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?

 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?

 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. +

 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.

 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.

 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. + +

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