Apply Distributive Property

Examples, solutions, and videos to help Grade 3 students learn how to apply the distributive property and the fact 9 = 10 - 1 as a strategy to multiply.

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 Grade 3, Module 3, Lesson 12

Worksheets for Grade 3

Application Problem

A scientist fills 5 test tubes with 9 milliliters of fresh water in each. She fills another 3 test tubes with 9 milliliters of salt water in each. How many milliliters of water does she use in all? Use the break apart and distribute strategy to solve.

Note: The Application Problem is meant to reinforce the 5 + n break apart and distribute strategy to support Problem 1 in the Problem Set, and also to provide a point of comparison between the 5 + n strategy and the 9 = 10 – 1 strategy for multiplying with a factor of 9. Notice that in order to add 45 and 27, the student has taken 3 from 45 to make 30 from 27.

Concept Development

Use the 9 = 10 – 1 strategy to solve 9 × n facts.

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Lesson 12 Problem Set

1. Each cube has a value of 9. Find the value of each row. Then add the rows to find the total.
   a. 6 × 9 = ____
   6 × 9 = (5 + 1) × 9
   = (5 × 9) + (1 × 9)
   = 45 + ____
   = ____
   b. 7 × 9 = _____
   7 × 9 = (5 + ) × 9
   = (5 × 9) + ( × 9)
   = 45 + _____
   = _____
   c. 8 × 9 = _____
   8 × 9 = (5 + ) × 9
   = (5 × 9) + ( × _____)
   = 45 + _____
   = _____
   d. 9 × 9 = _____
   9 × 9 = (5 + ) × 9
   = (5 × 9) + ( × _____)
   = 45 + _____
   = _____

2. Find the total value of the shaded blocks.
   a. 9 × 6 = _
   9 sixes = 10 sixes − 1 six
   = − 6
   = _____
   b. 9 × 7 = ______
   9 sevens = 10 sevens − 1 seven
   = _____ − 7
   = _____
   c. 9 × 8 = ______
   9 eights = 10 eights − 1 eight
   = _____ − 8
   = _____
   d. 9 × 9 = ______
   9 nines = 10 nines − 1 nine
   = _____ − _____
   = _____

3. Matt buys a pack of postage stamps. He counts 9 rows of 4 stamps. He thinks of 10 fours to find the total number of stamps. Show the strategy that Matt might have used to find the total number of stamps.

Lesson 12 Homework

1. Find the value of each row. Then add the rows to find the total.
   b. 9 × 7 = (5 + ) × 7
   = (5 × 7) + ( × 7)
   = 35 + _____
   = _____
   c. 9 × 8 = (5 + ) × 8
   = (5 × 8) + ( × _____)
   = 40 + _____
   = _____
2. Match.
   a. 9 fives = 10 fives − 1 five
   = 50 − 5
   b. 9 sixes = 10 sixes − 1 six
   =_____ − 6
   c. 9 sevens = 10 sevens − 1 seven
   = _____ − 7
   d. 9 eights = 10 eights − 1 eight
   = _____ − 8
   e. 9 nines = 10 nines − 1 nine
   = _____ − _____
   f. 9 fours = 10 fours − 1 four
   = _____ − _____

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