1.3.3 Distributive Property Task

SWBAT:1) Use distributive property to simplify expressions and write equivalent expressions

In this lesson you will use what you already know about the areas of rectangles to model the multiplication of a constant and a binomial.

Getting started: What does multiplication look like?

Using the grid, create a model rectangle (array) to represent the multiplication problem:

1) Explain how your model shows the factors and the product.

2) Compare your model to you partner’s or group members’ models. How are they the same? How are they different?

136

Next, create a model for the expression that clearly shows the 6, 10 and 3.

3) Explain how your model shows each of the numbers and operations in the expression .

4) How does this model compare to the models of discussed in question 2?136

3106

5) What expressions are represented by each of these rectangle models? Write each expression next to the rectangle.

6) Explain how each model represents the expression you wrote.

These models represent the Distributive Property of Multiplication over Addition. As you have seen, sometimes in Algebra, we represent unknown or changing quantities with a variable. We can use a generic rectangle model to represent the distributive property when one or more of the quantities are represented by variables.

Consider the rectangle below:

This rectangle is called a generic rectangle because it can represent many different multiplication problems involving the distributive property, all depending on what we fill in to the shaded boxes.

7) Fill in the shaded boxes so that this rectangle represents the expression .

8) Fill in the interior of each rectangle with the area of the rectangle.

9) Write an equation which relates the expression from part 7 with the areas you found in part 8. Explain how this equation is related to the generic rectangle.

+

8 10 7

10) Draw a generic rectangle below to represent the expression .

11) Fill in the interior of your generic rectangle with the corresponding areas.

12) Write an equation which relates the expression from part 10 with the areas you found in part 11. Explain how this equation is related to the product

13) Now rewrite the product with an equivalent expression that uses the distributive property. Represent your expression using a generic rectangle.

13 41

11 23

11 14 9

14) Use the rectangle to represent the expression .

15) Fill in the interior of each rectangle with the area of the rectangle.

16) Write an equation which relates the expression from part 14 with the areas you found in part 15. Explain how this equation is related to the generic rectangle.

17) Draw a generic rectangle to model the expression . Write the corresponding equation that relates the expression with the areas in the generic rectangle. 4 2 3x

9 4x

Generic rectangles can be used to model expressions with more than 1 variable quantity.

  18) Draw a generic rectangle to model the

expression . Write the corresponding equation that relates the expression with the areas in the generic rectangle. 3 5a b

+ +

pp. 99 – 101 1 – 4, 9- 13, 23 – 27 odd, 33, 47, 48