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### Lesson plan

# Distributive Property

#### Learning Objectives

Students will be able to apply the distributive property of multiplication.

#### Introduction

*(5 minutes)*

- 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.

#### Differentiation

**Support:**

- 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)**).

**Enrichment:**

- Have students use the internet to research other properties of multiplication.
- Have students solve word problems using the distributive property (see optional materials).

#### Assessment

*(5 minutes)*

- 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).