 # Distributive Property

Videos and solutions to help Grade 3 students learn how to use the distributive property as a strategy to multiply and divide using units of 6 and 7.

Common Core Standards: 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.9, 3.OA.1, 3.OA.2, 3.OA.6

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

Application Problem

Mabel cuts 9 pieces of ribbon for an art project. Each piece of ribbon is 7 centimeters long. What is the total length of the pieces of ribbon that Mabel cuts?

Note: This problem reviews multiplication using units of seven. It is the same problem that is used in the first example in the concept development. Here it is given a context, while in the Concept Development it is not because the focus shifts to using the distributive property.

Concept Development

Part 1: Apply the distributive property to multiply using units of 6 and 7.

Part 2: Use addition number bonds to apply the distributive property to divide using units of 6 and 7.

Use the break apart and distribute strategy with number bonds to evaluate 48 ÷ 6.

Lesson 6 Homework

1. Label the tape diagrams. Then fill in the blanks below to make the statements true.
a. 6 × 7 = _____
(6 × 7) = (5 + 1) × 7
= (5 × 7) + (1 × 7)
= 35 + ______
= ______
b. 7 × 7 =_____
(7 × 7) = (5 + 2) × 7
= (5 × 7) + (2 × 7)
= 35 + ______
= ______
2. Break apart 54 to solve 54 ÷ 6.
54 ÷ 6 = (30 ÷ 6) + (_____ ÷ 6)
= 5 + ________
= __________

3. Break apart 56 to solve 56 ÷ 7.
56 ÷ 7 = (_____ ÷ _____) + (_____ ÷ _____)
= 5 + ________
= __________
4. Forty-two third grade students sit in 6 equal rows in the auditorium. How many students sit in each row? Show your thinking.
5. Ronaldo solves 7 × 6 by thinking of it as (5 × 7) + 7. Is he correct? Explain Ronaldo’s strategy.

Lesson 6 Homework

1. Label the tape diagrams. Then fill in the blanks below to make the statements true.
c. 8 × 7 = (5 + _____) × 7
= (5 × 7) + (____ × 7)
= 35 + ______
= ______
d. 9 × 7 = (5 + _____) × 7
= (5 × 7) + (____ × 7)
= 35 + ______
= ______
3. Break apart 56 to solve 56 ÷ 7.
56 ÷ 7 = (_____ ÷ _____) + (_____ ÷ _____)
= 5 + ________
= __________
5. Ronaldo solves 7 × 6 by thinking of it as (5 × 7) + 7. Is he correct? Explain Ronaldo’s strategy.

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