We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 6 Lesson 4 Use Area Models and the Distributive Property to Divide** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 6 Lesson 4 Answer Key Use Area Models and the Distributive Property to Divide

I Can solve multi-digit division problems using area models and the Distributive Property.

**Spark Your Learning**

Shawn is building a rectangular pen for holding sheep. The area of the pen needs to be 63 square feet, and the pen must be 3 feet wide. How long should the pen be?

**Show your thinking.**

Answer:

Explanation:

the pen should be 21 feet long and 3 feet wide.

**Turn and Talk** How can thinking about multiplication help you solve this area problem?

**Build Understanding**

1. Reggie shears sheep for their wool. He places all the wool in this bag. Each sheep provides 4 kilograms of wool. How many sheep does Reggie shear?

Find 92 ÷ 4.

A. How can you break apart 92 into smaller parts that are easier to divide by 4?

92 = 80 + _____

92 ÷ 4 = (___ + ___) ÷ 4

B. Complete the area model representing the division.

C. How does the area model represent the whole dividend and the dividend broken into smaller parts?

________________________________

D. How does the area model represent the divisor?

________________________________

E. How does it show the whole-number quotient is equal to 20 + 3?

________________________________

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F. 92 ÷ 4 = ___. so Reggie shears ___ sheep.

Answer:

Explanation:

A. 92 = 80 + 12

92 ÷ 4 = ( 80 + 12) ÷ 4

B. I have made the area model representation

C. The area model represents the whole dividend as a big rectangle and the dividend divided into smaller parts as small rectangles.

D. The area model represents the divisor as the width of the rectangle.

E. It show the whole number quotient as 20 + 3 as the width of the whole rectangle is 23.

F. 92 ÷ 4 = 23 . so Reggie shears 23 sheep.

**Turn and Talk** How can you use multiplication and the area model to check your answer?

**Step It Out**

2. Use an area model and the Distributive Property to find 217 ÷ 7.

A. Break apart 217 into numbers that are easier to divide by 7.

217 = ___ + ___

B. Use the easier numbers to divide.

217 ÷ 7 = (___ + ___) ÷ 7

= (___ ÷ 7) + (___ ÷ 7)

= ____ + ____

= _____

Answer:

Explanation:

A. Break apart 217 into numbers that are easier to divide by 7.

217 = 182 + 35

B. Use the easier numbers to divide.

217 ÷ 7 = (182 + 35) ÷ 7

= (182 ÷ 7) + (35 ÷ 7)

= 26 + 5

= 31

So, 217 ÷ 7 = 31.

**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:

(10 + 8) × 2 = (10 × 2) + (8 × 2)

The Distributive Property also applies to division. Example:

(10 + 8) ÷ 2 = (10 ÷ 2) + (8 ÷ 2)

**Check Understanding Math Board**

Question 1.

Ajay has 54 pounds of wool. He uses 3 pounds to make a blanket. How many blankets can he make? Use an area model to find 54 ÷ 3.

Ajay can make ___ blankets.

Answer:

Explanation:

Ajay can make 18 blankets.

54 ÷ 3 = 18.

**Use the Distributive Property to divide.**

Question 2.

72 ÷ 4

= (___ + ___) ÷ 4

= (___ ÷ 4) + (___ ÷ 4)40

= ___ + ____

= _____

Answer:

72 ÷ 4 = 18

Explanation:

72 ÷ 4

= (40 + 32) ÷ 4

= (40 ÷ 4) + (32 ÷ 4)

= 10 + 8

= 18.

Question 3.

115 ÷ 5

= (___ + ___) ÷ 5

= (___ ÷ 5) + (___ ÷ 5)

= ___ + ____

= _____

Answer:

115 ÷ 5 = 23

Explanation:

115 ÷ 5

= (100 + 15) ÷ 5

= (100 ÷ 5) + (15 ÷ 5)

= 20 + 3

= 23.

**On Your Own**

Question 4.

**Use Tools** Debra raises alpacas for their wool. She feeds each alpaca 7 pounds of food each week. She uses 98 pounds of food each week. How many alpacas does Debra have? Use an area model to find 98 ÷ 7.

Debra has ___ alpacas.

Answer:

Explanation:

98 ÷ 7 = 14

Debra has 14 alpacas.

Question 5.

**Use Structure** Malik hand spins wool yarn in 3-pound batches. He now has 126 pounds of yarn. How many batches has he spun? Use the Distributive Property to find 126 ÷ 3.

Answer:

126 ÷ 3 = 42

Explanation:

126 ÷ 3

= (90 + 36 ) ÷ 3

= (90 ÷ 3) + (36 ÷ 3)

= 30 + 12

= 42.

**Divide.**

Question 6.

248 ÷ 8 = ___

Answer:

248 ÷ 8 = 31

Explanation:

248 ÷ 8

= (200 + 48) ÷ 8

= (200 ÷ 8) + (48 ÷ 8)

= 25 + 6

= 31.

Question 7.

135 ÷ 5 = ___

Answer:

135 ÷ 5 = 27

Explanation:

135 ÷ 5

= (100 + 35) ÷ 5

= (100 ÷ 5) + (35 ÷ 5)

= 20 + 7

= 27.

Question 8.

138 ÷ 6 = ___

Answer:

138 ÷ 6 = 23

Explanation:

138 ÷ 6

= (90 + 48) ÷ 6

= (90 ÷ 6) + (48 ÷ 6)

= 15 + 8

= 23.

**I’m in a Learning Mindset!**

How did using an area model help me understand using the Distributive Property to divide?

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