Math Background

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 = blank box and6 x 4 = blank box on the board.
    3 x 2 x 4 = blank box
    6 x 4 = blank box
  • Ask: How are these two number sentences related?
    Lead students to discover that the first factor in 6 x 4 = blank box is the product of the first and second factors in 3 x 2 x 4 = blank box.
  • 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 blank box with 24 in the multiplication sentences.
  • Write3 x (2 x 4) = blank box and3 x 8 = blank box on the board.
    3 x (2 x 4) = blank box 3 x 8 = blank box
  • 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 blank box 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 = blank box 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.


Houghton Mifflin Math Grade 3