# The Relationship of Multiplication and Addition

Videos and solutions to help Grade 6 students build and clarify the relationship of multiplication and addition by evaluating identities such as 3 • g = g + g + g

New York State Common Core Math Module 4, Grade 6, Lesson 3

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Lesson Plans and Worksheets for Grade 6
Lesson Plans and Worksheets for all Grades

Opening Exercise

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

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

2. Write an equivalent expression to demonstrate the relationship of multiplication and addition.
a. 6 + 6
b. 3 + 3 + 3 + 3 + 3 + 3
c. 4 + 4 + 4 + 4 + 4
d. 6 × 2
e. 4 × 6
f. 3 × 9
g. h + h + h + h + h
h. 6y

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.

4. Tell whether the following number sentences are true or false. Then explain your reasoning.
a. x + 6g - 6g = x
b. 2f - 4e + 4e = 2f

5. Write an equivalent expression to demonstrate the relationship between addition and multiplication.
a. 6 + 6 + 6 + 6 + 4 + 4 + 4
b. d + d + d + w + w + w + w
c. a + a + b + b + b + c + c + c + c
Problem Set
Write an equivalent expression to show the relationship of multiplication and addition. 1. 10 + 10 + 10
2. 4 + 4 + 4 + 4 + 4 + 4 + 4
3. 8 × 2
4. 3 × 9
5. 6m
6. d + d + d + d + d

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