EM2 APPLY Level 4 Module 1 Lesson 1 Thin Slice

A Story of Units®

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

Student

APPLY

A Story of Units®

Fractional Units ▸ 4 APPLY

Module

1 2 3 4 5 6

Place Value Concepts for Addition and Subtraction

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

Foundations for Fraction Operations

Place Value Concepts for Decimal Fractions

Angle Measurements and Plane Figures

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EUREKA MATH2 4 ▸ M1

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

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

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

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

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

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

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

Describe relationships between measurements by using multiplicative comparison.

Name numbers by using place value understanding.

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

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

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

1,000,000

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

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

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

Rounding Multi-Digit Whole Numbers

less than a given number.

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

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

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

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

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

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

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

Multi-Digit Whole Number Addition and Subtraction

Metric Measurement Conversion Tables

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

Express metric measurements of length in terms of smaller units.

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

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

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

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

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

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

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

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

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

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Module 1 Topic A

FAMILY MATH Multiplication as Multiplicative Comparison Dear Family, Key Term

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

dollars

dimes

pennies

10¢

Figure E

Figure F

12 8

8

9

10

11

13

14

15

16 15 14 13 12 11 10 9

8

8

3

3

4

4

10

10

5

6

6

7

7

9

9 5

7

7

11 12

12

0CM 1

2

2

11 0CM 1

6

6

Amy’s Tower

Gabe’s Tower

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

15 = 3 × 5

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

16

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

Measurement

Comparison

weight liquid volume capacity height length width distance

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

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

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

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•

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

•

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

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

•

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

FA M I LY M AT H ▸ Module 1 ▸ Topic A

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

Complete the statement and equation to match the tape diagram.

1.

8

48​is ​

6

​times as many as ​8​.

48

​= ​

6

​× 8​

48

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

8

8 8

8

8

8

8

8

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

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

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EUREKA MATH2

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

3 × 7 = 21 Luke eats 2 ​ 1​ grapes.

I can draw a tape diagram to represent the problem.

I draw ​1​unit of 7​ ​for Pablo.

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

7

Pablo Luke ?

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

6

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

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1

REMEMBER Add or subtract.

3. ​714 − 235 = ​ 479 ​​​

I can write the problem vertically.

714 - 235

I start by making my units ready to subtract.

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

0 14

714 - 235

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

714 - 235

10 6 0 14

714 - 235 479

Now I am ready to subtract.

4. 252 + 388 = ​ 640

10 6 0 14

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

252 200 50 2

+

388 300 80 8

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

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

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EUREKA MATH2 4 ▸ M1 ▸ TA ▸ Lesson 1

Name

1

Date

Complete the statement and equation to match the tape diagram.

1.

36 is

9

times as many as 9.

= 9

9

9

×9

9

36 2.

42 is

6

times as many as 6.

=

×6

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

3. 21 is 3 times as many as 7.

21 =

×7

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

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

b. 497 + 213 =

10

P R ACT I C E

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