​ fives is ​4 × 5 =

​​

. ​​

2. Fill in the blanks to match the picture.

+

+

​+

+

​​groups of three is

​5​ threes is ​5 × 3 =

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​=

​

. .

​​

13

3 ▸ M1 ▸ TA ▸ Lesson 2

EUREKA MATH2

REMEMBER 3.

Read Eva has ​57​ dollars. ​ ​one-dollar bills.

Luke has ​1​twenty-dollar bill, ​2​ten-dollar bills, ​1​five-dollar bill, and 5 Who has more money?

Draw

Write

14

P R ACT I C E

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 3

3

Name

1. Use the picture for parts (a) and (b).

5

,

10

15

,

20

,

5

is

30

​​ fives is

30

,

25

,

30

a. Skip-count by ​5.​ b. Fill in the blanks to match the picture.

6

​​ groups of ​​

6 6

​×

5

=

The product is ​ 30

​​ .

​.​

30 ​ ​ .

I can multiply the number in each group by the number of groups.

In multiplication, the total is called the product.

6 ​ × 5

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= ​

30 Product

15

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 3

2. Use the array for parts (a)–(c).

10 20 30 40 50 60

a. Skip-count by ​10​down the side of the array. b. Fill in the blanks to match the array. ​​

7

tens is ​​ 70

7

​×

10

.

= ​ 70

c. Circle the product in the equation.

70

I record my skip-count next to each row of the array.

The product is 7​ 0​because it is the total in the multiplication problem.

16

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

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 3

REMEMBER Add. Show how you know.

3. 3 ​ 38 + 196 = ​

534

Sample:

338 + 196

334 196

+4

4 200

+ 334

534

I can make this an easier problem. I see ​1 96​ needs ​4​more to make the next hundred, which is​ 200​. I know I can get the ​4​ from ​338​. I decompose ​338​ into ​334​ and ​4​.

338

334

4

I add the ​4​to ​1 96​ to make​ 200​.

196

+4

200

​334 + 200​is an easier problem for me than​ 338 + 196​.

Now I add ​334​ to ​200​.

196

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+4

200

+ 334

534

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

17

EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 3

3

Name

1. Use the picture for parts (a) and (b).

,

,

,

a. Skip-count by ​10​. b. Fill in the blanks to match the picture. groups of

is

tens is

×

​

. .

=

The product is ​

​ ​ .

2. Use the array for parts (a)–(c). a. Skip-count by ​5​down the side of the array. b. Fill in the blanks to match the array. ​

​fives is ​

​

×

​ .

=

​

c. Circle the product in the equation.

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19

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 3

REMEMBER Add. Show how you know.

3. 1 ​ 48 + 297 =​ ​

20

P R ACT I C E

​

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 4

4

Name

1. Use the equal groups for parts (a)–(c).

a.

How many groups of crabs are there?

b.

How many crabs are in each group?

c.

Complete the multiplication equation.

6

​

Number of groups

×

4

6 4 =

​groups ​crabs are in each group.

24

Number in each group

​

Product

I can multiply the number in each group by the number of groups.

In a multiplication equation, the two numbers we multiply together are called factors. ​

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4 = 24 ​ × 6 Factor Factor Product

21

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 4

2. Use the array for parts (a)–(c). a. How many rows of crabs are there?

6

rows of crabs

b. How many crabs are in each row?

4 c.

crabs are in each row.

Complete the equation. ​

6 Number of rows

×

4 Number in each row

=

24

​

Product

I notice the total number of crabs is the same as in problem 1, but now the crabs are organized in an array.

22

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

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 4

REMEMBER Use compensation to subtract. Draw a tape diagram if needed.

3. ​276 − 97 = 279​ − ​100​​ ​​ ​​= ​179​ ​ Sample:

279

3

279 – 100 179

276

3 97 100

?

I notice that​97​is close to the benchmark number ​1 00​.

I can use the compensation strategy to subtract.

I add​ 3​ to ​97​ to make ​1 00​.

Then I add ​3​ to ​276​ to make ​279​.

279 3 3

​279 − 100​is an easier problem for me than ​276 − 97.​

276 97 100

?

I can subtract ​1 00​ from​ 279​to get ​179​. ​279 − 100 = 179​ The compensation strategy is useful when one number is close to a benchmark number.

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

23

EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 4

4

Name

1. Use the equal groups for parts (a)–(c).

a.

How many groups of ducks are there?

​groups

b.

How many ducks are in each group?

​ducks are in each group.

c.

Complete the equation. ​

Number of groups

×

=

Number in each group

​

Product

2. Use the array for parts (a)–(c). a. How many rows of ducks are there? rows of ducks b. How many ducks are in each row? ducks are in each row. c.

Complete the equation. ​

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× Number of rows

= Number in each row

Product

​

25

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 4

REMEMBER Use compensation to subtract. Draw a tape diagram if needed.

3. 9 ​ 22 − 198 =

26

P R ACT I C E

​ =​​ ​

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 5

5

Name

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

1. Jayla has ​3​ buckets of toy cars.

There are ​5​toy cars in each bucket.

How many toy cars does Jayla have? ​3 × 5 = 15​ Jayla has ​ 15

toy cars.

I read the problem. I read again.

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

I draw ​3​circles to represent the ​3​ buckets.

I draw ​5​small circles in each bucket to represent the ​5​ toy cars.

I see 3 ​ ​groups of 5 ​ ​.

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27

EUREKA MATH2

3 ▸ M1 ▸ TA ▸ Lesson 5

2. Ray organizes his coins into 5 ​ ​ rows.

Each row has ​6​ coins.

How many coins does Ray have? ​5 × 6 = 30​ Ray has 3 ​ 0​ coins.

I read the problem. I read again.

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

I draw circles to show ​5​ rows with ​6​ coins in each row.

6 coins in each row

5 rows I can use my drawing to write a multiplication equation.

28

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

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EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 5

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

I read the problem. I read again.

3. Shen and Oka are counting their stickers.

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

Shen has 1 ​ 8 ​fewer stickers than Oka.

I draw a tape diagram with one tape to show the number of Oka’s stickers.

Oka has ​49​ stickers. a. How many stickers does Shen have? b. How many stickers do Shen and Oka have in total?

O

49

I know Shen has ​1 8​ fewer ­stickers than Oka. I draw a shorter tape to show Shen’s stickers and label the ​1 8​ fewer stickers.

18 Sample:

S

​49 − 18 = 31​ Shen has 3 ​ 1​ stickers.

?

O

​31 + 49 = 80​

49

I can subtract ​1 8​ from ​49​ to find the number of Shen’s stickers.

They have 8 ​ 0​stickers in total.

Now I know that Shen has 31 stickers.

S

31 ?

O

49

To find the total number of stickers, I can add ​31​ and ​49​.

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

29

EUREKA MATH2 3 ▸ M1 ▸ TA ▸ Lesson 5

5

Name

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

1. Mia sells 4 ​ ​bags of lemons.

There are ​6​lemons in each bag.

How many lemons does Mia sell?

Mia sells

​​lemons.

2. There are ​5​rows of chairs in the room.

Each row has ​10​ chairs.

How many chairs are in the room?

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31

3 ▸ M1 ▸ TA ▸ Lesson 5

EUREKA MATH2

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

3. Adam and Ivan find acorns.

Adam finds 1 ​ 9​fewer acorns than Ivan.

Ivan finds ​34​ acorns. a. How many acorns does Adam find? b. How many acorns do Adam and Ivan find in total?

32

P R ACT I C E

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Module 1 Topic B

FAMILY MATH Conceptual Understanding of Division Dear Family, Your student is exploring how multiplication connects to division.

They represent real-world division situations with equal-groups models, arrays, and equations using the division symbol.

Sometimes the total and the number of groups are known, and sometimes the total and the number in each group are known.

divide division division symbol ​÷​

Mia puts 10 pencils into equal groups.

She puts 2 pencils in each group. How many equal groups of pencils are there?

Share 10 crackers.

2 equal groups of 5 crackers

Key Terms and Symbols

5 equal groups of 2 crackers

20 ÷ 5

There are 5 equal groups.

=

4

total number number in each of rows row

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33

3 ▸ M1 ▸ TB

EUREKA MATH2

At-Home Activity Everyday Division Look for opportunities to practice division situations at home.

34

•

While making snacks, invite your student to help share the food equally among those sharing the snack. For example, ask, “If we have 1 ​ 5​apple slices to share equally among 3 people, how many apple slices will each person get?”

•

While playing with toy cars or building blocks, invite your student to make an array with the objects to match a division equation. For example, write 1 ​ 5 ÷ 3 = 5. ​ Together ​ ​rows. Then have them explain with your student, arrange ​15​blocks into an array with 3 where they see each part of the division equation in the array.

FA M I LY M AT H ▸ Module 1 ▸ Topic B

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 6

6

Name

Use the pictures to help you fill in the blanks.

1. There are ​12​ carrots in equal groups.

a. The total number is

12

.

b. The number in each group is c. The number of equal groups is

4

.

3

​ .

I know there is a total of ​1 2​ carrots.

I can draw circles to show the equal groups.

1

2

3

There are ​3​ equal groups.

There are ​4​ carrots in each group.

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35

EUREKA MATH2

3 ▸ M1 ▸ TB ▸ Lesson 6

2. There are ​18​ flowers. a. Circle groups of ​6​ flowers.

b. There are

3

groups of ​6​.

c. Circle two correct statements.

​3​ is the number of equal groups.

​3​ is the number in each group.

​6​ is the number of equal groups.

​6​ is the number in each group.

I count ​6​ flowers and circle them.

1

2 3 4 5 6

I continue to count and circle groups of 6​ ​until all the flowers are circled.

​6​ is the number in each group.

1

2

3

4 5 6 I see that I have ​3​ groups.

1

2

3

So, ​3​ is the number of groups.

36

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

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 6

REMEMBER 3. Circle the best unit and tool to use to measure the length of the alarm clock.

Object

10:00

Unit

Tool

inch

yardstick

foot

12-inch ruler

yard

inch tile

I know I can measure inches with inch tiles, feet with a 12-inch ruler, and yards with a yardstick.

I can use benchmarks to help me determine which unit to measure with.

I know a paper clip is about 1 inch, a math book is about 1 foot, and a table is about 1 yard.

The alarm clock is smaller than a table and a math book, but it is larger than a paper clip. I can measure with inches.

I can measure the length of the alarm clock with any of the tools, but I will use inch tiles.

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

37

EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 6

6

Name

Use the pictures to help you fill in the blanks.

1. There are ​10​ flowers in equal groups.

a. The total number is

​ .

b. The number in each group is ​​ c. The number of equal groups is

. .

2. There are ​15​ clovers. a. Circle groups of ​5​ clovers.

b. There are ​​

​​ groups of ​5​.

c. Circle two correct statements.

​3​ is the number in each group.

​3​ is the number of equal groups.

​5​ is the number in each group.

​5​ is the number of equal groups.

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39

EUREKA MATH2

3 ▸ M1 ▸ TB ▸ Lesson 6

REMEMBER 3. Circle the best unit and tool to use to measure the length of the bus.

Object

40

P R ACT I C E

Unit

Tool

inch

yardstick

foot

12-inch ruler

yard

inch tile

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 7

7

Name

1. There are ​18​ pears.

They are in ​3​ equal groups.

How many pears are in each group? a. What are you trying to find? Circle it. the number in each group

the number of groups

b. Draw to show the pears equally shared in 3 groups.

c. Fill in the blanks to match your drawing.

The total is

18

.

The number in each group is

6

3

.

The number of groups is

.

I draw ​3​ circles to represent the ​3​ groups.

I show how to equally share the ​1 8​ pears by first drawing one dot in each group.

I keep drawing one dot in each group until I have equally shared ​1 8​ dots.

Another way to think about an equal-sharing problem is to use the word divide.

There are ​1 8​ pears in ​3​ equal groups.

A problem that includes sharing equally is called a division problem.

My drawing shows there are ​ 6​pears in each group.

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41

EUREKA MATH2

3 ▸ M1 ▸ TB ▸ Lesson 7

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

2. Jayla throws a football 39 yards.

Deepa throws a football 12 fewer yards than Jayla.

How many total yards are the two footballs thrown?

Sample:

39 − 12 = 27 27 + 39 = 66 The two footballs are thrown 66 yards in total.

I read the problem. I read again.

As I reread, I think about what I can draw. I draw a tape diagram with two tapes.

I draw one tape to represent how far Jayla throws her football. I know Deepa throws her football ​1 2​ fewer yards than Jayla, so I draw a shorter tape to represent how far Deepa throws.

Jayla

39 yd

Deepa

?

?

12 yd I label the difference between the two tapes, which is ​1 2​ yards.

I need to find how many total yards the footballs are thrown. I draw arms and a question mark to represent the unknown, the total of the two tapes.

I see that I need to add the distance Jayla throws and the distance Deepa throws to find the unknown.

When I look at the tape diagram, I see another unknown. I need to find how far Deepa throws her football before I can find the total.

The tape diagram shows me that I can subtract ​1 2​ from ​39​ to find Deepa’s distance.

Now I can add to find the total.

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 7

7

Name

1. There are ​20​ plums.

They are in ​4​ equal groups.

How many are in each group? a. What are you trying to find? Circle it. the number in each group

the number of groups

b. Draw to show the plums equally shared in ​4​ groups.

c. Fill in the blanks to match your drawing.

The total is

. .

The number in each group is The number of groups is

​​ .

2. There are ​15​ sticks. a. Draw to show the sticks divided into ​3​ equal groups.

b. How many sticks are in each group?

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43

3 ▸ M1 ▸ TB ▸ Lesson 7

EUREKA MATH2

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

3. The length of Pablo’s hallway rug is ​91​ centimeters.

His bathroom rug is ​60​ centimeters shorter than the hallway rug.

What is the total length of Pablo’s hallway rug and bathroom rug?

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P R ACT I C E

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 8

8

Name

Fill in the blanks to match the array.

1. There are ​15​ soccer balls in equal rows. a. The number in each row is ​

3

b. The number of rows is ​

.

c.

15 total

​ ÷ ​

5

3 number in each row

.

​=

5 number of rows

I know a row is a horizontal group.

I see there are 3 ​ ​balls in each row.

1

I can count the number of rows.

There are 5 rows.

1

Now I can write a division equation with the division ­symbol.

2

​1 5 ÷ 3 = 5​

3

2

3

4 5

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45

EUREKA MATH2

3 ▸ M1 ▸ TB ▸ Lesson 8

2. Liz puts ​18​ trophies on ​3​ shelves.

She puts an equal number of trophies on each shelf.

How many trophies does Liz put on each shelf? a. Draw an array to represent the problem.

I can draw ​3​ lines to represent the shelves. I draw circles to ­represent the trophies. b. Write a division equation to represent the problem.

I put one circle in each row.

That’s 3.

​18 ÷ 3 = 6​

c. Liz puts

6

trophies on each shelf.

I write a division equation.

I see that the 18 trophies are divided into 3 equal groups.

I keep putting circles in each row, one at a time, until I reach ​1 8​.

3,

6,

9,

12,

15,

18

I can skip-count by ​3​up to ​18​.

18 ÷ 3 I can see each group has 6 trophies.

18 ÷ 3 = 6 So, Liz puts 6 trophies on each shelf.

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

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 8

REMEMBER Complete each statement and write a related repeated addition equation.

3. Circle rows.

​2​ rows of 6

+

Circle columns.

6 6

is

=

12

6​ columns of

.

2

is

12

.

2 + 2 + 2 + 2 + 2 + 2 =

12

12

A row is a horizontal group.

A column is a vertical group.

I circle all the acorns in each row.

I circle all the acorns in each column.

6 6 There are ​2​ rows. I count ​6​acorns in each row.

I can repeatedly add the number in each row to show there are ​1 2​ acorns in all.

2

2

2

2

2

2

There are ​6​columns. I count ​2​acorns in each column.

I can repeatedly add the number in each column to show there are ​1 2​ acorns in all.

​2​ rows of 6 ​ ​and ​6​­columns of ​2​ have the same total, which is ​1 2​.

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47

EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 8

8

Name

Fill in the blanks to match the array.

1. There are ​12​ keys in equal rows.

a. The number in each row is ​ b. The number of rows is ​​ c.

total

​ ÷ ​

number in each row

. .

=

number of rows

2. Carla hangs ​10​ pictures on the wall.

She hangs the pictures in ​2​ equal rows.

How many pictures does Carla put in each row? a. Draw an array to represent the problem.

b. Write a division equation to represent the problem.

c. Carla puts ​

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​​pictures in each row.

49

EUREKA MATH2

3 ▸ M1 ▸ TB ▸ Lesson 8

REMEMBER Complete each statement and write a related repeated addition equation.

3.

Circle rows.

Circle columns.

4​rows of ​

50

+

P R ACT I C E

is

+

5​columns of

.

+

=

+

is

+

+

.

+

=

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 9

9

Name

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

1. David puts ​24​ jars in a box.

He puts the jars in ​3​equal rows.

How many jars does he put in each row? ​24 ÷ 3 = 8​ David puts ​8​ jars in each row.

I read the problem. I read again.

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

I draw ​3​ lines to represent the ​3​ rows. I put one circle on each line. That is ​3​ circles.

I keep putting circles on each line until I reach ​24​.

3, 6, 9, 12, 15, 18, 21, 24 Now that ​24​ jars are in ​3​ equal rows, I can see how many jars are in each row.

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51

EUREKA MATH2

3 ▸ M1 ▸ TB ▸ Lesson 9

2. Oka puts ​36​party favors into bags.

She puts ​4​party favors in each bag.

How many bags does Oka use? ​36 ÷ 4 = 9​ Oka uses 9 ​ ​party bags.

I read the problem. I read again.

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

Because each bag holds 4 party favors, I draw groups of ​4​ until I get to the total, which is 3 ​ 6​.

4

8

12

16

20

24

28

32

36

I circle each group of ​4​ and count the number of groups to find how many bags Oka uses.

1

2

3

4

5

6

7

8

9

I see from my drawing that there are ​9​ equal groups.

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

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EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 9

REMEMBER Add. Show how you know.

3. ​ 34 + 16 = ​ 50

I can break apart addends and add like units.

I decompose, or break apart, ​34​ into ​30 and 4​ .

I decompose ​1 6​ into ​1 0 and 6​. +

34

30

4

16

10

6

I add the tens: ​30 + 10 = 40​ . +

34

30

4

16

10

6

40 I add the ones: ​4 + 6 = 10​ .

+

34

30

16

4

10

40

10

6

Then I add the tens and ones together: ​40 + 10 = 50​ .

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

53

EUREKA MATH2 3 ▸ M1 ▸ TB ▸ Lesson 9

Name

9

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

1. Pablo and Casey play a game with ​20​ cards.

They put the cards in ​4​ equal rows.

How many cards are in each row?

2. A farmer puts ​15​pigs into pens.

He puts ​3​pigs in each pen.

How many pens does the farmer use?

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55

3 ▸ M1 ▸ TB ▸ Lesson 9

EUREKA MATH2

REMEMBER Add. Show how you know.

3. 2 ​ 2 + 68 = ​

56

P R ACT I C E

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Module 1 Topic C

FAMILY MATH Properties of Multiplication Dear Family, Your student is exploring strategies to multiply with large factors. They learn that they can rotate an array and skip-count either by rows or columns and the total stays the same. Another strategy involves breaking the array into two smaller, simpler multiplication problems and then adding the totals.

Key Terms and Symbols break apart and distribute strategy commutative property of multiplication parentheses ( ) rotate

2 4 6

5

8

10

10 5 × 2 = 10 2 × 5 = 10

Rotating an array helps to show that the order of the factors can change without changing the product. This is called the commutative property of multiplication.

5 fours (5 × 4) 20

+ 1 four = + (1 × 4) = + 4 =

6 fours (6 × 4) 24

When the factors are large or unfamiliar, breaking the array apart into smaller and more familiar multiplication facts can make the total easier to find. Students call this the break apart and distribute strategy.

At-Home Activity Tile Multiplication If you have a wall or floor with square tiles, use chalk, masking tape, or another similar material to draw an outline around an array of tiles. With your student, discuss different strategies for counting the total number of tiles inside the array. Write down or say the multiplication equations to match. Then look at the array from another angle to notice other ways to count the tiles. Consider splitting the original array into smaller arrays to notice more strategies for finding the total number of tiles.

Instead of tiles, you could draw an array of squares outside with sidewalk chalk or create an array with square sticky notes to complete the activity.

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57

EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 10

10

Name

Fill in the blanks to match each array.

2.

1.

2

× 4 = 8​

I see ​4​ rows of ​2​ bows, which is ​8​ bows total.

4

I know that ​4​ must be the ­unknown factor in the equation.

× 2 = 8​

I see 2​ ​rows of 4 ​ ​bows, which is also 8 ​ ​bows total.

I know that 2​ ​must be the unknown factor in the equation.

There are ​2​ rows with ​8​ balls in each row.

I see there are ​1 6​ balls in all. ​2 × 8 = 16

3.

​

2

× ​

8

​= ​ 16

8

× ​

2

​=

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​​

I can turn, or rotate, the array to show 8​rows with ​2​ balls in each row. The product, ​1 6​, stays the same.

16

​8 × 2 = 16

59

3 ▸ M1 ▸ TC ▸ Lesson 10

EUREKA MATH2

4. a. Draw an array to show 2 ​ × 5.​

I can draw an array that has 2 rows with 5 objects in each row.

b. Explain how the array also shows ​5 × 2.​ ​ ​rows of 2 ​ ​. I did not add or take The array also shows ​5 × 2​because when I rotate it, there are 5 away any shapes in the array. The product, or total, stayed the same.

I know that my array can be rotated to show 5 ​ ​rows of 2​ ​.

I notice both arrays have 10 circles.

I can change the order of the factors and have the same product.

This is how to show the ­commutative property of multiplication.

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 10

REMEMBER 5. Miss Diaz measures the heights of her flowers. Use the table to create a line plot.

Title: Height of Miss Diaz’s Flowers Height of Flowers (centimeters)

Number of Flowers

3​ 1​

​3​

3​ 3​

​2​

3​ 4​

​3​

3​ 6​

​5​

3​ 8​

​4​

×

×

0

30

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

33

34

31

32

35

36

37

38

39

Height (centimeters)

I use the information given and the headings in the table to help me write the title.

I look at the table. The first column tells me the heights that I need to label on my line plot.

I use the heights to label each tick mark. I draw slashes to show that I am skipping all the numbers from zero to our first height measurement.

Title: Height of Miss Diaz’s Flowers

The second column tells me how many flowers of each height there are.

I use an X to r­ epresent ​1​ flower on my line plot.

I put ​3​Xs above ​31​.

I put 2​ ​Xs above ​33​. I put ​3​Xs above ​34​. I put ​5​ Xs above ​36​. I put ​4​ Xs above ​38​.

0 30 31 32 33 34 35 36 37 38 39 Height (centimeters)

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

61

EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 10

10

Name

Fill in the blanks to match each array.

1.

2.

× ​ 5 ​ = 1​ 0

× ​2 ​= ​10 3.

×​

​=​

×​

​=​

4. a. Draw an array to show 2 ​ × 3.​

b. Explain how the array also shows ​3 × 2​.

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63

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 10

REMEMBER 5. Mia records the lengths of the fish she catches. Use the table to create a line plot.

Title: Length of Fish (inches)

Number of Fish

​3

1​

​5

4​

​7

​3

​8

​5

​11

​3 Length (inches)

64

P R ACT I C E

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 11

11

Name

1. Skip-count by fours.

4

8

12

16

20

24

28

32

36

40

I can whisper-count by twos to help me count by fours.

I can say every other skip-count of twos in a slightly louder voice to help me skip-count by fours.

2

6

10

14

4

8

12

16

4

8

12

16

Complete the equations.

2. ​3 × 4 = ​ 12

3.

4

× 3 = 12​

4. ​12 = ​

4

× 3​

I can use my skip-count from problem 1 to help me find the unknown.

4

8

12

I see that ​3​ fours is ​1 2​, so ​3 × 4 = 12​.

I use the commutative property of multiplication to help me find the unknown factor in the last two equations.

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65

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 11

5. Draw to show why the statement in the box is true. 4 × 7 = 7 × 4

7 14 21 28 4,

8,

12, 16, 20, 24, 28

I can draw an array with ​4​ rows of ​7​ objects.

I can also think of my array as ​7​ columns with ​4​ objects in each column.

It’s the same array.

I can think of the rows as the number of groups and ­skip-count by sevens.

7 14 21 28 Or, I can think of the columns as the number of groups and ­skip-count by fours.

4, 8, 12, 16, 20, 24, 28 Either way, the array has ​28​ circles. So, I know that ​4 × 7 = 7 × 4​.

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

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 11

REMEMBER Use the line plot to answer each question.

Height of Miss Diaz’s Flowers

×

0

×

×

I find the number of flowers that are shorter than ​ 36​centimeters by counting all the Xs that are above the numbers less than ​36​.

×

×

×

×

×

× ×

×

×

I see 3 ​ ​Xs above ​34​, ​2​ Xs above ​33​, and ​3​Xs above ​31​.

×

× ×

×

×

​3 + 2 + 3 = 8​

30 31 32 33 34 35 36 37 38 39 Height (centimeters)

There are ​8​flowers shorter than ​36​ centimeters.

6. How many flowers are shorter than 36 centimeters?

7. What is the least frequent height of Miss Diaz’s flowers?

33 inches

8. How many total flowers does Miss Diaz have?

17 flowers

8 flowers

I find the least frequent flower height by finding the height with the least number of Xs. I only see ​2​ Xs above​ 33​ . The least frequent flower height is ​33​ inches.

To find the total number of flowers, I count all the Xs that are in the line plot. There are ​17​ Xs. So, Miss Diaz has ​17​ flowers.

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

67

EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 11

11

Name

1. Skip-count by fours.

4

8

Complete the equations.

2. 5 ​ ×4=

3. ​

5. ​9 × 4 =

6. ​4 × ​

​ × 5 = 20​

4. 2 ​ 0 = ​

​ × 5​

= 36​

7. 3 ​ 6 = ​

​ × 9​

8. Draw to show why the statement in the box is true. 4 × 8 = 8 × 4​

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69

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 11

REMEMBER Use the line plot to answer each question.

Fish Mia Catches

× ×

× 0

3

4

×

×

×

×

×

×

×

×

×

×

×

×

×

7

8

5

6

9

10

11

12

Length (inches)

9. How many fish are longer than 7 ​ ​ inches?

10. What is the most frequent length of fish Mia catches?

11. How many total fish does Mia catch?

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 12

12

Name

Fill in the blanks to describe each array.

1.

5 fours + 4 fours = 9 fours 5 fours

4 fours

(5 × 4) + (4 × 4) = 9 × 4 20

+

16

= 36

9 fours

The number bond shows me that 5 fours and 4 fours make 9 fours.

I can rewrite the equation with parentheses, which are symbols we use in an expression to show groups. They help us know what to do first.

I see 5 ​ × 4 = 20​ .

I can skip-count by fours to find 4 ​ × 4​. ​4​, ​8​, ​1 2​, ​1 6​ ​4 × 4 = 16​ I add the totals, ​20​ and ​1 6​, to show that ​ 9 × 4 = 36​.

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71

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 12

I see 5 ​ threes​and ​1 three​ is ​ 6 threes​.

2.

I use this to complete the first equation. ​​( 5 threes

+ +

3

1

​ × 3)​ = 6 × 3​

I know ​5 × 3 = 15​and ​1 × 3 = 3​ , so I complete the second equation.

1 three = 6 threes

( 5 × 3) + ( 1 × 3) = 6 × 3 15

× 3)​ + ​(​

5

= 18

15

​ +

3

​ = 18​

I add the totals, ​1 5​ and ​3​, to show that ​6 × 3 = 18​ .

3. Shade the array to show two parts. Then fill in the blanks to describe the array.

5 ​fours + 3 fours = 8 fours ​ ​(​ 5 ​ ×

4 ​)​ + ​ ​( 3

× ​ 4 ​)​ =

20 ​ + I know how to multiply by ​5​, so I shade ​5​ fours.

Now the large array is decomposed into two smaller arrays. It shows that ​5​ fours and ​3​ fours make ​8​ fours.

12

=

32 ​​ 32

I use my array to complete the equations.

The shaded array, ​5​ fours, can be written as ​5 × 4​ , which is ​20​.

The unshaded array, ​3​ fours, can be written as ​3 × 4​ , which is ​1 2​.

I add the totals of the two smaller arrays to find the total number of squares in the larger array. ​20 + 12 = 32​

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 12

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

4. There are ​3​ groups of bananas.

There are ​5​bananas in each group.

How many bananas are there in all?

5 + 5 + 5 = 15​ 3 × 5 = 15 There are ​15​ bananas in all.

I read the problem. I read again.

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

I draw ​3​ circles to represent the groups of bananas.

I draw ​5​ dots in each circle to represent the bananas in each group.

I write a repeated addition equation to show how many ­bananas there are in all.

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

73

EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 12

12

Name

Fill in the blanks to describe each array.​​ 1.

5 fours + 2 fours = 7 fours (5 × 4) + (2 × 4) = 7 × 4 5 fours

20

2 fours

+

= 28

5 fours

+

× 4)

+

7 fours

2.

3.

5 twos

+

3 twos = 8 twos

(5 × 2)

+

(3 × 2) = 8 × 2

+

= 16 (

+

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4 fours = 9 fours (

× 4) = 9 × 4 = 36

75

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 12

Shade each array to show two parts. Then fill in the blanks to describe each array.

4.

​​(

5.

​

twos +

​ × ​

​)​ +​ ​(​

​ twos = 6 twos​

​ fours + ​ ×

​ fours = 6 fours ​

×

​)​ = ​

​ (

​)​ +​ ​(

​ × ​

​)​ = ​

​ + ​

​= ​

​

​ +

​= ​

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

6. There are 4 ​ ​ flowers.

There are ​6 ​petals on each flower.

How many petals are there in all?

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 13

13

Name

1. Use the array to fill in the blanks.

3 6

a. Skip-count the rows by 3 and the columns by 10. b. ​10 ​rows of ​3 ​is ​​

30

9

​10​ threes is ​​ 30 ​​ .

12

​ 10

15

​ ×

=

30 ​​

c. ​3​ columns of 10​​is ​​

30 ​​ .

18

​3​ tens is

21

​

24 27 30

3

3

.

30 ​​ .

× ​ 10 ​ = ​ 30 ​​

d. Complete the equation to show how ​10​threes and ​ 3​tens are related. ​ 10

​ × ​

3

​= ​

3

​ ×

10 ​

10 , 20 , 30

Because ​1 0​ rows of ​3​ and ​3​ columns of ​1 0​ both equal ​30​, I can say 1​ 0 × 3 = 3 × 10​ .

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77

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 13

Complete the equations.

2. ​2 × 3 = ​

6

​

3. ​

3

× 2 = 6​

4. ​6 = ​

2

× 3​

I can use my skip-count from problem 1 to help me find the unknown.

3 6 I see ​2​ threes is ​6​, so ​2 × 3 = 6​.

I use the commutative property of multiplication to complete ​ × 2 = 6​.

I use the commutative property of multiplication to help me find the unknown factor.

5. Draw to show why ​3 × 6 = 6 × 3.​ Sample:

6 12 18 3,

6,

9,

I can draw an array with 3 ​ ​rows of 6 ​ ​ objects.

6 12 18

12, 15, 18

I can also think of my array as 6​ ​columns with ​ 3​objects in each column.

3, 6, 9, 12, 15, 18 My array shows ​3​ rows of ​6​ equals ​1 8​ and ​ 6​columns of ​3​ equals ​1 8​.

So, ​3 × 6 = 6 × 3​ .

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 13

REMEMBER Make pairs. Then circle whether the total number is even or odd.

6.

even / odd

There are ​2​ snowflakes in a pair.

I circle ​5​ groups of ​2​.

I have 1 extra snowflake.

There are ​1 1​ snowflakes in all.

A number is even if each object has a partner.

There is ​1​snowflake that does not have a partner.

Numbers that are not even are called odd ­numbers. ​1 1​is an odd number.

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

79

EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 13

13

Name

1. Use the array to fill in the blanks. a. Skip-count the rows by ​3​and the columns by 5 ​ ​. b. ​5 ​rows of 3 ​ ​is ​​

.

​5​threes is ​

​​ .

​×

​=

c. ​3​columns of 5 ​ ​is ​​

3​ ​fives is ​​ ,

​× ​

,

.

​​ . ​=

d. Complete the equation to show how ​5​ threes and ​3​fives are related.

​×

​= ​

​× ​

​

Complete the equations.

2. ​3 × 2 =

​

3.

5. ​4 × 3 =

​ ​= 15​

8. ​5 ×

​ × 3 = 6​

4. ​6 = ​

​× 3​

6. ​3 × ​

​= 12​

7. ​12 = ​

× 3​

9. ​3 ×

​= 15​

10. 1 ​5=

​× 3​

11. Draw to show why 4 ​ × 3 = 3 × 4​.

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3 ▸ M1 ▸ TC ▸ Lesson 13

EUREKA MATH2

REMEMBER Make pairs. Then circle whether the total number is even or odd.

12.

even / odd

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 14

14

Name

Fill in the blanks to describe the array.

1.

​6 threes = 5 threes + 1 three​

6​ × 3 = ​(5 × 3)​ + ​(1 × 3)​​

6 threes

5 threes

1​ 8 =

15

+

3

​

1 three

The number bond shows that ​6​ threes can be decomposed into ​5​ threes and ​1​ three.

I can skip-count by threes to find ​5 × 3​. ​3​, ​6​, ​9​, ​1 2​, ​1 5​ ​5 × 3 = 15​ I see from my skip-count that ​1 × 3 = 3​.

I can add the totals, ​1 5​ and ​3​, to show that 6 ​ × 3 = 18​.

This is called the break apart and distribute strategy.

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83

EUREKA MATH2

3 ▸ M1 ▸ TC ▸ Lesson 14

2. Show two different ways to make 8 ​ ​threes. Shade the arrays and complete the equations.

Sample: a.

b.

​8 threes =

5

threes +

3

threes​

8​ × 3 = ​(

5

× 3)​ + ​(

3

× 3)​​

​24 =

15

+

9

​8 threes =

​

I know how to multiply by ​5​, so I shade ​5​ threes.

Now the array shows that ​5​ threes and 3 ​ ​threes makes ​8​ threes.

I use the array to complete the equations.

4

threes +

4

threes​

8​ × 3 = ​(

4

× 3)​ + ​(

4

× 3)​​

2​ 4 =

12

+

12 ​

I can also show ​4​ threes and ​ 4​threes because that way I only have to find 4 ​ × 3 = 12​.

I know 1​2 + 12 = 24​.

The shaded array of ​5​threes can be written as ​ 5 × 3​, or ​1 5​.

The unshaded array of ​3​ threes can be written as ​ 3 × 3​, or ​9​.

I add the totals of the two smaller arrays to find the total number of squares in the larger array. ​1 5 + 9 = 24​ So, 8 ​ × 3 = 24​.

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EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 14

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

3. There are 4 bags of limes.

There are 5 limes in each bag.

How many limes are there in all? ​5 + 5 + 5 + 5 = 20​ There are 20 limes in all.

I read the problem. I read again.

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

I draw ​4​ circles to represent the bags of limes.

I draw ​5​ dots in each circle to represent the number of limes in each bag.

I write a repeated addition equation to show how many limes there are in total.

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85

EUREKA MATH2 3 ▸ M1 ▸ TC ▸ Lesson 14

14

Name

Fill in the blanks to describe the array.

1.

7 threes

​7 threes = 5 threes + 2 threes​

7​ × 3 = ​(5 × 3)​ + ​(2 × 3)​​ ​21 =

5 threes

+

​

2 threes

2. Show two different ways to make 7 ​ ​threes. Shade the arrays and complete the equations. a.

b.

7​ threes =

threes +

threes​

7​ × 3 = ​(

× 3)​ + ​(

× 3)​​

​7 × 3 =

+

​7 × 3 =

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​

​

​7 threes =

threes +

threes​

7​ × 3 = ​(

× 3)​ + ​(

× 3)​​

​7 × 3 =

+

7​ × 3 =

​

​

87

3 ▸ M1 ▸ TC ▸ Lesson 14

EUREKA MATH2

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

3. There are 7 ​ ​ friends.

Each friend eats ​3​jelly beans.

How many jelly beans do they eat in all?

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Module 1 Topic D

FAMILY MATH Two Interpretations of Division Dear Family,

Key Term

Your student continues to deepen their understanding of equal groups. They relate finding an unknown factor in multiplication to finding the quotient, the answer in a division problem.

Drawing equal groups and arrays helps to represent the situation when finding either the size of each group or the number of groups.

Tape diagrams can also help to identify what is known and what is unknown.

Eva puts flowers into vases.

She has 8 flowers.

She puts 2 flowers in each vase.

How many vases have flowers?

8

quotient

12 apples are placed equally into 3 bags.

How many apples are in each bag?

2 4 6 8

?

?

?

12

8÷2= 4

4 ×2=8

4 vases have flowers.

4 vases have flowers.

equal groups model

array model

The unknown in both equations is the number of groups.

12 ÷ 3 =

This tape diagram shows that the total and number of groups are known, but the size of each group is unknown.

12 apples are placed equally into bags.

There are 3 apples in each bag.

How many bags of apples are there?

3 12 3×

= 12

This tape diagram shows that the total and the size of each group are known, but the number of groups is unknown.

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89

3 ▸ M1 ▸ TD

EUREKA MATH2

At-Home Activity Two Types of Everyday Division Look for opportunities to discuss different types of division in everyday life.

•

Count the total number of socks in a drawer and ask your student how many pairs ​ ​is the size of the group in there are when there are ​2​socks in each pair. Discuss why 2 this situation.

•

Select 9 ​ ​shirts. Ask your student how many should go in each pile if you want to make 3​ ​equal piles. Discuss why 3​ ​is the number of groups in this situation.

Ask your student, “What equation can help you solve the problem?” For example, if there are ​ 8​socks total and 2​ ​socks in each pair, the division equation is ​8 ÷ 2 = ​_​​ and the unknown factor equation is ​ _​× 2 = 8​.

90

FA M I LY M AT H ▸ Module 1 ▸ Topic D

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 15

15

Name

1. Oka sorts ​15​ toy cars into bins.

Each bin holds ​5​ cars.

How many bins does Oka use? a. Circle groups of ​5​ to show the cars in each bin.

There are many ways to make groups of 5 ​ ​.

This is another way I can circle equal groups.

I know there are 5 ​ ​cars in each group. b. Complete the equations and statement.

3

​ × 5 = 15​

​15 ÷ 5 =

3

Oka uses

3

I need to find the number of groups Oka uses.

There are ​3​ fives in ​1 5​, so ​3​ is the number of groups in both equations.

​​ bins.

c. What do the unknowns in the equations represent? Circle the correct answer. the number of groups

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the size of each group

91

EUREKA MATH2

3 ▸ M1 ▸ TD ▸ Lesson 15

2. James gives ​18​ stickers to his friends.

He gives ​3​ stickers to each friend.

How many friends get stickers? a. Draw a picture to represent the problem.

Sample:

3

3

3

3

3

3

I draw a tape diagram to represent the problem.

I know the total is ​18​ and the size of each group is ​3​.

3 18

18

I think about how many threes are in ​1 8​ to find the number of groups.

I keep drawing groups of ​3​ until I get to ​1 8​.

b. Complete the equations to find the unknown.

6

​18 ÷ 3 = ​

× 3 = 18

6

c. Complete the solution statement.

6

friends get stickers.

I know there are ​6​ threes in ​1 8​, so ​6​ is the number of groups.

When we divide, we call the answer the quotient.

Once I find the quotient, ​6​, I can complete the solution statement.

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 15

REMEMBER Add. Show how you know.

3. ​31 + 23 + 19 + 14 =

87

​​

Sample:

I can add like units to find the sum.

I decompose each number into tens and ones.

31

+ 23 +

19

30 1

20 3

10 9

+

14 10 4

I add the tens. ​30 + 20 + 10 + 10 = 70​ I add the ones. ​1 + 3 + 9 + 4 = 17​ I add the tens and ones. ​7 0 + 17 = 87​ So ​31 + 23 + 19 + 14 = 87​ .

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93

EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 15

15

Name

1. Amy has ​12​ pens.

She gives ​2 ​pens to each friend.

How many friends get pens? a. Circle groups of ​2​ to show the pens each friend gets. b. Complete the equations and statement. ​

​ × 2 = 12​

​12 ÷ 2 = ​

​friends get pens.

c. What do the unknowns in the equations represent? Circle the correct answer. the number of groups

the size of each group

2. David puts ​20​ grapes into bowls.

He puts ​5 ​grapes in each bowl.

How many bowls does he use? a. Draw a picture to represent the problem. b. Complete the equations to find the unknown.

× 5 = 20

20 ÷ 5 = c. Complete the solution statement.

David uses ​​

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​ ​bowls.

95

EUREKA MATH2

3 ▸ M1 ▸ TD ▸ Lesson 15

REMEMBER Add. Show how you know.

3. 21 + 16 + 33 + 12 =

​​

4. ​14 + 27 + 22 + 15 =

​​

96

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 16

16

Name

1. Divide ​12​ birds into groups of ​4.​

How many groups of ​4​ are there? ​

3

× 4 = 12

I circle groups of ​4​ birds until all ​1 2​ birds are circled.

I see there are ​3​ groups of four.

12 ÷ 4 =

3

There are ​

3

​ ​groups of ​4​.

To help me solve, I can relate the situation to an unknown factor problem and think about how many fours are in ​1 2​.

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97

EUREKA MATH2

3 ▸ M1 ▸ TD ▸ Lesson 16

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

2. Friends sort ​24​ note cards into piles. Each pile has ​4​ note cards.

How many piles of note cards do the friends make?

​24 ÷ 4 = 6​ The friends make ​6​ piles of note cards.

I read the problem. I read again.

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

I draw a tape diagram to show that the total is ​24​ and the size of each group is ​4​.

The unknown is the number of groups.

4 24 I find the number of groups by a ­ sking ­myself how many fours are in ​24​.

I s­ kip-count by fours until I get to ​24​. ​4, 8, 12, 16, 20, 24​ I complete the tape diagram to show there are ​6​ fours in ​24​.

4

4

4

4

4

4

24

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 16

REMEMBER Subtract. Use addition to check your work.

3. ​711 – 295 = ​ Sample:

416

​​

711 – 295

411

300 ​300 – 295 = 5​ ​ 411 + 5 = 416​

+ 300

−5

416

711 716 I see that ​295​ is close to the benchmark number ​300​.

So, I decompose ​7 11​ into ​300​ and ​411​.

711 – 295

I subtract ​295​ from ​300​.

I add ​5​ to ​411​ to get ​416​.

411

So, ​7 11 − 295 = 416​ .

300

​300 − 295 = 5​ ​411 + 5 = 416​

I check my answer by using addition and an open number line.

I need to check whether 4 ​ 16 + 295 = 711​.

I start at ​416​and add ​300​to get 7​ 16​. Then I subtract 5 ​ ​to get 7​ 11​. + 300

–5

416

711 716

I know my answer is correct because 4 ​ 16 + 295 = 711​.

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99

EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 16

16

Name

1. ​15​ butterflies are divided into groups of ​5​.

How many groups of ​5​ are there?

2. Divide ​20​ fish into groups of ​10​.

How many tens are in ​20​?

× 5 = 15

​15 ÷ 5 = There are

​​ ​​ groups of ​5​.

× 10 = 20

​20 ÷ 10 = ​

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

3. Pablo sorts ​36​ rocks into piles.

Each pile has ​4​ rocks.

How many piles of rocks does he make?

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101

3 ▸ M1 ▸ TD ▸ Lesson 16

EUREKA MATH2

REMEMBER Subtract. Use addition to check your work.

4. ​528 – 392 = ​

102

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 17

17

Name

1. ​18​ flowers are divided into ​2​ equal groups.

I see that there are ​9​ flowers in each group.

I know ​2 × 9 = 18​ . I can use the multiplication fact to help me find ​1 8 ÷ 2 = .

How many flowers are in each group?

​18 ÷ 2 = There are ​ 2.

15

9

2×

= 18

9

9

​flowers in each group.

​​bears are divided into ​​

3

equal rows.

I can count the bears to find the total.

I see the total, ​1 5​, is divided into ​3​ equal rows.

There are ​5​ bears in each row.

3

How many bears are in each row?

​15 ÷ ​ There are ​​

5

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3

​=

5

×

5

= 15

​​

​​bears in each row.

103

EUREKA MATH2

3 ▸ M1 ▸ TD ▸ Lesson 17

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

3. ​21​ napkins are shared equally between ​3​ tables.

How many napkins are on each table?

​21 ÷ 3 = 7​ There are ​7​ napkins on each table.

I read the problem. I read again.

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

I draw a tape diagram that has a total of ​2 1​ to ­represent the ​2 1​ napkins. I partition the tape diagram into 3 ​ ​equal parts to represent the 3 ​ ​tables, or groups.

21 To find the unknown, I divide ​2 1​ equally into ​3​ groups.

I draw 1​ ​dot in each group. That’s a total of ​3​ napkins.

I draw another dot in each group and skip-count by threes until I get to ​2 1​.

21

3 6 9 12 15 18 21

I see there are ​7​ dots in each group, and I counted by threes ​7​ times.

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 17

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

4. Deepa makes ​42​ hats.

She makes ​17​ more hats than Eva. How many hats does Eva make?

​42 − 17 = 25​ Eva makes ​25​ hats.

I read the problem. I read again.

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

I draw a tape and label it as ​42​ to represent the number of hats Deepa makes.

D

42

I know Deepa makes ​17​ more hats than Eva. I draw a shorter tape to represent the number of hats Eva makes. I label the difference ​17​.

17 E

?

D

42

I can subtract ​17​ from ​42​ to find the number of hats Eva makes. I use compensation to subtract the arrow way.

42

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- 20

22

+3

25

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105

EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 17

17

Name

1. ​12​ ladybugs are divided into 3 ​ ​equal groups.

2.

​​fish are divided into ​​ equal rows.

​​

How many ladybugs are in each group?

How many fish are in each row?

3×

20 ÷

12 ÷ 3 = There are ​​

×

= 12

​​ladybugs in each group.

There are ​​

= 20

= ​fish in each row.

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

3. ​18​ flowers are shared equally among 3 How many flowers are in each vase?

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107

3 ▸ M1 ▸ TD ▸ Lesson 17

EUREKA MATH2

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

4. Casey practices the piano for ​62​ minutes.

She practices the piano ​16​ minutes more than Gabe.

How many minutes does Gabe practice the piano?

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 18

18

Name

1. ​4​ friends equally share ​36​ jelly beans.

How many jelly beans will each friend get? a. Circle the tape diagram that represents the problem.

4 36

36

I know the total number of jelly beans, ​36​, and the number of groups, ​4​.

The tape diagram on the left represents the problem ­because it shows ​36​ partitioned into ​4​ equal parts (friends). The ­number in each group is unknown.

The tape diagram on the right represents a problem with a total of ​36​ and ​4​ in each group. The number of groups is u ­ nknown.

b. Complete the equation and statement.

​36 ÷ 4 = ​

9

​

Each friend gets ​

9

​jelly beans.

Because I know the total is ​36​ and the number of groups is ​4​, I can think: ​4​ groups of what number is ​36​? I can divide to find the unknown.

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109

EUREKA MATH2

3 ▸ M1 ▸ TD ▸ Lesson 18

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

2. Mia divides ​55​ crackers equally onto ​5 ​trays.

How many crackers are on each tray?

​55 ÷ 5 = 11​ There are ​11​ crackers on each tray.

I read the problem. I read again.

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

I draw a tape diagram that has a total of ​55​to represent the 5 ​ 5​crackers.

I partition the tape diagram into ​5​ equal parts to represent the 5 ​ ​ trays.

55

The unknown is the size of each group.

To help me solve, I can think: ​5​ groups of what number is ​55​?

11 11 11 11 11 I know 5 ​ × 11 = 55​ , so I complete the tape diagram to show 55 ​5​groups of ​1 1​.

3. Mr. Lopez has 40 paintbrushes for art class. He puts all of them on tables. Each table gets 5 paintbrushes. How many tables get paintbrushes?

​40 ÷ 5 = 8​ 8​tables get paintbrushes.

I read the problem. I read again.

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

I draw a tape diagram that has a total of ​4 0​.

I know the size of the group is ​5​. The unknown is the number of groups.

5 40

To help me solve, I think about how many fives are in ​4 0​.

I know ​8 × 5 = 40​ , so I complete the tape diagram to show 8 ​ ​groups of 5 ​​ .

5 5 5 5 5 5 5 5 40 110

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EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 18

REMEMBER Subtract. Show how you know.

4. ​92 – 68 =

24

​​

I notice that ​6 8​ is close to ​7 0​. I choose to use compensation to ­subtract. I show my thinking on an open number line.

I start at ​92​ and subtract ​7 0​.

But I need to subtract ​6 8​, not ​7 0​. So, I add back ​2 ​.

- 70

+2

22 24

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111

EUREKA MATH2 3 ▸ M1 ▸ TD ▸ Lesson 18

18

Name

1. ​15 ​rings are sorted into ​3​ equal groups.

How many rings are in each group? a. Circle the tape diagram that represents the problem.

3 15

15

b. Complete the equation and statement.

​15 ÷ 3 = ​ There are ​

​rings in each group.

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

2. ​5​ friends equally share ​35​ glow sticks.

How many glow sticks does each friend get?

3. The store has ​70​ books on shelves. There are ​10​ books on each shelf.

How many shelves have books?

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113

EUREKA MATH2

3 ▸ M1 ▸ TD ▸ Lesson 18

REMEMBER Subtract. Show how you know.

4. ​64 − 37 =

114

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​​

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Module 1 Topic E

FAMILY MATH Application of Multiplication and Division Concepts Dear Family,

Your student is using the familiar break apart and distribute strategy to solve more challenging problems, including two-step word problems. They explore different ways of breaking apart problems into smaller or familiar parts. These parts can be simpler to work with and result in the same answer. In multiplication, breaking apart a factor into smaller parts to make simpler problems uses the associative and distributive properties. However, your student does not name these properties until grade 4. Instead, they use arrays and write equations to describe the strategies.

8 × 5 = 40

10 fours 32 ÷ 4 = 5 + 3 = 8 20 12

4×5

4×5 1 four 9 fours = 10 fours − 1 four 9 × 4 = (10 × 4) − (1 × 4) 9 × 4 = 40 − 4 9 × 4 = 36

At-Home Activities Fact Fluency Hide-and-Seek Hide known multiplication and division problems around your home using the factors 2 ​ ,​ ​3​, ​4​, ​5​, and ​10​.

•

Write multiplication and division problems on brightly colored paper. Examples of problems you could write for your student are ​2 × 4 =​ _​​ , ​16 ÷ 2 =​ _​​ , ​ 5 ×​ _​= 20,​ or​​ _​ × 3 = 15.​

•

Hide the facts in common places where your student can find them such as inside a cupboard or on the back of a door. Have your student solve each problem. Encourage your student to use a strategy, such as break apart and distribute, to solve more challenging problems.

•

Consider asking your student to write similar problems for you to solve. Ask your student to check your work.

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115

3 ▸ M1 ▸ TE

EUREKA MATH2

Problem Solving

116

•

Look for opportunities to show how multiplying and dividing is used in daily life.

•

“I am making our lunches for the week. I have ​15​carrot sticks and I want to put ​3​ in each lunch. How many lunches can I make? What if I add ​6​ more carrot sticks?”

•

“You get ​32​ pieces of candy at the Fall Carnival, but you are only allowed to eat ​ 4​pieces each day. How many days will it take to eat all the candy?”

FA M I LY M AT H ▸ Module 1 ▸ Topic E

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 19

19

Name

Use the array to complete the equations.

1.

6 threes = 5 threes + 1 three

(5 (5 × 3) ×= 3) =15 15

(1 (1 × 3) ×= 3) = 3 3

​6 × 3 = (​ ​

5

× 3)​ + ​(

6×3=

15

​ +

6×3=

18

3

1

× 3)​

​

The array shows ​5​threes and ​1​ three.

The shaded array, ​5​ threes, can be written as ​5 × 3​, or ​1 5​.

5 threes

The unshaded array, ​1​three, can be written as ​1 × 3​, or ​3​.

I add the totals of the two smaller arrays to find the total number of squares in the larger array.

I can also draw a number bond to represent how I broke apart ​6​threes.

1 three

6 threes

​6​threes represents the total number of rows of three. ​5​threes represents the number of shaded rows. ​1​three represents the number of unshaded rows.

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5 threes

1 three

117

EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 19

Use the array to complete the equations.

2.

​​9 fours = 10 fours − 1 four 9 × 4 = ​(10 × 4)​ − ​(​​1 × 4)​ ​

10 × 4 =

40

1×4=

4

​9 × 4 = 40 − ​ 9 × 4 =

4

36

​ ​fours is ​1​four less than ​1 0​ fours. So, I can think 9 about ​9​fours as ​1 0​ fours minus ​1​ four.

10 fours

9 fours

1 four I know ​1 0​ fours is ​4 0​ and ​1​ four is ​4​.

So, ​9 × 4​is the same ​4 0 − 4​ , which is ​36​.

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 19

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

3. Mr. Davis has 4 ​ 1​ tomatoes.

He uses some tomatoes to make sauce.

He has ​19​ tomatoes left.

How many tomatoes does Mr. Davis use?

Sample:

41 − 19 = 22​ Mr. Davis uses 2 ​ 2​ tomatoes.

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 total number of tomatoes, 4 ​ 1​.

I know there are 1​ 9​tomatoes left, so I label one part as ​1 9​.

41 ?

19

Mr. Davis’s Sauce

Left

I can subtract ​1 9​ from ​41​ to find the number of tomatoes Mr. Davis uses to make sauce.

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119

EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 19

19

Name

Use the array to complete the equations.

1.

8 fours = 5 fours + 3 fours ​​(5 × 4)​ =

8 × 4 = ​(5 × 4)​ + ​(​​3 × 4​)​​ 8 × 4 = 20 +

(​​ 3 × 4)​ =

​ 8×4=

Complete the number bond. Then, use it to complete the equations.

2.

7 fours

​7 fours = 5 fours +

fours

7 × 4 = (5 × 4)​ + ​(

​ × 4)​

7 × 4 = 20 + ​ 5 fours

​

7×4=

Use the array to complete the equations.

3.

9 fives = 10 fives − 1 five ​​​9 × 5 = ​(10 × 5)​ − ​(​​1 × 5​)​​

10 50× 5 =

10 × 5 =

1 ×5 5 =

9 × 5 = 50 − 9×5=

1×5=

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3 ▸ M1 ▸ TE ▸ Lesson 19

EUREKA MATH2

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

4. There are ​65​ apples in a basket.

Miss Diaz uses some apples to make pies.

There are ​27​apples left in the basket.

How many apples does Miss Diaz use to make pies?

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 20

20

Name

Complete the equations. Use each part of the array to help you divide.

1.

15 ÷ 3 =

There are ​2 1​ squares in the array. I can use the break apart and distribute strategy to find ​2 1 ÷ 3​ .

5 7

21 ÷ 3 = 6÷3=

I can decompose the total into smaller parts. I know ​5​ threes is ​1 5​ and ​2​ threes is ​6​. ​5​ and ​2​ make ​7​. So, ​2 1 ÷ 3 = 7​ .

2

Divide by using the break apart and distribute strategy. Explain your thinking.

18 ÷ 3 = 5 +

2.

15

1

=

6

3

I broke apart 18 into 15 and 3 to make simpler problems.

​15 ÷ 3 = 5​and 3​ ÷ 3 = 1.​ ​5​and 1​ ​make 6​ ​. So, 1​ 8 ÷ 3 = 6.​

I know 3 is the unknown part of the number bond because 15 + 3 = 18. I divide each part of 18 by 3.

15 ÷ 3 = 5. 3 ÷ 3 = 1.

Then I find the answer by adding the quotients, ​5​ and ​1​.

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123

EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 20

REMEMBER 3. Write the name of the polygon. hexagon

quadrilateral

a.

b.

quadrilateral

triangle c.

pentagon

I know that a polygon is a closed shape that has straight sides.

A polygon has the same number of sides as the number of angles.

pentagon d.

hexagon

triangle

A pentagon has 5 sides.

2

1

I can name a polygon by counting the number of sides.

5

A triangle has 3 sides.

2

2

1

A quadrilateral has 4 sides.

2 1

4

A hexagon has 6 sides.

3

1

3

3

4 5

6

3 4

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 20

20

Name

Complete the equations. Use each part of the array to help you divide.

1.

2.

12 ÷ 3 = 18 ÷ 3 = 16 ÷ 4 =

6÷3=

8÷4=

24 ÷ 4 = Use the arrays to help you complete the equations.

3.

4.

24 ÷ 3 = 5 + 15

36 ÷ 4 = 5 +

9 20

16

Divide by using the break apart and distribute strategy. Explain your thinking.

27 ÷ 3 = 5 +

5.

=

15

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125

EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 20

REMEMBER 6. Write the name of the polygon. hexagon a.

126

quadrilateral b.

P R ACT I C E

triangle c.

pentagon d.

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 21

21

Name

Fill in the blanks to match the arrays.

1.

I see 3 ​ ​arrays, so there are 3 ​ ​ groups.

Each array has 4 ​ ​rows of​ 2​, which is represented as ​4 × 2​.

I see ​3​ groups of

4

×

2

.

2. Draw a line to break apart the array into ​2​ equal groups. Fill in the blanks to match the array.

I see ​2​ groups of

​​​​​2 × ​(​

4

​×

4 5

×

5

.

​​)​​​​

I draw a line that breaks the array into ​2​ equal groups.

I could also draw a line to make 2​ ​groups of ​2 × 10​ .

Each group has ​4​ rows of ​5​, which is represented as ​4 × 5​ .

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127

EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 21

REMEMBER 3. Draw 2 different arrays. Write a related repeated addition equation to represent each array.

​14​ square tiles

Sample:

=

14

2+2+2+2+2+2+2 =

14

7+7

I have 14 square tiles.

I can make 2 rows with 7 square tiles in each row.

7 + 7 = 14 I can rotate the array to show 7 rows of 2.

2 + 2 + 2 + 2 + 2 + 2 + 2 = 14 2 rows of 7 and 7 rows of 2 have the same total, 14.

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

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 21

21

Name

Fill in the blanks to match the arrays.

1.

2.

I see 3 ​ ​groups of

​​3 × ​(

× ×

​​ .

I see

×

​​ groups of

×(

​​ )​

​ × ​

​ . ​​ )

3. The array is broken apart into 2 ​ ​equal groups. Fill in the blanks to match the array.

I see ​2​ groups of

​​2 × ​(

×

× ​

​ .

)​​​​

4. Draw a line to break apart the array into ​2​ equal groups. Fill in the blanks to match the array.

I see ​2​groups of

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×

​ .

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EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 21

REMEMBER 5. Draw 2 different arrays. Write a related repeated addition equation to represent each array.

​15​square tiles = =

130

P R ACT I C E

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 22

22

Name

Use the Read–Draw–Write process to solve each problem. ​ ​bag of plant food.

1. David buys 4 ​ ​rose bushes and 1 Each rose bush costs ​$6.​ The bag of plant food costs ​$9.​ a. What is the total cost of the rose bushes? ​6 × 4 = 24​ The total cost of the rose bushes is $ ​ 24.​

I read the problem. I read again.

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

I draw a tape diagram with ​4​ groups to represent the 4 ​ ​rose bushes. I label each group with a ​6​ to show that each bush costs $ ​ 6​.

6

6

6

6

24 I can find the total cost of the rose bushes by multiplying 4 ​ ​and ​6​. b. How much does David spend altogether? ​24 + 9 = 33​ David spends ​$33​ altogether.

I draw a tape diagram to represent how much David spends altogether.

33 24

9

I add to find the total cost of the plant food and the rose bushes.

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131

EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 22

2. A gift shop divides ​45​ mugs equally onto ​5​ shelves. a. How many mugs are on each shelf? ​45 ÷ 5 = 9​ There are ​9​ mugs on each shelf.

I read the problem. I read again.

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

I draw a tape diagram that has a total of ​45​ to represent the ​45​ mugs. I make ​5​ equal parts to represent the ​5​ shelves.

45 I know the total and the number of groups. I need to find the size of each group.

I divide to find the number of mugs on each shelf.

b. What is the total number of mugs on 4 shelves?

​4 × 9 = 36​ The total number of mugs on 4 shelves is 36.

Now I know there are ​9​ mugs on each shelf.

9

9

9

9

9

45 I can use the same tape diagram to help me find how many mugs are on 4 shelves.

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

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 22

REMEMBER 3. Draw the array. Then fill in the blanks.

2 rows of seven

2 rows of seven is equal to ​

7

​ +

7

7 doubled is

​ = 14

14

14

.

​​

.

Is 7 doubled even or not even?

Even

I draw ​1​ row of ​7​. I double it by drawing ​ 1​more row of ​7​.

I now have ​2​ rows of ​7​.

I know the sum of a doubles fact is even. ​14​ is even.

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

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 22

22

Name

Use the Read–Draw–Write process to solve each problem. ​ ​first aid kit.

1. Amy buys 5 ​ ​flashlights and 1 Each flashlight costs ​$6​.

The first aid kit costs ​$12​. a. What is the total cost of the flashlights?

Flashlights

b. How much does Amy spend altogether?

2. A gardener spreads ​24​ seeds equally among ​4​ pots. a. How many seeds are in each pot?

b. What is the total number of seeds in 3 pots?

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135

EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 22

REMEMBER 3. Draw the array. Then fill in the blanks.

2 columns of five

2 columns of five is equal to ​

​ + ​

5 doubled is

.

= .

Is 5 doubled even or not even?

136

P R ACT I C E

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 23

23

Name

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

1. Robin earns $ ​ 7 ​each week for walking his dog.

He walks his dog for ​4​ weeks.

He gives ​$6​of his earnings to his younger brother. a. How much money does Robin earn for walking his dog? ​7 × 4 = 28​ Robin earns $ ​ 28​for walking his dog.

I read the problem. I read again.

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

I draw a tape diagram with ​ 4​equal parts to represent the ​ 4​weeks. I label each part ​7​ to represent how much money Robin earns each week.

The total is unknown.

7

7

7

7

? b. How much money does Robin have left after giving money to his brother? ​28 − 6 = 22​

I see ​4​ groups of ​7​. I can multiply 4 and 7 to find how much Robin earns for walking his dog.

Robin has ​$22​ left.

I draw a tape diagram to represent the problem in part 1(b).

I know one part is ​6​ and the total is ​28​. I need to find the unknown part.

28 6

22

To help me find how much money Robin has left, I can think: ​6​ and what number makes ​28​?

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EUREKA MATH2

3 ▸ M1 ▸ TE ▸ Lesson 23

2. Eva buys ​8​tickets for the school fair.

Each ticket costs $ ​ 3.​ She also spends ​$7​on food at the fair.

How much money does Eva spend altogether? ​3 × 8 = 24​

2​ 4 + 7 = 31​ Eva spends ​$31​ altogether.

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 8 ​ ​tickets by ­drawing ​8​equal parts.

I know that each ticket costs ​$3.​ 3 3 3 3 3 3 3 3 ?

My drawing shows that Eva spends ​$24​on tickets.

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

To find out how much Eva spends altogether, I can draw another tape diagram.

One part is the total she spends on tickets, ​24​, and the other part is ​7​, the amount she spends on food.

24

7 ?

I can add the two parts to find the amount Eva spends ­altogether.

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EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 23

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

3. There are 4 ​ ​ ladybugs.

Each ladybug has ​7​ spots.

How many spots are there in all?

Sample: ​7 + 7 + 7 + 7 = 28​ ​ 8​spots in all.

There are 2

I read the problem. I read again.

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

I draw a tape diagram with ​4​ equal parts to ­represent the ​4​ ladybugs.

I label each part ​7​ to represent the spots on each ladybug. The unknown is the total number of spots.

I use a question mark to label the unknown. ?

7

7

7

7

I see ​4​ groups of ​7​.

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

139

EUREKA MATH2 3 ▸ M1 ▸ TE ▸ Lesson 23

Name

23

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

1. Pablo has ​5​ pages of trading cards in a book.

Each page holds ​9​ cards. a. How many trading cards does Pablo have?

b. Pablo gives ​9​ trading cards to his friends. How many does he have left?

2. Ray bakes ​4​ batches of blueberry muffins.

Each batch has ​10​ blueberry muffins.

He bakes an additional ​6​ apple muffins.

How many muffins does he bake altogether?

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141

3 ▸ M1 ▸ TE ▸ Lesson 23

EUREKA MATH2

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

3. Luke buys ​2​ packs of yogurt.

Each pack has ​8​ yogurts.

How many yogurts does Luke buy in all?

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EUREKA MATH2 3 ▸ M1

Acknowledgments Kelly Alsup, Lisa Babcock, Cathy Caldwell, Mary Christensen-Cooper, Cheri DeBusk, Jill Diniz, Melissa Elias, Janice Fan, Scott Farrar, Krysta Gibbs, Julie Grove, Karen Hall, Eddie Hampton, Tiffany Hill, Robert Hollister, Rachel Hylton, Travis Jones, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Geoff Patterson, Victoria Peacock, Marlene Pineda, Elizabeth Re, Meri Robie-Craven, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Theresa Streeter, Mary Swanson, James Tanton, Julia Tessler, Saffron VanGalder, 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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143

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 Multiplication and Division with Units of 2, 3, 4, 5, and 10 Module 2 Place Value Concepts Through Metric Measurement Module 3 Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9 Module 4 Multiplication and Area Module 5 Fractions as Numbers Module 6 Geometry, Measurement, and Data

What does this painting have to do with math?

Swiss-born artist Paul Klee was interested in using color to express emotion. Here he created a grid, or array, of 35 colorful squares arranged in 5 rows and 7 columns. We will learn how an array helps us understand a larger shape by looking at the smaller shapes inside. Learning more about arrays will help us notice patterns and structure—an important skill for multiplication and division.

On the cover Farbtafel “qu 1,” 1930 Paul Klee, Swiss, 1879–1940 Pastel on paste paint on paper, mounted on cardboard Kunstmuseum Basel, Basel, Switzerland Paul Klee (1879–1940), Farbtafel “qu 1” (Colour Table “Qu 1” ), 1930, 71. Pastel on coloured paste on paper on cardboard, 37.3 x 46.8 cm. Kunstmuseum Basel, Kupferstichkabinett, Schenkung der KleeGesellschaft, Bern. © 2020 Artists Rights Society (ARS), New York.

ISBN 978-1-64497-648-7

9

781644 976487