Transcript generic rectangle

1.3.3 Distributive Property Task
SWBAT:
1) Use distributive property to simplify expressions and
write equivalent expressions
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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?
613
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?
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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 .
6  10  3
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4) How does this model compare to the models of
discussed in question 2? 613
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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.
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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.
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7) Fill in the shaded boxes so that this rectangle
represents the expression .
8  10  7 
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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.
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10) Draw a generic rectangle below to represent
the expression .
11 14  9
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
11 23
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13) Now rewrite the product with an equivalent expression that
uses the distributive property. Represent your expression using a
generic rectangle.
13 41
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14) Use the rectangle to represent the expression .
9   x  4
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 x  3
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Generic rectangles can be used to model
expressions with more than 1 variable quantity.
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18) Draw a generic rectangle to model the
expression . Write the corresponding equation that
relates the expression with the areas in the generic
rectangle.
a   3b  5
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pp. 99 – 101
1 – 4, 9- 13, 23 – 27 odd, 33, 47, 48