Houghton Mifflin Mathematics Grade 3: Chapter 6: Using a Multiplication Table: Introducing the Concept

Using a
Multiplication Table

Introducing the Concept

Developing the Concept

     Associative Property
     of Multiplication
  Introducing the Concept
  Developing the Concept

Associative Property of Multiplication

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 $times$ 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 $times$ 4 $times$ 2 = 8 describes the array.
Write and label 1 $times$ 4 $times$ 2 = 8 on the board.
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.
Write 2 $times$ 1 $times$ 4 = on the board.
Say: Show 2 arrays with 1 row of 4 counters in each array.
Ask: Is the product the same? (yes)
Replace in the number sentence on the board with 8.
Say: Let's change the order of the factors again. Write 4 $times$ 2 $times$ 1 = on the board.
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 in the number sentence on the board with 8.
Ask: Does the Commutative Property of Multiplication work for three factors? (yes)
Repeat this activity for 2 $times$ 3 $times$ 4. Have students suggest different ways to order the factors. (2 $times$ 4 $times$ 3, 3 $times$ 2 $times$ 4, 3 $times$ 4 $times$ 2, 4 $times$ 2 $times$ 3, 4 $times$ 3 $times$ 2)