Mathematics, Operations (+, -, x, /, etc.), Problem Solving

Grade 3- 5

### Objective

Students learn about the Commutative and Associative Properties of Multiplication.

### Directions

Facts to Know

**Commutative Property**
The Commutative Property of Multiplication states that when the order of the factors is changed, the product stays the same. Multiplication is a commutative operation. In the equation 2 x 4 = 4 x 2, for example, the order of the factors does not affect the answer

(4 x 2 = 8 and 2 x 4 = 8).

The commutative property works for any number of factors. Study the following samples:

Sample A

5 x 6 x 7 = 7 x 6 x 5

5 x 6 x 7 = 210

7 x 6 x 5 = 210

Sample B

70 x 90 = 6,300

90 x 70 = 6,300

Sample C

30 x 50 = 50 x 30

30 x 50 = 1,500

50 x 30 = 1,500

**Associative Property**
The Associative Property of Multiplication states that when the grouping of the factors is changed, the product stays the same. Multiplication is associative. The way the factors are grouped with parentheses does not affect the answer. Study the following samples:

Sample D

2 x (3 x 4) = (2 x 3) x 4

2 x (3 x 4) = 24

(2 x 3) x 4 = 24

Sample E

6 x (7 x 9) = (6 x 7) x 9

6 x (7 x 9) = 378

(6 x 7) x 9 = 378

Sample F

4 x (5 x 6) = (4 x 5) x 6

4 x (5 x 6) = 120

(4 x 5) x 6 = 120

Distribute the activity sheets to students and have them use their knowledge of these properties to solve the problems.

### Resources

- Commutative Property and Associative Property activity pages
- pencils