Commutativity of Multiplication

Examples, solutions, and videos to help Grade 3 students learn how to demonstrate the commutativity of multiplication and practice related facts by skip-counting objects in array models.

Common Core Standards:3.OA.1, 3.OA.5, 3.OA.3, 3.OA.4

New York State Common Core Math Grade 3, Module 1, Lesson 7, Lesson 8

Worksheets for Grade 3

Lesson 7 Concept Development

Problem 1: Rotate arrays 90 degrees.
Problem 2: Interpreting rows and columns in rotated arrays.

Word Problem: Sara bought 2 boxes of notecards. Each box has 8 cards in it.
a) Draw an array to show the total number of cards.
b) Write a multiplication sentence that shows the total number of cards.
c) Use the commutative property to write a related multiplication sentence.

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Lesson 7 Homework

1. a. Count by twos 7 times.
   b. Draw an array that matches your count-by.
   c. Write a multiplication sentence that represents the total number of objects in your array.
   ________ × ________ = ________
   
2. a. Count by sevens 2 times.
   _______, _______

b. Draw an array that matches your count-by.
c. Write a multiplication sentence that represents the total number of objects in your array.
________ × ________ = ________
5. Write and solve a different multiplication sentence to describe each array.

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Lesson 8 Concept Development

Problem 1: Rotate arrays 90 degrees.
Problem 2: Interpreting rows and columns in rotated arrays.
Draw an array with 5 rows and 3 columns.
Draw an array with 3 rows and 5 columns.
When we turn an array 90 degrees, columns become rows and rows become columns.
Count by 4s five times.
Count by 5s four times.
Word Problem:
George puts 3 stickers on each page of his notebook. He puts stickers on 8 pages.
a) Draw an array showing the total number of stickers.
b) write a multiplication sentence to find the total number of stickers.
George adds 2 more pages, with 3 stickers on each page. Draw x’s to show the new stickers on the array.
c) Write a multiplication sentence for the new total.

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Lesson 8 Homework

1. a. Count by threes 6 times.
   b. Draw an array that matches your count-by.
   
2. a. Count by sixes 3 times.
   _______, _______, _______
   b. Draw an array that matches your count-by.
   
3. Ivania recycles. She gets 3 cents for every can she recycles.
   a. How much money does Ivania make if she recycles 4 cans?
   __________ × __________ = ________ cents
   b. How much money does she make if she recycles 7 cans?
   __________ × __________ = ________ cents

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