Associative Property of Multiplication
Students will be able to apply the associative property to multiply single-digit factors.
- Ask students what the word associate means. Use it in a sentence. For example, "I associate with Matthew during recess," or "We often associate the color blue with sadness." Give students a moment to discuss the word with peers.
- Call on a few students to give a definition for the word associate and then develop a meaning with the class (i.e. joined or connected)
- On the board, draw a quick picture to illustrate the word (i.e. draw two people holding hands)
- Explain: Today we are going to explore the associative property of multiplication.
- Write the name of the property on the board and underline the word associative.
Explicit Instruction/Teacher modeling(10 minutes)
- Remind students that we can group numbers using parentheses.
- Explain: The associative property of multiplication states that an equation will have the same product regardless of how the factors are grouped.
- Write the definition on the board for student reference.
- Give an example, like (2 x 5) x 8 = 2 x (5 x 8). Solve each equation and show the students the product for each is 80.
- Point out that the factors are the same, and in the same order, but they are grouped differently.
- Write a second example on the board, like 3 x (2 x 4) = (3 x 2) x 4. Then solve.
- Summarize: When solving multiplication problems, factors can be grouped in any combination and it will not change the product. This is called the associative property of multiplication.
Guided Practice(10 minutes)
- Pair students with a partner.
- Hand out strips of paper, four pieces of macaroni pasta, and glue to each set of partners.
- Have students work with their partner to write an equation with three matching factors on either side of the equal sign (i.e. 4 x 5 x 6 = 4 x 5 x 6) leaving room between numbers.
- Instruct students to use their macaroni as parenthesis and glue them into their equation so that it illustrates the associative property ( i.e. (4 x 5) x 6 = 4 x (5 x 6) )
- Instruct partnerships to solve each side of the equation and discuss their conclusion about the placement of the parentheses.
Independent working time(20 minutes)
- Hand out the It’s Associative worksheet.
- Complete the first problem with the class, then instruct students to complete the worksheet independently.
- Circulate as students work and offer support as needed, then review the worksheet as a class.
- Provide partially completed problems, with parentheses around one set of factors, and have students add in parentheses to show the associative property.
- Have students use the internet to research other properties of multiplication.
- Have students make a comic or picture equation showing the associative property (see resources for an example).
- Collect and check for understanding.
Review and closing(5 minutes)
- Ask students, "What does the associative property help us understand about multiplication?"
- Discuss answers as a class.
- Some answers might include: Factors can be grouped in any combination, the product doesn’t change as long as the factors are the same, and multiplication has similar properties to addition.