## Engage NY Eureka Math 4th Grade Module 3 Lesson 20 Answer Key

### Eureka Math Grade 4 Module 3 Lesson 20 Problem Set Answer Key

Question 1.
Alfonso solved a division problem by drawing an area model.
a. Look at the area model. What division problem did Alfonso solve? Alfonso solved division problem of 72 ÷ 4 = 18,

Explanation:
Given Alfonso solved a division problem by drawing an area model. Looking at the area model, the division problem did Alfonso solved is 40 + 32 = 72 and
when 72 is divided by 4 we get 18 as quotient.

b. Show a number bond to represent Alfonso’s area model. Start with the total, and then show how the total is split into two parts. Below the two parts, represent the total length using the distributive property, and then solve. (___÷___) + (___÷___)
= ____ + ____
= _____ Explanation:
Shown a number bond to represent Alfonso’s area model.
Started with the total 72 and then showed how the total is split into two parts. Representing the total length
72 as (40 + 32) ÷ 4 using the distributive property as (40 ÷ 4) +  (32 ÷ 4) = 10 + 8 = 18 as shown above in the picture.

Question 2.
Solve 45 ÷ 3 using an area model. Draw a number bond, and use the distributive property to solve for the unknown length. Explanation:
Solved 45 ÷ 3 using an area model. Drawn a number bond and used the distributive property to solve for the unknown length as
(30 + 15) ÷ 3 = (30 ÷ 3) + (15 ÷ 3) = 10 + 5 = 15.

Question 3.
Solve 64 ÷ 4 using an area model. Draw a number bond to show how you partitioned the area, and represent the division with a written method. Explanation:
Solved 64 ÷ 4 using an area model. Drawn a number bond to show how I partitioned the area, and represented the division with a written method as shown in the above picture.

Question 4.
Solve 92 ÷ 4 using an area model. Explain, using words, pictures, or numbers, the connection of the distributive property to the area model. Explanation:
Used the area model to show how we can break a part a whole into pieces that make it easier to divide. The distributive property shows how the whole is broken apart as (80 + 12) ÷ 4 = (80 ÷ 4) + (12 ÷ 4) = 20 + 3 = 23.

Question 5.
Solve 72 ÷ 6 using an area model and the standard algorithm. Explanation:
Solved 72 ÷ 6 using an area model and the standard algorithm as shown above quotient = 12 and remainder = 0.

### Eureka Math Grade 4 Module 3 Lesson 20 Exit Ticket Answer Key

Question 1.
Tony drew the following area model to find an unknown length. What division equation did he model? Tony solved division problem of 72 ÷ 3= 24,

Explanation:
Given solved a division problem by drawing an area model. Looking at the area model.
The division problem did Tony solved is 60 + 12 = 72 and when 72 is divided by 3 we get 24 as quotient.

Question 2.
Solve 42 ÷ 3 using the area model, a number bond, and a written method. Explanation:
Solved 42 ÷ 3 using an area model. Drawn a number bond to show how I partitioned the area, and represented the division with a written method as shown in the above picture.

### Eureka Math Grade 4 Module 3 Lesson 20 Homework Answer Key

Question 1.
Maria solved a division problem by drawing an area model.
a. Look at the area model. What division problem did Maria solve? Maria solved division problem of 54 ÷ 3 = 18,

Explanation:
Given Maria solved a division problem by drawing an area model. Looking at the area model, the division problem did Maria solved is 30 + 24 = 54 and
when 54 is divided by 3 we get 18 as quotient.

b. Show a number bond to represent Maria’s area model. Start with the total, and then show how the total is split into two parts. Below the two parts, represent the total length using the distributive property, and then solve. (_30__÷_3__) + (_24__÷_3__)
= __10__ + __8__
= __18___ Explanation:
Shown a number bond to represent Maria’s area model.
Started with the total of 54 and then showed how the total is split into two parts. Representing the total length 54 as (30 + 24) ÷ 3 using the distributive property as (30 ÷ 3) +  (24 ÷ 3) = 10 + 8 = 18 as shown above in the picture.

Question 2.
Solve 42 ÷ 3 using an area model. Draw a number bond, and use the distributive property to solve for the unknown length. Explanation:
Solved 42 ÷ 3 using an area model. Drawn a number bond and used the distributive property to solve for the unknown length as (30 + 12) ÷ 3 = (30 ÷ 3) + (12 ÷ 3) = 10 + 4 = 14.

Question 3.
Solve 60 ÷ 4 using an area model. Draw a number bond to show how you partitioned the area, and represent the division with a written method. Explanation:
Solved 60 ÷ 4 using an area model. Drawn a number bond to show how I partitioned the area, and represented the division with a written method as shown in the above picture.

Question 4.
Solve 72 ÷ 4 using an area model. Explain, using words, pictures, or numbers, the connection of the distributive property to the area model.  