## Lesson: Associative Property of Multiplication Developing the Concept

In this lesson, students explore the Associative Property of Multiplication.

Materials: none

Preparation: none

Prerequisite Skills and Background: Students should know the multiplication facts for factors 0 through 10.

• Write3 x 2 x 4 = and6 x 4 = on the board.
3 x 2 x 4 =
6 x 4 =
• Ask: How are these two number sentences related?
Lead students to discover that the first factor in 6 x 4 = is the product of the first and second factors in 3 x 2 x 4 = .
• Say: To find the product of three factors, you multiply in groups of two factors. Parentheses are grouping symbols. They tell you which operation to complete first.
Put parentheses around 3 x 2.
• Ask: What is the product of 3 and 2? (6) What is the product of 6 and 4? (24) What is the product of 3 and 2 and 4? (24)
Replace with 24 in the multiplication sentences.
• Write3 x (2 x 4) = and3 x 8 = on the board.
3 x (2 x 4) = 3 x 8 =
• Ask: What two factors are grouped in the first multiplication sentence? (2 and 4) What is the product of 2 and 4? (8) What is the product of 3 and 8? (24) What is the product of 3 and 2 and 4? (24)
Replace with 24 in the multiplication sentences.
• Ask: Did the product change when we changed the grouping of the factors? (no)
• Say: The way factors are grouped never changes the product. This is called the Associative Property of Multiplication.
• Write5 x 2 x 3 = on the board twice.
• Ask: Which factors would you multiply first in this multiplication sentence? Why?
Some students may choose 2 and 3 because it is an easy fact. Other students may choose 5 and 2 because multiplying by 10 is easy. Have volunteers put parentheses around the two factors they would multiply first and solve the problem.
• Ask: Is the product the same in both sentences? (yes)
• Give students more examples of multiplying three factors. Encourage them to express their reasons for choosing which factors to multiply first.

Wrap-Up and Assessment Hints
Emphasize the importance of multiplying factors in parentheses first. Your students will apply this valuable skill when they perform more than one operation in a number sentence. Give them lots of practice multiplying three factors and have them explain how they found the product, including which factors they multiplied first and why.