## Engage NY Eureka Math 6th Grade Module 4 Lesson 3 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 3 Exercise Answer Key

Exercise 1.

Write the addition sentence that describes the model and the multiplication sentence that describes the model.

Answer:

5 + 5 + 5 and 3 × 5

Exercise 2.

Write an equivalent expression to demonstrate the relationship of multiplication and addition.

a. 6 + 6

Answer:

2 × 6

b. 3 + 3 + 3 + 3 + 3 + 3

Answer:

6 × 3

c. 4 + 4 + 4 + 4 + 4

Answer:

5 × 4

d. 6 × 2

Answer:

2 + 2 + 2 + 2 + 2+ 2

e. 4 × 6

Answer:

6 + 6 + 6 + 6

f. 3 × 9

Answer:

9 + 9 + 9

g. h + h + h + h + h

Answer:

5h

h. 6y

Answer:

y + y + y + y + y + y

Exercise 3.

Roberto is not familiar with tape diagrams and believes that he can show the relationship of multiplication and addition on a number line. Help Roberto demonstrate that the expression 3 × 2 is equivalent to 2 + 2 + 2 on a number line.

Answer:

Possible answer: The first number line shows that there are 3 groups of 2, resulting in 6. The second number line shows the sum of 2 + 2 + 2, resulting in 6.

Since both number lines start at 0 and end at 6, the expressions are equivalent.

Exercise 4.

Tell whether the following equations are true or false. Then, explain your reasoning.

a. x + 6g − 6g = x

The equation is true because it demonstrates the addition identity.

b. 2f − 4e + 4e = 2f

Answer:

The equation is true because it demonstrates the subtraction identity.

Exercise 5.

Write an equivalent expression to demonstrate the relationship between addition and multiplication.

a. 6 + 6 + 6 + 6 + 6 + 6 + 6

Answer:

4 × 6 + 3 × 4

b. d + d + d + w + w + w + w + w

Answer:

3d + 5w

c. a + a + b + b + b + c + c + c + c

Answer:

2a + 3b + 4c

### Eureka Math Grade 6 Module 4 Lesson 3 Problem Set Answer Key

Write an equivalent expression to show the relationship of multiplication and addition.

Question 1.

10 + 10 + 10

Answer:

3 × 10

Question 2.

4 + 4 + 4 + 4 + 4 + 4 + 4

Answer:

7 × 4

Question 3.

8 × 2

Answer:

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

Question 4.

3 × 9

Answer:

9 + 9 + 9

Question 5.

6m

Answer:

m + m + m + m + m + m

Question 6.

d + d + d + d + d

Answer:

5d

### Eureka Math Grade 6 Module 4 Lesson 3 Exit Ticket Answer Key

Write an equivalent expression to show the relationship of multiplication and addition.

Question 1.

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8

Answer:

9 × 8

Question 2.

4 × 9

Answer:

9 + 9 + 9 + 9

Question 3.

6 + 6 + 6

Answer:

3 × 6

Question 4.

7h

Answer:

h + h + h + h + h + h + h

Question 5.

j + j + j + j + j

Answer:

5j

Question 6.

u + u + u + u + u + u + u + u + u + u

Answer:

10u

### Eureka Math Grade 6 Module 4 Lesson 3 Opening Exercise Answer Key

Write two different expressions that can be depicted by the tape diagram shown. One expression should include addition, while the other should include multiplication.

a.

Answer:

Possible answers: 3 + 3 + 3 or 3 × 3

b.

Answer:

Possible answers: 8 + 8 or 2 × 8

c.

Answer:

Possible answers: 5 + 5 + 5 or 3 × 5