Students will be able to apply the distributive property of multiplication.
- Ask students what the word "distribute" means. Use it in a sentence (e.g., "A teacher will distribute your homework at the end of the day."). Then give students a moment to discuss the word with peers.
- Call on a few students to give a definition for the word distribute and then develop a meaning with the class (i.e., pass out or give shares of something).
- On the board, draw a quick picture to illustrate the word (i.e., draw a page of homework with arrows pointing from it to multiple students).
- Explain, "Today we are going to explore the distributive property of multiplication."
- Write the name of the property on the board and underline the word "distributive."
Explicit Instruction/Teacher modeling(10 minutes)
- Explain, "The distributive property of multiplication lets you multiply a sum by multiplying each addend separately."
- Write the definition on the board for student reference.
- Remind students that when we multiply, we can decompose (break apart) a factor into smaller parts to make it easier to multiply.
- Give an example, like 7 x 12. Explain that with the distributive property, we can decompose one of the factors and multiply by each part.
- Write the expression 7 x (10 + 2). Explain that 12 can be decomposed into numbers that are easier to multiply, like 10 and 2. Remind students that decomposing the number 12 does not change its value.
- Draw an arrow from 7 to each of the addends (10 and 2). Tell students that the distributive property lets you multiply the factor 7 by each of the parts, or addends.
- Write 70 + 14 under the previous expression and point out that 7 x 10 = 70 and 7 x 2 = 14.
- Explain, "Now, we can add the two partial products (parts of the total answer) to find the product of our original problem, 7 x 12 (i.e., 70 + 14 = 84 and 7 x 12 = 84)."
- Remind students that the distributive property allows us to multiply smaller parts to find the product.
- Write a second example on the board, like 6 x 15, and use the distributive property to solve.
- Summarize, "So, when solving multiplication problems, a factor can be decomposed into smaller parts. We can multiply by each part to find the product. This is called the distributive property of multiplication."
Guided Practice(10 minutes)
- Write a problem, like 9 x 13, on the board.
- Ask students, "Which factor should we decompose?"
- Write an expression on the board using student suggestions (e.g., 9 x (10 + 3)).
- Ask a student to draw arrows to show how to "distribute" or multiply the 9.
- Write a new expression using the distributed multiplication (i.e., (9 x 10) + (9 x 3)).
- Ask students to solve each part. and write the products on the board as a new expression (i.e., 90 + 27).
- Ask students to add to find the total product and call on a volunteer to answer.
- Write another problem, like 5 x 21, on the board and have students work with a partner to solve.
Independent working time(15 minutes)
- Hand out the Distributive Property worksheet.
- Go over the example and the "Try It" problem with the class, then instruct students to complete the worksheet independently.
- Circulate as students work and offer support as needed.
- Provide problems with one factor already decomposed and have students multiply by each part to show the distributive property (i.e., 4 x (5 + 10)).
- Have students use the internet to research other properties of multiplication.
- Have students solve word problems using the distributive property (see optional materials).
- Show examples of different properties (associative, identity, commutative, and distributive) and ask students to identify which example is a model of the distributive property.
- Provide a multiplication problem, like 4 x 16, and have students rewrite it using the distributive property. Collect and check for understanding.
- As an alternative assessment, have students draw a picture equation to illustrate the distributive property (see resources for example).
Review and closing(5 minutes)
- Ask students, "What does the distributive property help us understand about multiplication?"
- Discuss as a class (i.e., factors can be broken into parts, one factor can be multiplied by parts of the other factor, the distributive property makes it easier to multiply large factors).