EM2_G2_M1_Apply_23B_976425_Updated 04.23

2

A Story of Units®

Ten Tens Module 1 ▸ Place Value Concepts Through Metric Measurement and Data · Place Value, Counting, and Comparing Within 1,000

Student

APPLY

A Story of Units®

Ten Tens ▸ 2 APPLY

Module

1 2 3 4 5 6

Place Value Concepts Through Metric Measurement and Data ∙ Place Value, Counting, and Comparing Within 1,000

Addition and Subtraction Within 200

Shapes and Time with Fraction Concepts

Addition and Subtraction Within 1,000

Money, Data, and Customary Measurement

Multiplication and Division Foundations

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 978-1-64497-642-5

EUREKA MATH2 2 ▸ M1

Contents Part 1: Place Value Concepts Through Metric Measurement and Data Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Topic C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Represent Data to Solve Problems

Estimate, Measure, and Compare Lengths

Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Draw and label a picture graph to represent data.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Estimate and compare lengths.

Draw and label a bar graph to represent data.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Model and reason about the difference in length.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Use information presented in a bar graph to solve put together and take apart problems.

Estimate and measure height to model metric relationships.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Represent and compare students’ heights.

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

Use information presented in a bar graph to solve compare problems.

Topic B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Metric Measurement and Concepts About the Ruler Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Connect measurement to physical units by iterating a centimeter cube.

Topic D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Solve Compare Problems by Using the Ruler as a Number Line Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Use a measuring tape as a number line to add efficiently.

Make a 10 cm ruler and measure objects.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Use a measuring tape as a number line to subtract efficiently.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Measure lengths and relate 10 cm and 1 cm.

Represent and solve comparison problems by using measurement contexts.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Make a meter stick and measure with various tools.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Relate 1 cm, 10 cm, and 100 cm.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Reason about the relationship between the size of the unit and the number of units needed to measure.

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Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Solve compare with difference unknown word problems by using measurement contexts.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Solve compare with difference unknown word problems in various contexts.

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EUREKA MATH2

2 ▸ M1

Contents Part 2: Place Value, Counting, and Comparing Within 1,000 Topic E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Lesson 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Understand Place Value Units

Determine how many $10 bills are equal to $1,000.

Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Topic H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Count and bundle ones, tens, and hundreds to 1,000.

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Count efficiently within 1,000 by using ones, tens, and hundreds.

Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Use counting strategies to solve add to with change unknown word problems.

Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Organize, count, and record a collection of objects.

Topic F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Express Three-Digit Numbers In Different Forms Lesson 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Count up to 1,000 by using place value units.

Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Write three-digit numbers in unit form and show the value that each digit represents.

Lesson 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Write base-ten numbers in expanded form.

Lesson 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Read, write, and relate base-ten numbers in all forms.

Topic G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Model Base-Ten Numbers Within 1,000 with Money Lesson 28. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Use place value understanding to count and exchange $1, $10, and $100 bills.

Compose and Decompose with Place Value Disks Lesson 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Count the total value of ones, tens, and hundreds with place value disks.

Lesson 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Exchange 10 ones for 1 ten, 10 tens for 1 hundred, and 10 hundreds for 1 thousand.

Lesson 33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Model numbers with more than 9 ones or 9 tens.

Lesson 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Problem solve in situations with more than 9 ones or 9 tens.

Topic I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Compare Two Three-Digit Numbers In Different Forms Lesson 35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Compare three-digit numbers by using >, =, and <.

Lesson 36. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Apply place value understanding to compare by using >, =, and <.

Lesson 37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Organize, count, represent, and compare a collection of objects.

Lesson 38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Compare numbers in different forms.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 196

Lesson 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Count by $1, $10, and $100.

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Module 1 Topic A

FAMILY MATH Represent Data to Solve Problems Dear Family, Key Terms

Your student begins the year by collecting and representing data in tables and graphs. These activities show that math is part of the world around them. Your student explores how the same data can be represented in different graphs, such as a picture graph and a bar graph, and then uses the information in the graphs to solve problems.

bar graph

category

data

key

scale

table

Favorite Subject

Favorite Subject Reading

5

Writing

4

Math

9

Science

6

✓ ✓ ✓ ✓ ✓

Reading

This table shows the number of students who voted for each subject.

✓ ✓ ✓ ✓

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

Key: Each ✓stands for 1 vote.

Writing

Math

Our Birthdays Spring

✓ ✓ ✓ ✓ ✓ ✓

Summer

Fall

Winter

0

1

2

3

4

5

6

7

8

9

10

11

Science

In this picture graph, the categories are Reading, Writing, Math, and Science.

The key shows that each check mark stands for 1 vote.

In a bar graph, the value of each category is represented by rectangular bars. The scale on this bar graph counts by 1. Each blue box represents 1 birthday.

At-Home Activities Go on a Nature Walk Invite your student on a walk around your neighborhood or a park. Have them count or collect three or four types of objects they see, such as leaves, rocks, and sticks. Help your student make a table and use it to record the number of each object they saw. Consider asking questions about the data they’ve collected.

•

“How many objects did you find in all?”

•

“Which type of object did you find the most of?”

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3

2 ▸ M1 ▸ TA

•

“Which type of object did you find the least of?”

•

“How many more leaves did you find than rocks?”

•

“How many fewer sticks did you find than leaves?”

EUREKA MATH2

Make Real-World Graphs Encourage your student to collect data about something around their home or in their daily life (such as the number of different-colored cars that go by in 10 minutes or the number of plates, bowls, and cups in the kitchen). Use stickers or sticky notes to make a picture graph that includes a key. Then use the data to make a bar graph with a title and a scale.

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FA M I LY M AT H ▸ Module 1 ▸ Topic A

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 1

1

Name

Vegetables We Like

1. Make a picture graph.

Vegetables We Like

Broccoli Carrots Celery

Lettuce A table is a chart that shows information.

Pieces of information are called data.

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✓

2

✓ ✓

9

✓ ✓

3

✓ ✓

6 ✓ ✓

✓ ✓

✓

Carrots

✓

✓

✓

✓

✓

Key: Each ✓ stands for

Broccoli

✓

Celery

✓ ✓

Lettuce 1 vote.

First, I give the graph a title. I can use the title from the table, “Vegetables We Like.”

Next, I write the categories at the bottom of the graph. I use the same categories as the table: Broccoli, Carrots, Celery, and Lettuce.

I draw 1 check mark for each vote.

I need to make a key to show the value of the unit in my graph. My key is “Each ✓ stands for 1 vote.”

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EUREKA MATH2

2 ▸ M1 ▸ TA ▸ Lesson 1

2. Which vegetable has the fewest votes?

3. Which vegetable has the most votes?

Broccoli Carrots

Vegetables We Like

✓

I can use the data in the graph to answer the questions.

✓ ✓ ✓

✓

✓ ✓ ✓

✓ ✓

6

Carrots

✓

✓

✓

Key: Each ✓ stands for

Broccoli

✓

✓

✓ ✓

✓

Celery

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

✓

✓

I know that 1 check mark stands for 1 vote.

I see that broccoli has the fewest check marks.

So broccoli has the fewest votes.

Carrots has the most check marks. So carrots has the most votes.

Lettuce 1 vote.

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 1

REMEMBER 4.

Read

I read the problem. I read again.

The grasshopper is 3 centimeters long.

I can use a 10-stick and centimeter cubes to compare the lengths.

The bird is 13 centimeters long.

I see 3 centimeter cubes show the length of the grasshopper.

How much longer is the bird than the grasshopper?

I see one 10-stick and 3 centimeter cubes show the length of the bird.

Grasshopper Bird

Draw I can draw a picture to match the cubes. I can draw 3 centimeter cubes to match the length of the grasshopper and a 10-stick and 3 centimeter cubes to match the length of the bird. I can see that the length of the bird is 10 centimeters longer than the grasshopper.

Write

Sample:

3 + 10 = 13 The bird is Copyright © Great Minds PBC

10

centimeters longer than the grasshopper.

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

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 1

1

Name

1. Make a picture graph.

Fruit We Like Apples Bananas Grapes Oranges

8 7 4 9

Key: Each

stands for

vote.

2. Which fruit has the fewest votes?

3. Which fruit has the most votes?

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EUREKA MATH2

2 ▸ M1 ▸ TA ▸ Lesson 1

REMEMBER 4.

Read The bee is 4 centimeters long.

The frog is 14 centimeters long.

How much longer is the frog than the bee?

Bee Frog

Draw

Write

The frog is 10

P R ACT I C E

centimeters longer than the bee.

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 2

2

Name

1. Make a bar graph.

Favorite Season Spring Summer Fall

3 9

Favorite Season

Spring Summer Fall

5

Winter 0

Winter

1

2 3 4 5 6 7 8 9 10 11

2

I give the bar graph a title. I use the title in the table, “Favorite Season.”

There are four categories: Spring, Summer, Fall, and Winter. I write these on the bar graph.

The scale is a number line that shows the value of each unit. Each box stands for 1 vote, so I fill in the scale along the bottom of the graph from 0 to 11.

Spring has 3 votes. I color in 3 boxes on the graph.

I color in 1 box for each vote for the rest of the seasons.

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EUREKA MATH2

2 ▸ M1 ▸ TA ▸ Lesson 2

Summer

2. Which season got the most votes?

3. Which season got the fewest votes?

Winter

Summer has the longest bar.

Summer got the most votes.

Winter has the shortest bar.

Winter got the fewest votes.

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

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 2

2

Name

1. Make a bar graph.

Snacks We Like Carrots

Cookies

Crackers

Blueberries

5

8

3

7

0 2. Which snack has the most votes?

3. Which snack has the fewest votes?

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13

EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 3

3

Name

Shoes We Like to Wear Flip Flops

Dress Shoes

Boots

Tennis Shoes

0

1

2

3

4

1. How many votes are there in all?

Write a number sentence.

5

6

7

8

9

10

11

18 8 + 1 + 3 + 6 = 18

I count the votes for each category: 8 students voted for Flip Flops 1 student voted for Dress Shoes.

3 students voted for Boots.

6 students voted for Tennis Shoes.

8 + 1 + 3 + 6 = 18 9 9 9 + 9 = 18 Copyright © Great Minds PBC

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EUREKA MATH2

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2. Add 3 more votes for Flip Flops.

How many votes for Flip Flops are there now?

What is the new vote total?

The graph shows a total of 18 votes.

11

21

The graph shows that 8 students like Flip Flops.

I add 3 more votes to the total.

I add 3 more votes for Flip Flops.

18 + 3 = 21

8 + 3 = 11

REMEMBER 3. Color the faces of the shape.

A face is a flat surface.

A rectangular prism has six faces.

The faces are squares and rectangles.

I color the square and the rectangle.

square

Rectangular Prism rectangle

16

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

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 3

3

Name

Toys We Like Doll

Jump Rope

Toy Car

Ball

0

1

2

3

4

5

6

7

8

9

10

11

1. How many votes are there in all?

Write a number sentence.

2. Add 2 more votes for the ball.

How many votes are for the ball now?

How many votes are there in all now?

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EUREKA MATH2

2 ▸ M1 ▸ TA ▸ Lesson 3

REMEMBER

3. Color the faces of the shape.

Square Pyramid

18

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 4

4

Name

Animals at the Zoo

I can match up the colored boxes, 1 frog to 1 lizard.

11 10 9 8 7 6 5 4 3 2 1 0 Alligators Frogs

Then I count the extra boxes.

There are 5 more frogs than lizards at the zoo.

Animals at the Zoo

11 10 9 8 7 6 5 4 3 2 1 0 Alligators Frogs

Lizards Snakes

Lizards Snakes

I can match up the colored boxes, 1 alligator to 1 snake.

Then I count the empty boxes.

1. How many more frogs than lizards are there at the zoo?

5

Animals at the Zoo

2. How many fewer alligators than snakes are there at the zoo?

There are 6 fewer alligators than snakes at the zoo.

6

11 10 9 8 7 6 5 4 3 2 1 0 Alligators Frogs

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Lizards Snakes

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EUREKA MATH2 2 ▸ M1 ▸ TA ▸ Lesson 4

4

Name

Fruit in a Bowl Strawberries

Pears

Cherries

Blueberries

0

1

2

3

4

5

6

7

8

9

10

11

1. How many more blueberries than cherries are there?

2. How many more strawberries than pears are there?

3. How many fewer pears than cherries are there?

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21

Module 1 Topic B

FAMILY MATH Metric Measurement and Concepts About the Ruler Dear Family, Key Terms

Your student is learning that metric measurement is related to meter place value, as both include units of ones, tens, hundreds, and tick mark thousands. Your student uses centimeter cubes to measure objects and they make their own 10-centimeter ruler. As they practice measuring objects, your student comes to understand that the tick marks on the ruler represent the distance, or length units, from zero. Your student begins to select appropriate measuring tools based on the size and shape of objects.

I can make my own 10-centimeter ruler by using a centimeter cube to draw tick marks on a paper strip.

I can use ten 10-centimeter rulers to make a meter stick. 100 centimeters is equal to 1 meter.

At-Home Activities Measure with a Centimeter Ruler Encourage your student to find familiar objects that can be measured with a centimeter ruler.

For example, they may choose objects such as a toy car, a book, or a television remote. Help your student find the length of each object in centimeters.

Scavenger Hunt Encourage your student to find objects around the house that can be measured with a centimeter ruler (a key, a toothbrush, a book) or a meter stick (a table, a desk, the countertop).

Ask your student whether they would measure the length with a centimeter ruler or a meter stick and to explain why.

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23

EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 5

5

Name

1. Use the centimeter tile to find the length.

The pencil is

6

centimeter tiles long.

I cut out the centimeter tile and use it to measure.

I line up my tile with the end of the pencil. I mark where the tile ends. The mark I make at the end of the tile is called a tick mark.

I move the tile forward and make another tick mark. I do not leave any gaps. I do this until I get to the end of the pencil.

There are 6 spaces. Each space is 1 centimeter.

The pencil is 6 centimeter tiles long.

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25

EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 5

REMEMBER

Instruments We Like Drum

Trumpet

Guitar

Voice

0

1

2

3

4 5 6 7 8 9 2. What is the title of the graph? Instruments We Like 3. How many kinds of instruments are on the graph?

4. What instrument got the most votes?

5. What instrument got the fewest votes?

4

Guitar Trumpet

10

11

Guitar has 10 votes. It has the most votes.

Trumpet has 4 votes. It has the fewest votes.

Each blue square is equal to 1 vote.

I can count the squares to find the total number of votes for each instrument.

I count 8 votes for Drum.

I count 4 votes for Trumpet.

I count 10 votes for Guitar. I count 7 votes for Voice.

26

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

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 5

5

Name

Cut out the centimeter tile.

Use the centimeter tile to find the length.

1.

The dog bone is ​

​centimeter tiles long.

2.

The eye dropper is

​centimeter tiles long.

3. Pick an object. Use the line as an endpoint.

Measure the object with the centimeter tile.

The

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is

centimeter tiles long.

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EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 5

REMEMBER

Toys We Like Teddy Bear

Ball

Skateboard

Robot

0

1

2

3

4

5

6

7

8

9 10

11

4. What is the title of the graph?

5. How many kinds of toys are on the graph?

6. What toy got the most votes?

7. What toy got the fewest votes?

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P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 6

6

Name

Use your 10 cm ruler to measure.

1. The bow is

4

cm long.

I line up the edge of the ruler with the endpoint of the bow.

The numbers on a ruler tell me how many spaces or centimeters away from 0.

1

2

3 4

5

6 7

8

9 10

The bow is 4 cm long.

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EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 6

2. The fork is

14

cm long.

I line up the edge of the ruler with the endpoint of the fork.

The fork is longer than the 10 cm ruler.

I make a mark for 10 cm. I move the ruler to measure to the end of the fork.

1

2 3 4 5 6 7 8 9 10

1

2 3 4 5 6 7 8 9 10

I add the lengths.

10 + 4 = 14 The fork is 14 cm long.

30

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

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 6

6

Name

Cut out the 10 cm ruler.

Use the 10 cm ruler to measure.

1. The ticket is

cm long.

2. The spoon is

cm long.

1

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2

3

4

5

6 7

8

9 10

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 7

7

Name

1. Lan measures two ways.

Lan’s flashlight is 24 cm long.

He uses He uses

24 2

1 cm cubes.

4

10 cm rulers and

1 cm cubes.

I know that a 10 cm ruler is made up of ten 1 cm cubes.

I can measure 24 cm two ways. I can use twenty-four 1 cm cubes. Or I can use two 10 cm rulers and four 1 cm cubes.

24 cm

10 cm 1

2 3 4 5

4 cm

6 7 8 9 10

1

10 cm 2 3 4 5

6 7 8 9 10

10 + 10 + 4 = 24

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EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 7

2. Ling measures her skateboard. She uses five 10 cm rulers and eight 1 cm cubes.

Ling thinks her skateboard is 58 cm long.

Is she correct?

Ling is correct.

Sample: Show how you know. Sample:

10

10

10

10

10

1

1

1

1

1

1

1

1

50 cm + 8 cm = 58 cm

A 10 cm ruler is made up of 10 centimeters.

Five 10 cm rulers is the same length as 50 centimeters.

Eight 1 cm cubes is the same as 8 centimeters.

I can add 50 and 8.

The skateboard is 58 cm long.

34

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

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 7

REMEMBER 3. Use the 10-sticks and cubes.

Draw the tens and ones.

I count the 10-sticks and cubes.

I see 3 sticks of ten cubes and 12 extra cubes.

4 42

tens

2

ones

I can make another group of 10.

I compose ten ones into a group of 10.

total

Now I can draw 4 tens 2 ones.

I count the tens and ones to find the total.

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

35

EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 7

7

Name

Each friend measures two ways.

1. Hope’s stapler is 15 cm long.

She uses

1 cm cubes.

She uses

10 cm ruler and

1 cm cubes.

2. Matt’s gift is 26 cm long.

He uses

1 cm cubes.

He uses

10 cm rulers and

1 cm cubes.

3. Ann measures her desk. She uses six 10 cm rulers and five 1 cm cubes.

Ann thinks her desk is 56 cm long.

Is she correct?

Show how you know.

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37

EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 7

REMEMBER 4. Use the 10-sticks and cubes.

Draw the tens and ones.

tens

ones total

38

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 8

8

Name

Circle the tool you would use to measure each object.

1. The length around a balloon 1 cm cube

10 cm ruler

I can measure objects shorter than 10 cm with a 1 cm cube or a 10 cm ruler.

I can measure round objects with a measuring tape.

I can measure large objects with a meter stick. A meter is 100 cm.

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meter stick

measuring tape

The balloon is round. I will use a measuring tape to measure the length around the balloon.

39

EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 8

2. The length of a peanut 1 cm cube

10 cm ruler

meter stick

measuring tape

A peanut is shorter than a 10 cm ruler.

1

2

3 4

5

6 7

8

9 10

I can measure it with centimeter cubes.

3. The length of a sofa 1 cm cube

10 cm ruler

meter stick

measuring tape

A sofa is much longer than a 10 cm ruler.

I can measure it with a meter stick.

2 meters

40

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

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 8

8

Name

Circle the tool you would use to measure each object.

1. The length of a cracker 1 cm cube

10 cm ruler

meter stick

measuring tape

meter stick

measuring tape

meter stick

measuring tape

2. The length around a ball 1 cm cube

10 cm ruler

3. The length of a car 1 cm cube

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10 cm ruler

41

EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 9

9

Name

1. Circle the true statements.

5 m is the same length as 500 cm.

2 cm is the same length as 200 m.

1 m is the same length as 10 cm.

3 m 14 cm is the same length as 314 cm.

I know that 1 m is 100 cm.

So, 5 m is 500 cm. This is true!

2 cm is much shorter than 200 m.

1 m is 100 cm, not 10 cm.

3 m is 300 cm, so 3 m 14 cm is the same length as 314 cm. This is true!

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43

EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 9

2. A table is 127 cm long.

How can you make 127 cm with these units?

1 1 12

100 cm (1 m) 100 cm (1 m) 10 cm

7

2 27

10 cm

7

1 cm

1 cm

1 cm

I know that 1 m is 100 cm.

127 cm is 100 cm + 20 cm + 7 cm.

127 cm is 100 cm + 27 cm.

127 cm is twelve 10 cm and 7 cm.

Metric Units Chart

100 cm (1 m) 1

10 cm 2

1

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

7

27 12

44

1 cm

7

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 9

REMEMBER

3. Shade the triangle.

I color the triangle to make a new shape.

Trace the new shape.

4

Then I trace the outside of the shape and count the sides.

2 sides

What is the composed shape? rhombus

1

3 4

4. Add. Show how you know.

51 + 39 = 90 50 1 30 9 50 + 30 = 80 1 + 9 = 10 80 + 10 = 90

The composed shape has 4 sides that are the same length and 2 pairs of parallel sides.

It is a rhombus.

I can make the problem easier.

I break apart both numbers into tens and ones.

51 is 50 and 1. 39 is 30 and 9.

I add the tens. I add the ones.

The new equation is 80 + 10 = 90.

So, 51 + 39 = 90.

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

45

EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 9

9

Name

1. Circle the true statements.

3 cm is the same length as 300 m.

2 m is the same length as 200 cm.

1 m 25 cm is the same length as 125 cm.

10 cm is the same length as 1 m.

2. A sofa is 192 cm long.

How can you make 192 cm with these units?

100 cm (1 m)

10 cm

100 cm (1 m)

1 cm

10 cm

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1 cm

1 cm

47

EUREKA MATH2

2 ▸ M1 ▸ TB ▸ Lesson 9

REMEMBER

3. Shade the triangles.

Trace the new shape.

sides

What is the composed shape?

4. Add. Show how you know.

38 + 22 =

48

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 10

10

Name Cubit 1. Measure with cubits . Then measure with palms. Sample:

Object

Cubit Cubits

Palms

1

5

2. Circle the true statement.

Cubit It will take more cubits than palms to measure the length of a bed.

Cubit It will take more palms than cubits to measure the length of a bed.

A cubit is the length from my fingertips to my elbow.

I can use cubits to measure the shirt.

A palm is the width of my four fingers. I can use palms to measure the shirt again.

A palm is a smaller unit than a cubit.

It will take more palms than cubits to measure the length of a bed.

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49

EUREKA MATH2 2 ▸ M1 ▸ TB ▸ Lesson 10

10

Name Cubit

1. Measure with cubits. Then measure with palms.

Object

Cubit

Cubits

Palms

2. Circle the true statement.

Cubit It will take more palms than cubits to measure the length of a bike.

Cubit than palms to measure the length of a bike.

It will take more cubits

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51

Module 1 Topic C

FAMILY MATH Estimate, Measure, and Compare Lengths Dear Family, Key Terms

Your student is learning to make an estimate, or a thoughtful guess, for the length of familiar objects. They learn to draw tape diagrams to represent the difference between their estimate and the actual measurement. Then your student can use addition and subtraction number sentences to compare and solve.

benchmark difference estimate

Estimate benchmark “about 10 cm”

20

About how long?

E estimate

M

20 16 16 + 4 = 20

My pinkie finger is about 1 cm. I can use that as a benchmark to estimate the length of a pencil.

4

E

16 20

M

16

4

20 – 4 = 16

I can see the difference between 16 and 20 by comparing the tape diagrams.

At-Home Activities Estimate in Meters Use the distance from the floor to a doorknob as a benchmark for 1 meter. With your student, find objects around the house that are about 1 meter, such as the length of a desk, the height

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53

EUREKA MATH2

2 ▸ M1 ▸ TC

of a table, or the width of a window. Consider continuing the activity by looking for objects that are longer than 1 meter, such as the length of a sofa, length of a countertop, or the height of a door, and discuss the estimates.

Estimate and Measure in Centimeters Knowing that the width of their pinkie finger is about 1 centimeter, have your student estimate the length of familiar objects, such as a fork or a marker. Then take turns estimating and then measuring the length of items, such as a shoe or a tissue box. Have your student find and explain the difference between the estimate and actual measurement.

1

54

2

3 4

FA M I LY M AT H ▸ Module 1 ▸ Topic C

5

6 7

8

9 10

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 11

11

Name

1. Estimate the length of the cracker. Then measure.

Sample: Estimate:

4

cm

Estimate benchmark

“about 10 cm”

About how long? estimate

An estimate is a thoughtful guess.

A benchmark is something I can use to estimate the length of an object.

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5

Measurement:

cm

I can use my pinkie finger as a benchmark.. My pinkie finger is about 1 cm wide.

I estimate the square cracker to be about 4 cm long.

I measure the length by using a 10 cm ruler.

1

2

3 4

5

6 7

8

9 10

5 cm

The measurement of the cracker is 5 cm.

55

EUREKA MATH2

2 ▸ M1 ▸ TC ▸ Lesson 11

2. Pick one of the objects you measured.

Show the difference in length between the estimate and the measurement.

Sample:

E

4

M The difference is

4+1=5 5

1

cm.

I pick the square cracker.

I draw a tape diagram to show my estimate and my measurement.

E

4

M

5

4 is 1 less than 5.

So, the difference is 1.

56

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

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 11

REMEMBER

3. Draw and write a number sentence to compare. tens

ones

tens

ones

2

0

1

10

20

=

20

I look at the place value charts. I draw quick tens to show the numbers.

I see 2 tens 0 ones and 1 ten 10 ones.

I see a group of 10 ones. I can compose 10 ones into 1 ten.

I compare my drawings.

= I know 2 tens have a value of 20 20..

The place value charts both represent 20 20..

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

57

EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 11

11

Name

Cut out the 10 cm ruler.

1. Estimate the length of each pencil. Then measure.

Estimate:

cm

Measurement:

cm

Estimate:

cm

Measurement:

cm

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59

EUREKA MATH2

2 ▸ M1 ▸ TC ▸ Lesson 11

2. Pick one of the pencils you measured.

Show the difference in length between your estimate and the measurement.

The difference in length is

cm.

REMEMBER

3. Draw and write a number sentence to compare. tens

ones

tens

ones

8

10

9

0

1

60

P R ACT I C E

2

3 4

5

6 7

8

9 10

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 12

12

Name

1. Measure the object. Fill in the blank.

I estimate it is 10 cm long.

Measurement:

11

cm

To find the length of the envelope, I can use centimeter cubes or a 10 cm ruler.

The length of the envelope is 11 cm.

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61

EUREKA MATH2

2 ▸ M1 ▸ TC ▸ Lesson 12

2. Show the difference in length two ways. Write an equation for each way.

E

10

M

11

1

E

10

M

10 11

1

11

10 + 1 = 11 The difference in length is

1

cm.

The difference is the distance between two lengths.

E M

20

11 - 1 = 10 I can draw a tape diagram to compare the measurements.

The estimate is 10 cm. The measurement is 11 cm.

E

10

M

11

1

10 + 1 = 11

I can count on to show the difference.

16 difference

I start with the part I know and count on to 11 11..

11 is 1 more than 10 10..

The difference is 1.

E

10

M

10 11

1

11 – 1 = 10

11 I can count back to show the difference.

I start at the total and count back to 10 10..

10 is 1 less than 11 11..

The difference in length is 1 cm.

62

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

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 12

12

Name

1. Measure the object. Fill in the blank.

I estimate it is 5 cm long.

Measurement:

cm

2. Show the difference in length two ways. Write an equation for each way.

The difference in length is

1

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2

3 4

cm

5

6 7

8

9 10 63

EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 13

13

Name

1. How tall is each friend?

Friend

Height

Height (in centimeters)

1 meter stick 3 10 cm rulers Pam

135 cm

5 centimeter cubes

1 meter stick 17 centimeter cubes

117 cm

Lan I know that 1 m is 100 cm.

Three 10 cm rulers is 30 cm.

5 centimeter cubes is 5 cm.

100 + 30 + 5 = 135 135..

Pam is 135 cm tall.

1 m is 100 cm and 17 centimeter cubes is 17 cm.

100 + 17 = 117 117..

Lan is 117 cm tall.

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65

EUREKA MATH2

2 ▸ M1 ▸ TC ▸ Lesson 13

2. Jade is 124 cm tall. How many of each do you need?

1

2

meter sticks

10 cm rulers

4

centimeter cubes

124 = 100 + 20 + 4 I know that 1 meter is 100 cm, so I can use 1 meter stick.

Two 10 cm rulers is 20 cm.

4 centimeter cubes is 4 cm.

100

10

10

1 1 1 1

124 cm

3. Write another way to measure Jade’s height.

0

12

meter sticks

10 cm rulers

4

centimeter cubes

I know a meter stick is 100 cm.

I get 100 cm if I put ten 10 cm rulers together.

10

10

10

10

10

10

10

10

10

10

100 cm

Two 10 cm rulers is 20 cm.

I add on 2 more 10 cm rulers.

Twelve 10 cm rulers is 120 cm.

10

10

10

10

10

10

10

10

10

10

10

10

120 cm

4 centimeter cubes is 4 cm.

120 + 4 = 124 66

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

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 13

REMEMBER

4. Circle the word that matches the parts. halves fourths How many equal parts?

4

The cracker is partitioned into equal parts.

I see 4 equal parts.

I know 4 equal parts is the same as fourths.

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

67

EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 13

13

Name

1. How tall is each friend?

Friend

Height

Height (in centimeters)

1 meter stick 2 10 cm rulers 8 centimeter cubes Kevin

9 10 cm rulers 3 centimeter cubes Kate 2. Nick is 112 cm tall. How many of each do you need? meter sticks

10 cm rulers

centimeter cubes

3. Write another way to measure Nick’s height. meter sticks

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10 cm rulers

centimeter cubes

69

2 ▸ M1 ▸ TC ▸ Lesson 13

EUREKA MATH2

REMEMBER 4. Circle the word that matches the parts.

halves quarters How many equal parts?

70

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 14

14

Name

Kevin and Jack are different heights.

Kevin 149 cm

Jack 141 cm

I can draw a tape diagram to represent the heights.

K

149

J

141 8 141 + 8 = 149

I show the difference by counting on.

I start at 141 and count on to 149 149..

149 is 8 more than 141 141..

So, the difference is 8 cm.

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71

EUREKA MATH2

2 ▸ M1 ▸ TC ▸ Lesson 14

1. Show the difference in height two ways. Write an equation for each way.

149 K

149

J

141

K

141

J

8

149

8

141

141 141 ++ 88 == 149 149

149 149 –– 88 == 141 141

The difference in height is

8

cm.

I can use addition to find the difference in height.

K

149

J

141 8

141 + 8 = 149 I can also use subtraction to find the difference in height.

149 K J

141

149

8

141 149 – 8 = 141

72

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

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EUREKA MATH2 2 ▸ M1 ▸ TC ▸ Lesson 14

14

Name

Beth and Kate have different heights.

Beth 132 cm

Kate 136 cm

1. Show the difference in height two ways. Write an equation for each way.

The difference in height is

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cm.

73

Module 1 Topic D

FAMILY MATH Solve Compare Problems by Using the Ruler as a Number Line Dear Family,

Your student is learning to use a number line to add. They see a number line on a familiar tool—a measuring tape. The number line can help them count and make hops up and back as they solve problems. Your student looks for benchmark numbers (10, 20, 30, 40) on the number line. Benchmark numbers help your student add and subtract more efficiently.

Your student also uses tape diagrams to represent word problems. Flexibility is encouraged as they solve in a way that makes sense to them. Flexible thinking allows your student to notice the relationship between addition and subtraction and discover that different equations can be used to solve the same problem.

+4

To add 76 and 7, begin at 76 on the number line.

+3

Instead of counting by ones, hop 4 to get to the benchmark number 80.

70

76

80

83

90

Then hop 3 more to finish adding 7.

76 + 7 = 83

– 10

– 10

–4

30

40 54 – 4 = 50 50 – 10 = 40 40 – 10 = 30 54 – 24 = 30

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50

54

J

Choose to subtract or add to find the difference between 54 and 30.

54

T 30

?

30 + 10 = 40 40 + 10 = 50 50 + 4 = 54 30 + 24 = 54

To subtract, start at 54. Break apart 30 and count back.

To add, start at 30. Break apart 54 and count on.

75

EUREKA MATH2

2 ▸ M1 ▸ TD

At-Home Activity Benchmark Math Have your student practice using benchmark numbers to compare numbers. For example, “Use a benchmark number to find the difference between 26 and 33.” Your student can start at 26 and add 4 to get to 30 and then add 3 more to get to 33. Or they may show 4 fingers to add 4 all at once to get to 30 and then use their fingers to track counting on: 31, 32, 33. Your student may also draw a number line or tape diagram to show their thinking.

30

76

FA M I LY M AT H ▸ Module 1 ▸ Topic D

33 31

32

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EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 15

15

Name

1. Write the numbers on the number line.

43 50 48 55 40

43

A number line is a line with numbers and tick marks.

48

50

55

60

Each tick mark on this number line shows an equal length unit of 1.

I know the numbers increase from left to right on the number line. So, I put the numbers in order from least to greatest.

43 48 50 55 I begin at 40 40.. I touch each tick mark as I count on to 43 43.. I label that tick mark 43 43..

I touch each tick mark as I count on from 43 to 48 48.. I label that tick mark 48 48..

I keep counting on to label the tick marks for 50 and 55 55..

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77

EUREKA MATH2

2 ▸ M1 ▸ TD ▸ Lesson 15

2. Use the number line to add.

38 + 5 =

43 +2

30

A benchmark number is a number that helps me add or subtract.

38

+3

40

43

50

I label 38 on the number line.

30

38 40

50

The next ten is 40 40.. I can use 40 as a benchmark number.

I hop 2 from 38 to 40 40.. +2

30

38 40

50

I need to add 5. I already added 2.

2 and 3 is 5.

I hop 3 more from 40 to 43 43.. +2 +3

30

38 40

43

50

The number line shows that 38 + 5 = 43 43..

78

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

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EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 15

REMEMBER 3. Count up.

Write the numbers.

103, 104, 105, 106 , 107 , 108 , 109 , 110 37, 47, 57, 67 , 77 , 87 , 97 , 107 Patterns tell me which way to count.

I see the numbers go in order.

I count by ones to finish the first pattern. +1

+1

+1

+1

+1

105, 106, 107, 108, 109, 110 I count by tens to finish the second pattern. + 10 + 10 + 10 + 10 + 10

57, 67, 77, 87, 97, 107

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

79

EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 15

15

Name

1. Write the numbers on the number line.

30 25 28 37

20

40

Use the number line to add.

2. 35 + 8 =

30

40

50

50

60

3. 46 + 8 =

40

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81

EUREKA MATH2

2 ▸ M1 ▸ TD ▸ Lesson 15

REMEMBER 4. Count up.

Write the numbers.

82

113, 114, 115,

,

,

,

,

42, 52, 62,

,

,

,

,

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 16

16

Name

Use the number line to subtract.

1. 56 – 8 =

48 –2

48

40

-6

56

50

60

I label 56 56.. I know 50 is a benchmark number close to 56 56..

56 is 6 more than 50 50.. I hop back 6 to 50 50..

–6

40

56

50

60

I need to subtract 8. I already subtracted 6.

I know that 6 and 2 is 8.

So, I hop back 2 more.

–2

40

–6

48 50

56

60

I land on 48 48..

56 - 8 = 48 Copyright © Great Minds PBC

83

EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 16

16

Name

Use the number line to subtract.

1. 57 – 7 =

40

50

60

60

70

70

80

2. 64 – 6 =

50

3. 75 – 8 =

60

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85

EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 17

17

Name

1. How much farther does the big bee fly than the little bee?

57 cm

70 cm +3

+ 10

55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

Write an equation.

57 + 13 = 70

The big bee flies 13 cm farther than the little bee.

I can count on to find the difference between 57 and 70 70..

I start at 57 57.. I can use 60 as a benchmark number. I hop 3 from 57 to 60 60..

I hop 10 from 60 to 70 70..

I know 10 and 3 is 13 13..

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87

EUREKA MATH2

2 ▸ M1 ▸ TD ▸ Lesson 17

2. How much farther does the blue butterfly fly than the green butterfly?

181

181 cm

167 cm

14 cm ?

167 cm

181 – 14 = 167

Write an equation.

The blue butterfly flies 14 cm farther than the green butterfly.

I can use subtraction to find the difference.

I draw a number line to find the difference between how far each butterfly flies.

I count back 1 from 181 to get to 180 180..

I count back 10 from 180 to get to 170 170..

I count back 3 more to 167 167..

–3

160

167 170

– 10

–1

180

190

I subtracted 14 in all to get to 167 167..

88

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

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EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 17

REMEMBER 3.

Read Hope has 13 tennis balls.

Then she finds 5 more tennis balls.

How many tennis balls does Hope have now?

I read the problem. I read again. As I reread, I think about what I can draw.

I draw 13 solid dots to represent the tennis balls Hope has.

Then I can draw 5 open dots to represent the tennis balls she finds.

Draw

I’m trying to find how many tennis balls Hope has now.

10

3

5

10 + 3 + 5 = 18

I need to add 13 and 5.

I see a group of ten. I can circle ten dots.

I know 3 + 5 = 8 and 10 + 8 = 18 18..

10 + 8

I can write a number sentence to record my thinking. I add the ones first and then I add the ten.

Write

13 + 5 = 18 Hope has Copyright © Great Minds PBC

18

tennis balls now.

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

89

EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 17

17

Name

1. How much farther does the big bird go than the little bird?

68 cm 68 cm

80 cm 80 cm

65 66 67 68 69 70

65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80

Write an equation.

The big bird goes

farther than the little bird.

2. How much farther does the squirrel jump than the grasshopper?

Write an equation.

132 cm The squirrel jumps than the grasshopper.

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farther

117 cm

91

EUREKA MATH2

2 ▸ M1 ▸ TD ▸ Lesson 17

REMEMBER 3.

Read Tim sees 14 worms in the street.

He sees 5 worms in the grass.

How many worms does Tim see in all?

Draw

Write

Tim sees 92

P R ACT I C E

worms in all.

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EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 18

18

Name

Read

I read the problem.

Matt rides 53 miles on a train.

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

Jill rides 26 miles on a bus.

How many more miles does Matt ride than Jill?

Draw

M 26

?

‒4

26

- 20

30

I draw one tape to represent the miles Matt travels and one to represent the miles Jill travels I know I need to find the difference between 53 and 26 26..

I can use benchmark numbers to count back.

53

J

I draw a tape diagram.

‒3

50 53

I draw a number line.

I start at 53 and hop back 3 to get to 50 50..

I hop back 20 more to get to 30 30..

I hop back 4 more to get to 26 26..

I hopped back 27 altogether.

Write

Sample:

53 – 27 = 26 Matt rides

27

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more miles than Jill.

93

EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 18

18

Name

Read Jack rides 41 miles in a car.

Beth rides 18 miles on a bike.

How many more miles does Jack ride than Beth?

Draw

Write

Jack rides Copyright © Great Minds PBC

more miles than Beth.

95

EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 19

19

Name

1.

Read Nick walks 64 steps.

Lee walks 40 steps.

I read the problem.

How many more steps does Nick walk than Lee?

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

Draw

I draw a tape diagram to show Nick’s steps and Lee’s steps.

N

64

E

40

?

40 + ? = 64

I can find the unknown number.

I start at 40 and count on to 64 64..

40 + 20 = 60 60 + 4 = 64

Write

Sample:

40 + 24 = 64 Nick walks Copyright © Great Minds PBC

24

more steps than Lee. 97

EUREKA MATH2

2 ▸ M1 ▸ TD ▸ Lesson 19

REMEMBER 2.

Read Zan has 9 tokens.

She gets some more tokens.

Now she has 18 tokens.

How many more tokens did Zan get?

I read the whole problem.

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

Draw

9

Zan has 9 tokens. I draw 9 solid dots.

She gets some more tokens. Now she has 18 tokens.

I can draw open dots as I count from 9 to 18 to find the unknown part.

Write

Sample:

9 + 9 = 18 Zan got 98

9

tokens.

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

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EUREKA MATH2 2 ▸ M1 ▸ TD ▸ Lesson 19

19

Name

1.

Read Tam has 55 blocks.

Kevin has 30 blocks.

How many more blocks does Tam have than Kevin?

Draw

Write

Tam has Copyright © Great Minds PBC

more blocks than Kevin.

99

EUREKA MATH2

2 ▸ M1 ▸ TD ▸ Lesson 19

REMEMBER 2.

Read Dan has 7 stamps.

He gets some more stamps.

Now he has 15 stamps.

How many more stamps did Dan get?

Draw

Write

Dan got 100

P R ACT I C E

stamps.

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Module 1 Topic E

FAMILY MATH Understand Place Value Units Dear Family, Your student is exploring place value units (ones, tens, hundreds) as they bundle, or group together, craft sticks. They notice bundling makes it easier to count and keep track of numbers.

For example, 10 of a smaller unit can be bundled to make 1 of the next larger unit. Your student also applies place value knowledge and drawings of bundles to solve addition problems.

They use benchmark numbers, such as 10 or 100, to help count and record collections of objects efficiently.

Key Terms hundred thousand value

100

1 ten 1 hundred 1 thousand

10 ones

160

10 tens

+6 64 70

64

?

+ 10

+ 10

+ 10 100

Ming should bike 36 more miles.

10 hundreds

260 270 280 290 300 310 311 312 The value of one craft stick is 1. The value of 10 ones is 1 ten, or 10. The value of 10 tens is 1 hundred, or 100. The value of 10 hundreds is 1 thousand, or 1,000.

Benchmark numbers make counting from 160 to 312 more efficient. Drawing sticks and bundles of 10 and 100 helps keep track of the count.

I can start at 64 and hop up to 100. I count the hops to find the unknown part.

At-Home Activities Scavenger Hunt Help your student make a list of numbers greater than 100 that they find around the house, such as the pages of a book, the oven temperature in a recipe, the quantity on a box of tissues or cotton swabs, or the number of grams on a package of food (such as a cereal box or can

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101

2 ▸ M1 ▸ TE

EUREKA MATH2

of soup). After your student creates a list of numbers, have them represent each number by drawing sticks and bundles of tens and hundreds.

How Much Older Are You? Have your student determine the difference between their age and your age. Consider asking them to draw individual sticks for ones and bundles for tens as they count on from their age.

When they reach your age, ask your student to count the sticks and bundles they drew to determine the age difference. Repeat with another person’s age.

102

FA M I LY M AT H ▸ Module 1 ▸ Topic E

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 20

20

Name

1. Fill in the blanks to match the picture.

2

hundreds

The value of something is what it’s worth or what it represents.

4

tens

2

ones

I count 2 bundles of hundred.

I count 4 bundles of ten.

I count 2 ones.

The value of this bundle is 1 hundred.

A single stick is 1 one.

This value of this bundle is 1 ten.

10 tens can be bundled to make 1 hundred. A hundred is the next larger unit after tens.

The value of this single stick is 1.

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10 ones can be bundled to make 1 ten. A ten is the next larger unit after ones.

10 hundreds make 1 thousand. A thousand is the next larger unit after hundreds.

103

EUREKA MATH2

2 ▸ M1 ▸ TE ▸ Lesson 20

2. Draw hundreds, tens, and ones.

952

hundred

tens hundredhundred

tens ones tens

I draw bundles and sticks to show the value of each place value unit.

I draw 9 hundreds.

I draw 5 tens.

I draw 2 ones.

104

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

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 20

20

Name

Fill in the blanks to match the picture.

1.

hundred

tens

ones

2.

hundreds hundreds hundreds hundreds

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tens tens tens tens

ones ones ones ones

105

EUREKA MATH2

2 ▸ M1 ▸ TE ▸ Lesson 20

Draw hundreds, tens, and ones.

262

4. 509 hundred

5. 394

6. 815

3.

106

P R ACT I C E

tens hundredhundred

tens ones tens

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 21

21

Name

1. Draw units to count from 37 to 200.

Sample:

38 39 40 50 60 70 80 90 10

37

38 39 40 50 60 70 80 90 100 200 The next ten is 40. I draw ones to get to 40.

38 39 40

37

Next, I draw tens to get to 100.

37

38 39 40 50 60 70 80 90 100

Last, I draw 1 hundred to get to 200.

37

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38 39 40 50 60 70 80 90 100 200

107

EUREKA MATH2

2 ▸ M1 ▸ TE ▸ Lesson 21

2. Draw units to count from 222 to 600. Sample:

222

223 224 225 226 227 228 229 230

240 250 260 270 280 290 300 400 500 600

First, I draw 222.

222

222

223 224 225 226 227 228 229 230

223 224 225 226 227 228 229 230

240 250 260 270 280 290 300

240 250 260 270 280 290 300

400 500 600

Next, I draw ones to 230.

Then, I draw tens to 300.

Last, I draw hundreds to 600.

108

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

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400

EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 21

REMEMBER

Circle the tool you would use to measure each object.

3. The length of a dollar bill 1 cm cube

10 cm ruler

meter stick

measuring tape

meter stick

measuring tape

meter stick

measuring tape

meter stick

measuring tape

4. The length of a grasshopper 1 cm cube

10 cm ruler

5. The length around a basketball 1 cm cube

10 cm ruler

6. The length of a horse 1 cm cube

10 cm ruler

I use a centimeter cube to measure things that are very small.

I know that ten 1 cm cubes are the same length as one 10 cm ruler.

I know that using a ruler is faster than using ten cubes.

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I know that a meter stick is 1 meter.

1 meter is 100 centimeters.

I use a measuring tape to measure things that are round.

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

109

EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 21

21

Name

1. Draw units to count from 112 to 200.

112

2. Draw units to count from 476 to 800.

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111

EUREKA MATH2

2 ▸ M1 ▸ TE ▸ Lesson 21

REMEMBER

Circle the tool you would use to measure each object.

3. The length of a turtle 1 cm cube

10 cm ruler

meter stick

measuring tape

10 cm ruler

meter stick

measuring tape

10 cm ruler

meter stick

measuring tape

meter stick

measuring tape

4. The length around a soccer ball 1 cm cube

5. The length of a fly 1 cm cube

6. The length of a skateboard 1 cm cube

112

P R ACT I C E

10 cm ruler

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 22

22

Name

1.

Read Nick has 34 stamps.

He wants 110 stamps.

How many more stamps does Nick need?

Draw

+6

+ 70

34 40

110 I read the problem.

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

I know the total is 110 and one part is 34. I need to find the other part.

I draw a number line. I start at 34 and count on to 110 to find the unknown part.

Write Sample:

34 + 76 = 110 Nick needs Copyright © Great Minds PBC

76

more stamps.

I count by ones until I reach 40. Then I count by tens until I reach 110.

I counted on 76.

76 is the unknown part.

113

EUREKA MATH2

2 ▸ M1 ▸ TE ▸ Lesson 22

2. Draw units to count from 326 to 750.

326

327 328 329 330

340 350 360 370 380 390 400

500 600 700

710

720 730 740 750 First, I draw 326.

Next, I draw 4 ones to get to 330.

Then, I draw 7 tens to get to 400.

Then, I draw 3 hundreds to get to 700.

Last, I draw 5 tens to get to 750.

114

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

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 22

22

Name

1.

Read Kate baked 52 muffins.

She needs 110 muffins.

How many more muffins does Kate need?

Draw

Write

Kate needs

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more muffins.

115

2 ▸ M1 ▸ TE ▸ Lesson 22

EUREKA MATH2

2. Draw units to count from 578 to 920.

116

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 23

23

Name

REMEMBER 1. Find the unknown part.

Show how you know.

74 + 26 = 100 +6

74

+ 20

80

100

I add 6 to 74 because I know 4 + 6 = 10. So, 74 and 6 make the next ten, 80.

I add 20 to 80 because I know 8 + 2 = 10. So, 80 + 20 = 100.

I add 6 and 20 to 74.

The unknown part is 26.

6 + 20 = 26

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117

EUREKA MATH2

2 ▸ M1 ▸ TE ▸ Lesson 23

2. Ren and Nate have different heights.

Show the difference in height two ways.

Write an equation for each way.

I represent Ren and Nate’s height with a tape diagram.

R N

N

148 141

R

148

N

141

I subtract to make the tapes the same.

148 141

Nate 141 cm

I represent Ren and Nate’s height with a tape diagram.

I count on from 141 until I get to 148. I count on 7.

R

Ren 148 cm

I count back from 148 until I reach 141. I counted back 7.

7

I write an equation.

148

141 + 7 = 148

R 141 148 N

7

141

I write an equation.

148 – 7 = 141

The difference in height is 118

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

7

cm.

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EUREKA MATH2 2 ▸ M1 ▸ TE ▸ Lesson 23

23

Name

REMEMBER

1. Find the unknown part.

Show how you know.

58 +

= 100

2. Beth and Jill have different heights.

Show the difference in height two ways.

Beth 137 cm

Write an equation for each way.

The difference in height is Copyright © Great Minds PBC

Jill 133 cm

cm.

119

Module 1 Topic F

FAMILY MATH Express Three-Digit Numbers in Different Forms Dear Family, Key Terms

Your student is reading, writing, and counting numbers up to 1,000. They learn that 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called digits. The placement of a digit in a number tells us how much the digit is worth. To help them understand the meaning of the digits, your student learns to write numbers in different forms, including word form, expanded form, and unit form.

This understanding helps them to see that place value gives meaning to numbers and builds a strong foundation that will extend to work with decimal numbers.

hundreds

tens

ones

1

2

5

digit expanded form standard form unit form word form

125 100

5 20

The digits 1, 2, and 5 make up the number 125. The digit 1 has a value of 100. The digit 2 has a value of 20. The digit 5 has a value of 5.

Standard Form

Word Form

Expanded Form

Unit Form

125

one hundred twentyfive

100 + 20 + 5 20 + 5 + 100 5 + 100 + 20 The order of the addends does not change the total value.

1 hundred 2 tens 5 ones 12 tens 5 ones 5 ones 1 hundred 2 tens The order of the units does not change the total value.

At-Home Activity Numbers in Your World Have your student think about a familiar three-digit number or look for a three-digit number around their home. For example, your student may think about their home address or area Copyright © Great Minds PBC

121

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EUREKA MATH2

code, or they may find a three-digit number on a food label. Ask your student to tell you how many hundreds, tens, and ones are in each number. Then ask questions to help them compare the value of each digit.

122

•

“What is the value of the 2 in the number?”

•

“Do any digits repeat? What is the value of each digit?”

•

“Which digit has the greatest value? What is the value of that digit?”

FA M I LY M AT H ▸ Module 1 ▸ Topic F

Copyright © Great Minds PBC

EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 24

24

Name

1. Count from 76 to 400.

hundreds

tens

ones

1 2 3 4

7 7 7 7 8 9 0 0 0 0

6 7 8 9 0 0 0 0 0 0

I use ones, tens, and hundreds to count from 76 to 400.

76 is close to the benchmark number 80. I count by ones to 80.

76 77 78 79 80 80 is close to the benchmark number 100. I count by tens to 100.

90

100

Then I count by hundreds to 400.

200

300

400

Digits are the numerals we use to write numbers. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits.

For the number 76, the digit 7 is in the tens place, so its value is 70. The digit 6 is in the ones place, so its value is 6.

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123

EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 24

24

Name

1. Count from 84 to 300.

hundreds

Copyright © Great Minds PBC

tens

2. Count from 685 to 920.

ones

hundreds

tens

ones

125

EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 25

25

Name

Show the hundreds, tens, and ones.

Then write the unit form.

1. 216

216 200

6 10

Unit form:

2

hundreds

1

ten

6

ones

A number in standard form is written only with digits, or numerals. The number 216 is in standard form.

Unit form tells how many of each place value unit. The unit form for 216 is 2 hundreds 1 ten 6 ones.

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127

EUREKA MATH2

2 ▸ M1 ▸ TF ▸ Lesson 25

2. Ann has $350 in $100 and $10 bills.

How many $100 and $10 bills could Ann have?

Show one way.

Sample:

100 10 3 5

100 10

10

100 10

3 hundreds

10 5 tens

$100 bills $10 bills Ann has $350.

I use what I know about place value to find the value of each digit.

The 3 is in the hundreds place, so the value of the 3 is 300. I draw three $100 bills.

The 5 is in the tens place, so the value of the 5 is 50. I draw five $10 bills.

128

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

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EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 25

REMEMBER 3. Make 10 to add.

Show how you know.

9 + 5 = 14 Write a new number sentence.

9 + 1 + 4 = 14

I can draw dots to represent 9 + 5.

I draw 9 solid dots and 5 open dots.

I can move 1 open dot to make 10.

This helps me write a new number sentence.

9 and 1 make 10. Then I add 4 more.

9 + 1 + 4 = 14

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

129

EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 25

25

Name

Show the hundreds, tens, and ones.

Then write the unit form.

1.

385 385

Unit form:

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hundreds

tens

ones

131

2 ▸ M1 ▸ TF ▸ Lesson 25

EUREKA MATH2

2. Matt has $320 in $100 and $10 bills.

How many $100 and $10 bills could Matt have?

Show one way.

$100 bills $10 bills REMEMBER 3. Make 10 to add.

Show how you know.

7+6= Write a new number sentence.

132

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 26

26

Name

1. Write in expanded form.

234 =

Expanded form shows a number written as an addition expression. Each addend represents the value of a digit.

200 + 30 + 4

To write a number in expanded form, I can say it in unit form to help me.

234 is 2 hundreds 3 tens 4 ones.

I add the value of each unit.

200 + 30 + 4 Expanded form: 200 + 30 + 4

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133

EUREKA MATH2

2 ▸ M1 ▸ TF ▸ Lesson 26

2. Write in standard form.

60 + 500 + 4 =

564

When I write a number in standard form, I write the units in order from greatest to least: hundreds, tens, and ones.

I write a 5 in the hundreds place to represent 500.

I write a 6 in the tens place to represent 60.

Then I write a 4 in the ones place to represent 4.

134

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

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EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 26

Name

26

1. Write in expanded form.

452 = 245 = 205 = 250 = 2. Write in standard form.

400 + 30 + 1 = 40 + 1 + 300 = 600 + 7 = 60 + 700 =

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135

EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 27

27

Name

1. Write the number in word form. Use the word bank. nine hundred six

eight hundred thirty

one hundred sixty-five

165

one hundred sixty-five

830

eight hundred thirty

906

nine hundred six

A number in word form is written with words only.

I can use the word bank to help me.

906 is nine hundred six.

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137

EUREKA MATH2

2 ▸ M1 ▸ TF ▸ Lesson 27

2. Write 417 in each form.

Word form: Unit form: Expanded form:

four hundred seventeen 4 hundreds 1 ten 7 ones 400 + 10 + 7

417 is in standard form.

When I write word form, I write the words.

When I write in unit form, I write how many of each unit.

When I write in expanded form, I write an addition expression.

138

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

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EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 27

REMEMBER 3. Make 10 to add.

Show how you know.

2

+

4

+

6

=

12

There are 2 muffins in the first case.

There are 4 muffins in the second case.

I count 6 muffins in the third case.

I know that 4 and 6 make 10, so I add them first.

2+ 4 + 6 Then I add 2 and 10.

10

2 + 10 = 12

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

139

EUREKA MATH2

2 ▸ M1 ▸ TF ▸ Lesson 27

4. Add. Show how you know.

46 + 7 = 53 I can make a 10 to add.

50 is the next 10 after 46.

46 needs 4 more ones to make 50.

I can break apart 7 into 4 and 3.

46 + 7 4

3

Then I can make 50.

Now I add 50 and 3 to find the total.

46 + 4 + 3 50 + 3 = 53

140

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

Copyright © Great Minds PBC

EUREKA MATH2 2 ▸ M1 ▸ TF ▸ Lesson 27

27

Name

1. Write the number in word form. Use the word bank. three hundred seven forty-two two hundred fifty-seven four hundred eighteen five hundred seventy

257 42 570 418 307 2. Write 784 in these forms.

Word form: Unit form: Expanded form:

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141

EUREKA MATH2

2 ▸ M1 ▸ TF ▸ Lesson 27

REMEMBER 3. Make 10 to add.

Show how you know.

5

+

7

+

5

=

4. Add. Show how you know.

27 + 8 =

142

P R ACT I C E

Copyright © Great Minds PBC

Module 1 Topic G

FAMILY MATH Model Base-Ten Numbers Within 1,000 with Money Dear Family, Key Term

Your student continues to explore place value by using paper $1, exchange $10, and $100 bills to represent ones, tens, and hundreds. They exchange 10 of a smaller value bill for 1 of the next larger value bill and they see how the same amount of money can be represented in different ways. Your student counts by $1, $10, and $100 bills and shows their counts on an open number line. They also solve word problems involving money and choose a strategy that makes sense to them.

10

1 1 1 1 1

1 1 1 1 1

10 ones has the same value as 1 ten.

100

10 10 10 10 10

10 10 10 10 10

10 tens has the same value as 1 hundred.

1 hundred 4 ones

2 tens

776 780

790

800

900

This open number line shows skip-counting from 776 to 900 with one hop of 4, two hops of 10, and one hop of 100.

At-Home Activities Shopping Trip Pretend you and your student are going to buy something to donate to the local animal shelter. Use play money, or make $1, $10, and $100 bills with scraps of paper. Gather some of each type of bill (such as 15 one-dollar bills, 6 ten-dollar bills, and 2 hundred-dollar bills), and have your student figure out the total amount. Have them exchange some bills if they need to.

You can both take some bills and exchange as needed to make one amount. Together, think about what you might buy with that amount.

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143

2 ▸ M1 ▸ TG

EUREKA MATH2

Step, Hop, Skip to 1,000 With your student, practice skip-counting by ones, tens, and hundreds. Pick any three-digit number, such as your area code or street address. Act out the skip-counting by taking small steps to represent counting by ones, larger steps to represent counting by tens, and jumps to represent counting by hundreds.

•

144

Let’s start at 776. Take 4 small steps (777, 778, 779, 780). Then take 2 large steps (790, 800). Then jump 2 times (900, 1,000).

FA M I LY M AT H ▸ Module 1 ▸ Topic G

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EUREKA MATH2 2 ▸ M1 ▸ TG ▸ Lesson 28

28

Name

1. Draw bills for $121. Draw two ways. Sample:

100

10

100

10

I can show $100 with 1 hundred-dollar bill or 10 ten-dollar bills.

100

or

Copyright © Great Minds PBC

10

10

10

10

10

10

10

10

10

10

10

1

1 1 1 1 1

1 1 1 1 1

1

1 1 1 1 1

1 1 1 1 1

I can show $10 with 1 ten-dollar bill or 10 one-dollar bills.

10

or

1

1

1

1

1

1

1

1

1

1

145

EUREKA MATH2

2 ▸ M1 ▸ TG ▸ Lesson 28

I can draw $121.

100

10

10

1

I know that 1 ten-dollar bill has the same value as 10 one-dollar bills. So, I can exchange 1 ten-dollar bill for 10 one-dollar bills.

100

10

10

1

1

1

1

1

1

1

1

1

1

1

Exchange means trade one thing for another that has equal value.

146

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

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EUREKA MATH2 2 ▸ M1 ▸ TG ▸ Lesson 28

Name

28

1. Draw bills for $210.

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147

2 ▸ M1 ▸ TG ▸ Lesson 28

EUREKA MATH2

2. Draw bills for $212. Draw two ways.

148

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TG ▸ Lesson 29

29

Name

Count by ones, tens, and hundreds.

1. 378 to 700 +1

+1

378 379 380

+ 10

+ 100

+ 10

390

400

+ 100

500

+ 100

600

700

I label 378 on the open number line. I count by ones to the nearest ten: 379, 380. I draw and label the hops.

I count by tens to the nearest hundred: 390, 400. I draw and label the hops.

I count by hundreds: 500, 600, 700. I draw and label the hops.

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149

EUREKA MATH2

2 ▸ M1 ▸ TG ▸ Lesson 29

REMEMBER 2. Use the number line to subtract.

–2 40

48

54 – 6 = 3.

48

–4 50

54

60

I start at 54 on the number line.

I hop back 4 to 50.

Read

Then I hop back 2 more to 48.

Beth has 8 pretzels Peg has 6 pretzels.

How many pretzels do Beth and Peg have in all?

I read the problem.

I read again.

Draw

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

B

I draw 8 dots for the pretzels Beth has.

P

I draw 6 dots for the pretzels Peg has.

The total is unknown.

8 + 2 + 4 = 14

I make 10 to add.

10 Write Beth and Peg have 150

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

14

pretzels in all.

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EUREKA MATH2 2 ▸ M1 ▸ TG ▸ Lesson 29

Name

29

Count by ones, tens, and hundreds.

1. 200 to 830

2. 447 to 600

3. 500 to 744

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151

EUREKA MATH2

2 ▸ M1 ▸ TG ▸ Lesson 29

REMEMBER 4. Use the number line to subtract.

50

60

70

63 – 9 = 5.

Read Ling has 9 T-shirts.

Sal has 6 T-shirts.

How many T-shirts do Ling and Sal have in all?

Draw

Write Ling and Sal have 152

P R ACT I C E

T-shirts in all.

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EUREKA MATH2 2 ▸ M1 ▸ TG ▸ Lesson 30

30

Name

1. How many more $100 bills make $1,000?

Show how you know.

$100

$100

$100

$100

$100

$100

$100 $100

100 100

2

I know there are 10 hundreds in 1,000.

I count 8 groups of $100.

I know that is $800.

I need 2 more groups of $100 to make $1,000.

more $100 bills make $1,000.

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153

EUREKA MATH2

2 ▸ M1 ▸ TG ▸ Lesson 30

2. How many more $10 bills make $1,000?

Show how you know.

$100

$100

$100

$100

$100

$100

$100

Sample:

100 = 10 tens 100 = 10 tens 10 + 10 = 20

$100 20

more $10 bills make $1,000.

I know I need 2 more groups of $100. There are 10 tens in 100.

100

100

I have 2 groups of 10 bundles of ten.

I know 2 groups of 10 is 20.

I need 20 more $10 bills to make $1,000.

154

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

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EUREKA MATH2 2 ▸ M1 ▸ TG ▸ Lesson 30

30

Name

1. How many more $100 bills make $1,000?

Show how you know.

$100

$100

$100

$100

$100 $100 $100 more $100 bills make $1,000.

Copyright © Great Minds PBC

155

EUREKA MATH2

2 ▸ M1 ▸ TG ▸ Lesson 30

2. How many more $10 bills make $1,000?

Show how you know.

$100

$100

$100

$100

$100 $100 $100 more $10 bills make $1,000.

156

P R ACT I C E

Copyright © Great Minds PBC

Module 1 Topic H

FAMILY MATH Compose and Decompose with Place Value Disks Dear Family, Key Term

Your student is using place value disks to represent numbers rename up to 1,000. They exchange disks and rename numbers by using unit form. Flexibly naming numbers sets the foundation for adding larger numbers when there are more than 9 of a unit and for subtracting larger numbers when there are not enough of one unit to subtract. They can also draw place value disks as dots on a place value chart. The value of each dot is based on which column it is in.

Representing numbers with place value disks helps your student now, as they learn to add and subtract, and later when they learn to multiply and divide.

100 100

10

100s

10s

1s

2 hundreds 2 hundreds

4 tens 5 tens

17 ones 7 ones

1 1

100 100 100 100

10

1

Bundles, bills, and place value disks represent numbers.

All three representations develop an understanding of the units in the place value system.

Place value disks are similar to bills. The value of the disk is written on the disk. 512 is shown as 5 hundreds 1 ten 2 ones.

10 ones is exchanged for 1 ten.

2 hundreds 4 tens 17 ones is renamed as 2 hundreds 5 tens 7 ones.

At-Home Activities Drawing Dots Write a three-digit number such as your area code or a street address. Help your student create a place value chart on paper with three columns labeled “100s”, “10s”, and “1s” from left to right. Help them represent the number on the chart by drawing dots in the correct columns.

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Bundle and Exchange Names Use the table that shows a number for each letter. Have your student find the numbers that go with the initials of their first, middle, and last names. For example, the initials J, R, and M go with the numbers 10, 18, and 13. Create a place value chart and place dots in the correct columns for those amounts. Exchange disks as needed to say the total as a number. Repeat the activity with other names or initials.

A B C D E F G H I J K L M N O P Q R S T U VW X Y Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

158

FA M I LY M AT H ▸ Module 1 ▸ Topic H

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 31

31

Name

Write the number in expanded form. Then write it in standard form.

1.

10

Expanded form: Standard form:

1

10

10

10

10

10

10

10

10

1

90 + 2 92 I count 9 tens disks. That’s 90.

I count 2 ones disks. That’s 2.

I write 90 + 2 to show expanded form.

I know 90 + 2 is equal to 92.

The standard form is 92.

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EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 31

REMEMBER 2. Make a picture graph.

Insects We Like

Insects We Like Ants Bees Ladybugs Butterflies

7 9

I write “Insects We Like” as the title of my picture graph.

I write the categories at the bottom of the graph.

I use the same categories as the table.

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

✓ ✓

✓ ✓ ✓ ✓ ✓

Ants

✓

✓

2

I read the title of the table.

160

✓

4

✓

✓ ✓ ✓

✓

✓

✓

✓

✓

✓

✓

✓

✓ stands for _____ 1 vote.

Key: Each _____ Bees

Ladybugs

Butterflies

I know each ✓ stands for 1 vote.

I read the key and add my data.

Ants has 4 votes. I put 4 ✓ above Ants.

Bees has 2 votes. I put 2 ✓ above Bees.

Ladybugs has 7 votes. I put 7 ✓ above Ladybugs.

Butterflies has 9 votes. I put 9 ✓ above Butterflies.

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 31

31

Name

Write the number in expanded form. Then write it in standard form.

1.

100

10

1

100

10

1

100

10

1

1

100

10

1

1

1

1

10

10

Expanded form: Standard form: 2.

100

1

100

1

100

100

1

100

100

1

100

100

1

1

Expanded form: Standard form: Copyright © Great Minds PBC

161

EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 31

REMEMBER 3. Make a picture graph.

Fruit We Like Apples Bananas Blueberries

9 4 5 8

Grapes

Key: Each

162

P R ACT I C E

stands for

vote.

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 32

32

Name

1.

100

10

1

100

10

1

100

10

1

100

10

1 1

100

1

How many more ones make a new ten?

What is the new number?

4

ones

550

I need 4 more ones disks to make a ten.

100

10

1

1

100

10

1

1

100

10

1

1

100

10

1

1

1

1

100

I exchange 10 ones for 1 ten.

100

10

1

1

100

10

1

1

100

10

1

1

100

10

1

1

100

10

1

1

Now there are 5 hundreds disks and 5 tens disks. The new number is 550.

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163

EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 32

2.

100

10

100

10

100

10

100

100

10

100

100

10

How many more tens make a new hundred?

What is the new number?

5

800

tens

I need 5 more tens disks to make a hundred.

100

10

10

100

10

10

100

10

10

100

100

10

10

100

100

10

10

I exchange 10 tens for 1 hundred.

100

10

10

100

10

10

100 100

10

10

100

100

10

10

100

100

10

10

Now there are 8 hundreds disks. The new number is 800.

164

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

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 32

32

Name

1.

100

10

1

100

10

1

100

10 10

10

10

10

How many more ones make a new ten?

ones

What is the new number?

2.

100

10

100

10

100

10

100

10

100

How many more tens make a new hundred?

tens

What is the new number?

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165

EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 33

33

Name

1. Draw 521 with hundreds, tens, and ones.

100s

10s

1s

I draw dots on the place value chart to represent the units.

100s

10s

1s

I know 521 is 5 hundreds 2 tens 1 one.

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EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 33

Draw 521 with only hundreds and ones.

100s

10s

1s

To use only hundreds and ones to show 521, I can rename 2 tens as 20 ones.

100s

10s

1s

Now I have 5 hundreds 21 ones.

When we make an exchange or unbundle a unit, we rename it with a different unit. The total stays the same.

168

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

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 33

REMEMBER

T

P

W

2. Put in order from shortest to tallest.

P

W

Shortest

T Tallest

I see the items are lined up by their endpoints. I can compare the heights.

I know the pinwheel is the W P shortest because all the other things are taller. I write the letter P first.

T

The water bottle is next. It is taller than the pinwheel but shorter than the trophy. I write the letter W. The trophy is last because it is the tallest item. I write the letter T.

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

169

EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 33

3. Circle the shapes with square corners.

A square fits perfectly in a square corner.

Squares fit perfectly in the corners of the rectangle and the square.

Squares do not fit perfectly in the corners of the other shapes.

So, only the rectangle and the square have square corners.

170

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

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 33

33

Name

1. Draw 27 with tens and ones.

100s

10s

1s

2. Draw 419 with hundreds, tens, and ones.

100s

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10s

1s

Draw 27 with only ones.

100s

10s

1s

Draw 419 with only hundreds and ones.

100s

10s

1s

171

EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 33

REMEMBER

B

C

R

3. Put in order from shortest to tallest.

Shortest Tallest

4. Circle the shapes with square corners.

172

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 34

34

Name

1. Draw on the place value chart.

Rename 10 ones as 1 ten.

5 hundreds 7 tens 17 ones 100s

5

10s

hundreds

Then write in unit form.

5

hundreds

8

8 tens

1s

7

tens

7

ones

ones

I draw 5 dots in the hundreds place and 7 dots in the tens place. Then I draw 17 dots in the ones place.

I circle 10 ones to show that I can rename 10 ones as 1 ten. I draw an arrow to the tens place. I add another dot there.

Now there are 5 hundreds, 8 tens, and 7 ones.

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EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 34

2. Draw on the place value chart.

Rename.

2 hundreds 1 ten 15 ones 100s

10s

Standard form:

1s

225

Then write in standard form.

Standard form:

225 I draw 2 dots in the hundreds place. I draw 1 dot in the tens place. I draw 15 dots in the ones place.

I can rename 10 ones as 1 ten. I circle 10 ones.

I draw an arrow to the 10s place. I add another dot there.

Now there are 2 hundreds, 2 tens, and 5 ones.

174

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

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EUREKA MATH2 2 ▸ M1 ▸ TH ▸ Lesson 34

34

Name

1. Draw on the place value chart.

Rename 10 ones as 1 ten.

2 hundreds 3 tens 13 ones 100s

hundreds Then write in unit form. hundreds

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10s

tens tens

1s

ones ones

175

EUREKA MATH2

2 ▸ M1 ▸ TH ▸ Lesson 34

2. Draw on the place value chart.

Rename.

4 hundreds 16 tens 5 ones 100s

10s

1s

Standard form: Then write in standard form.

Standard form:

176

P R ACT I C E

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Module 1 Topic I

FAMILY MATH Compare Two Three-Digit Numbers in Different Forms Dear Family,

Your student is learning to use place value to compare three-digit numbers. Students draw on a place value chart and use their place value understanding to help them explain why one number is greater than or less than another number. Your student uses the greater than (>), equal to (=), and less than (<) symbols to write comparison statements.

427 100s

10s

1s

472 100s

10s

1s

427 and 472 have the same digits but different values.

Both have a 4 in the hundreds place.

427 has a 2 in the tens place and 472 has a 7 in the tens place.

20 is less than 70, so 427 is less than 472.

427 < 472

100s

10s

1s

324

100s

10s

1s

324

3 hundreds 1 ten 14 ones and 3 hundreds 24 ones each have more than 9 ones.

When the ones are renamed with the next largest unit (tens), the numbers have the same digits in the same places.

324 = 324

At-Home Activities Around the House Build three-digit numbers with your student by using household items to represent the different values. For example, a plate represents a hundred, a bowl represents a ten, and a spoon represents one. Take turns selecting objects to build a number. Then ask your student to rename and compare the numbers represented.

•

“Here are 2 plates, 2 bowls, and 3 spoons. What number is represented by these objects?”

•

“Here are 5 more spoons. What number is represented now?”

•

“How can you rename that amount a different way?”

•

“Which number is greater than (or less than) the other number? How do you know?”

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EUREKA MATH2

Phone Number Write each digit from a seven-digit phone number on separate slips of paper. Invite your student to pick three paper slips. Have them rearrange the three slips to make the smallest three-digit number they can make. Choose three slips from the remaining paper slips and arrange yours to make the smallest possible three-digit number. Discuss which of you has the smaller number and how they can tell. Then you both rearrange your paper slips to make the greatest possible three-digit number. Ask your student which number is greater than (or less than) the other number and how they know.

178

FA M I LY M AT H ▸ Module 1 ▸ Topic I

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EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 35

35

Name

Draw the number on the place value chart.

Then circle >, =, or < to compare.

382

1.

100s

10s

349 1s

is greater than

100s

10s

1s

> =

is equal to is less than

<

I draw 3 hundreds, 8 tens, and 2 ones for 382.

100s

10s

1s

100s

10s

1s

I draw 3 hundreds, 4 tens, and 9 ones for 349.

I compare the hundreds.

Both numbers have 3 hundreds.

I compare the tens.

382 has 8 tens, and 349 has 4 tens.

I know 8 tens is greater than, or more than, 4 tens.

382 is greater than 349.

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179

EUREKA MATH2

2 ▸ M1 ▸ TI ▸ Lesson 35

Write >, =, or < to compare.

2.

129

<

3.

308

= three hundred eight

133

I can use place value charts to compare.

129

100s

10s

1s

10s

When I read 308, I say “three hundred eight.”

I know they are equal.

133

100s

I know that 308 has 3 hundreds, 0 tens, and 8 ones.

1s

I look at the hundreds place first, then tens, then ones.

Both numbers have 1 hundred.

129 has 2 tens and 133 has 3 tens.

I know 2 tens is less than 3 tens, so 129 is less than 133.

180

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

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EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 35

REMEMBER

4. Circle the hexagon made with fewer blocks.

The first hexagon is made of 2 trapezoids.

The second hexagon is made of 2 triangles and 2 rhombuses.

The hexagon made with 2 trapezoids is made with fewer blocks.

5. Kevin measures a pencil.

Write the length.

12

I see one 10-centimeter stick. cm

I see 2 extra centimeter cubes.

I know 10 + 2 = 12.

The pencil is 12 cm long.

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

181

EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 35

35

Name

Draw the number on the place value chart.

Then circle >, =, or < to compare.

276

1.

100s

10s

376 1s

is greater than

100s

10s

1s

> =

is equal to is less than

<

Write >, =, or < to compare.

2.

588

569

3.

223

two hundred twenty-three

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EUREKA MATH2

REMEMBER

4. Circle the trapezoid made with fewer blocks.

5. Ling measures a frog.

Write the length.

cm

184

P R ACT I C E

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EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 36

36

Name

1. Draw each number on the place value chart.

Then write >, =, or < to compare.

3 hundreds 17 ones 100s

10s

1s

371 100s

3 hundreds 17 ones

10s

1s

< 371

I draw 3 hundreds 17 ones in the first chart.

I rename 17 ones as 1 ten 7 ones.

I draw 3 hundreds 7 tens 1 one for 371 in the next chart.

I compare the hundreds.

Both numbers have 3 hundreds.

100s

10s

1s

100s

10s

1s

100s

10s

1s

I compare the tens.

3 hundred 17 ones has 1 ten, and 371 has 7 tens.

So, 3 hundred 17 ones is less than 371.

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185

EUREKA MATH2

2 ▸ M1 ▸ TI ▸ Lesson 36

Write >, =, or < to compare.

2.

752

>

five hundred seventy-two I can use place value charts to compare.

I show 7 hundreds 5 tens 2 ones for 752.

Five hundred seventy-two has 5 hundreds 7 tens 2 ones.

100s

10s

1s

100s

10s

1s

I compare the hundreds.

752 has 7 hundreds, and five hundred seventy-two has 5 hundreds.

7 hundreds is greater than 5 hundreds.

So, 752 > five hundred seventy-two.

3. 834

=

30 + 800 + 4 I know 834 is the same as 8 hundreds 3 tens 4 ones.

I know 30 + 800 + 4 is the same as 3 tens 8 hundreds 4 ones.

I can use place value charts to compare.

100s

10s

1s

100s

10s

1s

The hundreds, tens, and ones are the same for both numbers.

So, 834 = 30 + 800 + 4.

186

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

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EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 36

36

Name

1. Draw each number on the place value chart.

Then write >, =, or < to compare.

591 100s

10s

591

5 hundreds 19 ones 1s

100s

10s

1s

5 hundreds 19 ones

Write >, =, or < to compare.

2.

467

60 + 400 + 7

3.

705

seven hundred fifty

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187

EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 37

37

Name

REMEMBER Read Pam’s pet rat is 5 cm long.

Lan’s pet rat is 10 cm longer than Pam’s rat How long is Lan’s pet rat?

P L I read the problem.

Draw

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

5 P

1 1 1 1 1

L

1 1 1 1 1

I notice the cubes look like a tape diagram.

10

I draw a tape diagram to match the cubes.

15

Write

Pat’s tape has 5 cubes.

Lan’s tape has 5 cubes and a 10-centimeter stick.

Sample:

5 + 10 = 15 Lan’s pet rat is Copyright © Great Minds PBC

15

I count the centimeter stick and cubes to find how long Lan’s pet rat is.

cm long.

189

EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 37

37

Name

REMEMBER Read Ann’s lizard is 9 cm long.

Nick’s lizard is 10 cm longer than Ann’s lizard.

How long is Nick’s lizard?

A N Draw

Write

Nick’s lizard is Copyright © Great Minds PBC

cm long.

191

EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 38

38

Name

Write the numbers from least to greatest. Use standard form.

1. 338

three hundred twenty 1 + 90 + 400 320 , 338 , 491

First, I write each number in standard form.

338

320

491

three hundred twenty

1 + 90 + 400

I can use place value charts to compare 338, 320, and 491.

100s

10s

1s

100s

10s

1s

100s

10s

1s

491 is the greatest number because it has 4 hundreds.

338 and 320 both have 3 hundreds.

338 has 3 tens, and 320 only has 2 tens.

So, 320 < 338.

From least to greatest, the numbers are 320, 338, 491.

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193

EUREKA MATH2

2 ▸ M1 ▸ TI ▸ Lesson 38

Write the numbers from greatest to least. Use standard form.

2. 2 hundreds 14 ones

60 + 200 + 3

255 263 , 255 , 214

I write each number in standard form.

214

263

2 hundreds 14 ones

60 + 200 + 3

255

I can use place value charts to compare 214, 263, and 255.

100s

10s

1s

100s

10s

1s

100s

10s

1s

All the numbers have 2 hundreds.

214 has 1 ten, 263 has 6 tens, and 255 has 5 tens.

So, I know 263 is the greatest number.

I also know that 255 > 214.

From greatest to least, the numbers are 263, 255, 214.

194

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

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EUREKA MATH2 2 ▸ M1 ▸ TI ▸ Lesson 38

38

Name

Write the numbers from least to greatest. Use standard form.

1. 432

2. 529

871

four hundred fifty-one

650

5 + 400 + 30 ,

,

,

,

Write the numbers from greatest to least. Use standard form.

3. 47 tens 4 ones

4. 711

3 + 80 + 400

7 hundreds 15 ones

three hundred eight

9 + 10 + 700

,

Copyright © Great Minds PBC

,

,

,

195

2 ▸ M1

EUREKA MATH2

Acknowledgments Beth Barnes, Dawn Burns, Karla Childs, Mary Christensen-Cooper, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Lacy Endo-Peery, Krysta Gibbs, Melanie Gutierrez, Torrie K. Guzzetta, Eddie Hampton, Andrea Hart, Sara Hunt, Rachel Hylton, Travis Jones, Jennifer Koepp Neeley, Liz Krisher, Leticia Lemus, Marie Libassi-Behr, Ben McCarty, Cristina Metcalf, Ashley Meyer, Bruce Myers, Marya Myers, Maximilian Peiler-Burrows, Marlene Pineda, Carolyn Potts, Meri Robie-Craven, Colleen Sheeron-Laurie, Robyn Sorenson, Tara Stewart, Theresa Streeter, James Tanton, Julia Tessler, Philippa Walker, Rachael Waltke, Lisa Watts Lawton, MaryJo Wieland 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

196

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

Or estimate how many bees are in a hive?

Or calculate your batting average?

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

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

Module 1 Place Value Concepts Through Metric Measurement and Data • Place Value, Counting, and Comparing Within 1,000 Module 2 Addition and Subtraction Within 200 Module 3 Shapes and Time with Fraction Concepts Module 4 Addition and Subtraction Within 1,000

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

Module 5 Money, Data, and Customary Measurement

Ready to get started?

Module 6 Multiplication and Division Foundations

What does this painting have to do with math?

The bold brushstrokes and vivid colors in Maurice Prendergast’s painting invite us to step inside this lively street scene in Venice, Italy. A group of ladies with parasols is crossing a bridge. Getting lost in a crowd can be intimidating, but as we learn about base ten, counting large numbers—of people, parasols, or anything—will be a breeze.

On the cover Ponte della Paglia, 1898–1899; completed 1922 Maurice Prendergast, American, 1858–1924 Oil on canvas The Phillips Collection, Washington, DC, USA Maurice Prendergast (1858–1924), Ponte della Paglia, ca. 1898/reworked 1922.

Oil on canvas. The Phillips Collection, Washington, DC, USA. Acquired 1922.

ISBN 978-1-64497-642-5

9

781644 976425