Math Background

Lesson: Associative Property of Multiplication
Introducing the Concept

Before students explore the Associative Property of Multiplication, they need to use the Commutative Property of Multiplication to multiply three factors.

Materials: 20 counters for each student or pair of students

Preparation: none

Prerequisite Skills and Background: Students should know how to use arrays to multiply.

  • Say: Show an array with 4 rows of 2 counters.
  • Ask: What multiplication sentence describes the array?
    Students should say 4 x 2 = 8.
  • Ask: What multiplication sentence with 3 factors describes the array?
    Elicit from students that there is 1 array with 4 rows of 2 counters, so 1 x 4 x 2 = 8 describes the array.
  • Write and label1 x 4 x 2 = 8 on the board.
    multiplication sentence
  • Ask: What did you learn about the Commutative Property of Multiplication when you multiplied two factors?
    Students should recall that changing the order of the factors does not change the product.
  • Say: Let's see if the Commutative Property of Multiplication works for three factors.
  • Write2 x 1 x 4 = blank box on the board.
    multiplication sentence
  • Say: Show 2 arrays with 1 row of 4 counters in each array.
  • Ask: Is the product the same? (yes)
    Replace blank box in the number sentence on the board with 8.
  • Say: Let's change the order of the factors again. Write4 x 2 x 1 = blank box on the board.
    multiplication sentence
  • Say: Show 4 arrays with 2 rows of 1 counter in each array.
    Give students ample time to make all four arrays.
  • Ask: Is the product the same? (yes)
    Replace blank box in the number sentence on the board with 8.
  • Ask: Does the Commutative Property of Multiplication work for three factors? (yes)
  • Repeat this activity for2 x 3 x 4. Have students suggest different ways to order the factors. (2 x 4 x 3, 3 x 2 x 4, 3 x 4 x 2, 4 x 2 x 3, 4 x 3 x 2)

Houghton Mifflin Math Grade 3