We included **HMH Into Math Grade 3 Answer Key**** PDF** **Module 4 Lesson 2 Understand the Distributive Property** to make students experts in learning maths.

## HMH Into Math Grade 3 Module 4 Lesson 2 Answer Key Understand the Distributive Property

I Can understand and know how to use the Distributive Property to decompose factors as a strategy to multiply one-digit numbers.

**Spark Your Learning**

Taj is drawing a map of the blocks in his town. There are 4 rows with 5 blocks ¡n each row. What is the total number of blocks?

**Use the arrays and facts you know to show two ways to find the total number of blocks.**

Answer:

Explanation:

Taj is drawing a map of the blocks in his town

There are 4 rows with 5 blocks in each row

I drew arrays and facts to find the number of blocks

4 x 5 = 20 or

I divided the arrays in 2 parts

2 rows with 5 blocks and 2 more rows with 5 more blocks

2 x 5 = 10

10 + 10 = 20

So, there are 20 blocks in all.

**Turn and Talk** What facts did you use to solve the problem? Explain.

Answer:

I used 4’s fact with 5 and 2’s fact with 5.

**Build Understanding**

1. A map of Nell’s neighborhood shows 6 rows with 8 blocks in each row. How many blocks J are there? How can you use an array to help solve the problem?

**Draw a horizontal line to break apart the array into two smaller arrays for facts you know.**

A. How many blocks are in each smaller array?

_______________________

B. Why do you need to add the products of the two smaller arrays?

_______________________

_______________________

C. Nell broke apart her array vertically to show 6 rows of 5 blocks and 6 rows of 3 blocks. What equations can you write for Nell’s arrays?

Answer:

Explanation:

A map of Nell’s neighborhood shows 6 rows with 8 blocks in each row

I drew a horizontal line to break apart the array into two smaller arrays for facts i know

The facts are 3 x 8 = 24

There are 24 blocks in the smaller arrays

Double the product

24 + 24 = 48

So, there are 48 blocks in Nell’s Neighborhood.

If Nell brake apart her array vertically to show 6 rows of 5 blocks and 6 rows of 3 blocks

The equations will be 6 x 5 = 30 and 6 x 3 = 18

30 + 18 = 48

So, there are 48 blocks in Nell’s Neighborhood.

**Connect to Vocabulary**

The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Example: 5 × 7 = 5 × (3 + 4)

5 × 7 = (5 × 3) ÷ (5 × 4)

5 × 7 = 15 + 20

5 × 7 = 35

D. How many blocks are in Nell’s neighborhood? ____

Answer:

There are 48 blocks in Nell’s Neighborhood.

**Turn and Talk** With your classmates, compare how you broke apart your arrays. Compare the sums of the products of your smaller arrays. What can you conclude?

Answer:

First i broke the arrays in 2 equal parts with 3 rows of 8 objects

3 x 8 = 24

24 + 24 = 48

And next i broke into 6 rows of 5 blocks and 6 rows of 3 blocks

6 x 5 = 30, 6 x 3 = 18

30 + 18 = 48

The sums of the products of my smaller arrays is same

So, in both ways i found that there are 48 blocks in all.

2. A map of Jodi’s village shows there are 4 rows with 9 blocks in each row. How many blocks are there? How can you use an array and the Distributive Property to help solve the problem?

- Draw a vertical line to break apart the array into two smaller arrays for facts you know.
- Use your arrays to complete the equations to show the Distributive Property.

A. Break apart the factor 9. 4 × 9 = 4 × (___ + ___)

B. Multiply each addend by4. 4 × 9 = (4 × __) + (4 × ____)

C. Add the products of the smaller arrays. 4 × 9 = ____ + ____

D. How many blocks are in Jodi’s village? 4 × 9 _______

Answer:

Explanation:

A map of Jodi’s village shows there are 4 rows with 9 blocks in each row

I drew a vertical line to break apart the array into two smaller arrays for facts i know

Break apart the factor 9

4 x 9 = 4 x ( 4 + 5 )

Multiply each addend by4

4 x 9 = ( 4 x 4 ) + ( 4 x 5 )

Add the products of the smaller arrays

4 x 9 = 16 + 20

4 x 9 = 36

So, there are 36 blocks in Jodi’s village.

**Check Understanding Math Board**

Question 1.

A map of Tran’s town shows 5 rows with 4 blocks in each row. How many blocks are in Tran’s town?

Answer:

20

Explanation:

A map of Tran’s town shows 5 rows with 4 blocks in each row

5 x 4 =

Break apart the factor 4

5 x ( 2 + 2 )

Multiply each addend by 5

( 5 x 2 ) + ( 5 x 2 )

Add the products

10 + 10 = 20

So, there are 20 blocks in Tran’s town.

**On Your Own**

Question 2.

**Use Structure** A kitchen counter has 4 rows of tiles with 7 tiles in each row. How many tiles are on the counter?

Answer:

28 tiles

Explanation:

A kitchen counter has 4 rows of tiles with 7 tiles in each row

4 x 7

Break apart the factor 7

4 x ( 5 + 2 )

Multiply each addend by 4

( 4 x 5 ) + ( 4 x 2 )

Add the products

20 + 8

= 28

So, there are 28 tiles on the counter.

Question 3.

A box has 8 gemstones in each row. There are 5 rows. How many gemstones are in the box?

Answer:

40 gemstones

Explanation:

A box has 8 gemstones in each row

There are 5 rows

5 x 8 =

Break apart the factor 8

5 x ( 5 + 3 )

Multiply each addend by 5

( 5 x 5 ) + ( 5 x 3 )

Add the products

25 + 15

= 40

So, there are 40 gemstones in the box.

**Use the array to complete the equations to show the Distributive Property.**

Question 4.

5 × 7 =

5 × 7 = 5 × (___ + ___)

5 × 7 = (5 × ___) + (5 × __)

5 × 7 = ___ + ___

5 × 7 = ___

Answer:

5 x 7 = 35

Explanation:

5 × 7 =

5 × 7 = 5 × (5 + 2)

5 × 7 = (5 ×5) + (5 × 2)

5 × 7 = 25 + 10

5 × 7 = 35.

Question 5.

3 × 9 =

3 × 9 = 3 × (___ + ___)

3 × 9 = (3 × ___) + (3 × __)

3 × 9 = ___ + ___

3 × 9 = ___

Answer:

3 x 9 = 27

Explanation:

3 × 9 =

3 × 9 = 3 × (5 + 4)

3 × 9 = (3 × 5) + (3 × 4)

3 × 9 = 15 + 12

3 × 9 = 27.

**I’m in a Learning Mindset!**

How did the way I approached the Distributive Property compare to my partner’s approach?

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