We included **HMH Into Math Grade 3 Answer Key**** PDF** **Module 1 Lesson 4 Understand the Commutative Property of Multiplication** to make students experts in learning maths.

## HMH Into Math Grade 3 Module 1 Lesson 4 Answer Key Understand the Commutative Property of Multiplication

I Can use the Commutative Property of Multiplication to write related multiplication equations.

**Spark Your Learning**

Andy designed the game board shown. Suppose you are designing a game board. The game will have 21 squares. The squares need to be in equal rows.

**Show two different game board designs.**

Answer:

Explanation:

Andy designed the game board shown

Suppose you are designing a game board

The game will have 21 squares

I made an array of 3 rows and 7 columns

So, 3 x 7 = 21.

**Turn and Talk** Andy turns his game board, as shown. What multiplication equations can you write to model Andy’s arrays?

**Build Understanding**

1. Toby designs this game board. Nita notices that she can design a different game board with the same number of squares by turning Toby’s game board. How would a turn of Toby’s game board look?

A. Describe how Nita can arrange the squares in equal rows to show a turn of Toby’s game board.

B. What multiplication equation can you write to model Toby’s original game board?

**Show how a turn of Toby’s game board would look.**

Answer:

B. What multiplication equation can you write to model Toby’s original game board?

Answer:

C. What multiplication equation can you write to model a turn of Toby’s game board?

Answer:

Explanation:

Toby designs this game board

Nita notices that she can design a different game board with the same number of squares by turning Toby’s game board

Toby made a game board with 4 rows of 5 squares

Nita made a game board with 5 rows of 4 squares

The equation is 4 x 5 = 20

The related equation is 5 x 4 = 20.

Question 2.

Katya is designing a rectangular game board. One version of her game board is shown.

A. Katya wants to see if there is another way to arrange the board. Show another way Katya can arrange her game board using equal rows.

B. What multiplication equation can you write to model each game board?

Answer:

Explanation:

Katya is designing a rectangular game board

One version of her game board is shown

She makes 5 rows of 3 squares each row

Katya wants to see if there is another way to arrange the board

The another way is to make 3 rows of 5 squares in each row

I drew to show another way Katya can arrange her game board using equal rows

The multiplication equation that match with my model is 3 x 5 = 15.

**Connect to Vocabulary**

You previously learned to multiply factors to find the product. The Commutative Property of Multiplication states that you can multiply factors in any order and the product stays the same.

C. What do you notice about the factors in the two equations? What do you notice about the products?

Answer:

The factors in the two equations are same but the order of the factors is different

The products in the 2 equations are same.

**Turn and Talk** How can you find other pairs of related multiplication equations? Give two examples.

Answer:

2 x 5 = 10 is a multiplication equation

The related equation is 5 x 2 = 10

Another example is 3 x 5 = 15 and 5 x 3 = 15.

**Check Understanding Math Board**

Question 1.

Lamar’s game board has 5 rows with 6 squares in each row. Ruby’s game board has 6 rows with 5 squares in each row. Do their game boards have the same number of squares? Explain.

Answer:

Yes, their boardgames have same number of squares

Explanation:

Lamar’s game board has 5 rows with 6 squares in each row

5 x 6 = 30

Ruby’s game board has 6 rows with 5 squares in each row

6 x 5 = 30

So, both the products are same and the number of squares are also same.

**On Your Own**

Question 2.

**Model with Mathematics** A frame can be hung two different ways. One way shows 3 rows with 6 photos in each row. The other way shows 6 rows with 3 photos in each row.

• Write equations to model the two ways the photos can be shown. How many photos are there?

________________________

Answer:

3 x 6 = 18

6 x 3 = 18

Explanation:

A frame can be hung two different ways

One way shows 3 rows with 6 photos in each row

3 x 6 = 18

The other way shows 6 rows with 3 photos in each row

6 x 3 = 18

There are 18 photos in all.

**Draw an array. Then write related equations to show the Commutative Property of Multiplication.**

Question 3.

**Use Tools** A page in Abdul’s stamp book has 5 stamps in each row. There are 8 rows. How many stamps are on the page?

Answer:

Explanation:

A page in Abdul’s stamp book has 5 stamps in each row

There are 8 rows

8 x 5 = 5 x 8 = 40

So, there are 40 stamps on the page.

**Use Structure Write the unknown factor.**

Question 4.

8 × 7 = 7 ×

Answer:

Explanation:

8 x 7 = 7 x 8

The order of the factors is different

So, The unknown factor is 8.

Question 5.

4 × 10 = × 4

Answer:

Explanation:

4 x 10 = 10 x 4

The order of the factors is different

So, the unknown factor is 10.

**I’m in a Learning Mindset!**

How did using an array of tiles help me understand the Commutative Property of Multiplication?