3.OA.5

In this standard, students are asked to use the commutative, distributive, and associative properties of multiplication.

Commutative Property: the order of the factors does not matter (ex. 6 x 4 = 24 = 4 x 6).

Associative Property: when multiplying 3 factors, the grouping of factors can change in order to make the multiplication easier [ex. 4 x 6 x 2 can be solved as (4 x 6) x 2 = 24 x 2 = 48 or 4 x (6 x 2) = 4 x 12 = 48]

Distributive Property: a factor can be broken down into two smaller parts/sections

[example 1: 8 x 16= 8 x 10 + 8 x 6 = 80 + 48 = 128]

[example 2: 8 x (10 + 6)= 8 x 16 = 8 x 10 + 8 x 6 = 80 +48 = 128]

Real world example of the distributive property: Hamza goes to the store and buys 8 bags of candy. In each bag, there are 10 red candies and 6 blue candies. How many pieces of candy does he have in all?

There are two ways to solve this problem.

1) Multiply 8 bags x 10 candies. Multiply 8 bags x 6 blue candies. Add them together.

8 x 10 + 8 x 6 = 80 + 48 = 128

2) Add the candies in the bag (10 + 6). Then, multiply by the number of bags (8).

(10 + 6) x 8 = 16 x 8 = 10 x 8 + 6 x 8 = 128

Both answers will be 128.

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