# Commutative, Associative, Distributive Properties (Grade 3)

Videos and lessons to help Grade 3 students learn to apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Common Core: 3.OA.5

### Suggested Learning Target

• I can explain the commutative, associative, and distributive property of multiplication.
• I can apply the commutative, associative, and distributive properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.
• I can explain how the operation properties can and cannot apply to division and use those properties that can apply to make it easier to find the quotient.

Related Topics:

Apply properties of operations as strategies to multiply and divide--Lesson 1 of 5 (CCSS: 3.OA.5)
In this lesson, you will learn ways to name a multiplication number sentence by counting the rows and columns of its array.

Apply properties of operations as strategies to multiply and divide--Lesson 2 of 5
In this lesson you will learn a strategy of solving multiplication word problems by using your knowledge of arrays to draw diagrams.

Apply properties of operations as strategies to multiply and divide--Lesson 3 of 5
In this lesson you will learn that division is the inverse operation of multiplication by visualizing the parts of a division problem.

Apply properties of operations as strategies to multiply and divide--Lesson 4 of 5
In this lesson you will learn a strategy for solving multiplication problems with 3 factors by diagramming each step of the process.
Example: You get a summer job making \$5 an hour. You work for two hours each day. How much money will you make if you work for three days?

Apply properties of operations as strategies to multiply and divide--Lesson 5 of 5
In this lesson you will learn another strategy for solving multiplication facts by breaking apart their arrays into more familiar facts.

Distributive Property

Commutative Property of Multiplication
The order of numbers does not matter when multiplying.

Associative Property of Multiplication
The sum or product stays the same when grouping of addends or factors is changed.

Distributive Property
When multiplying a factor and a sum, you can distribute the factor across the addition.