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.
- 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 =
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.
Write4 x 2 x 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 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)