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1
Using a set of Algebra Tiles, arrange the tiles pictured below into one large rectangle.
a. On your paper, sketch your rectangle.
b. What are the dimensions (length and width) of the rectangle you made?
Label your sketch with its dimensions.
c. Write a statement showing that .
[ b: , c: ]
Problem 217 Category 1: Factoring quadratics
2
Joanne and Jermaine studied a rectangle formed by algebra tiles. They disagree about the correct expression for the tiles. Joanne wrote the expression . Jermaine wrote the expression . Who is correct? How can you be sure? Explain your reasoning.
[ Jermaine’s rectangle can be built: . Joanne’s expression does not form a rectangle. ]
Problem 218 Category 1: Factoring quadratics
3
Build rectangles with the dimensions given below. Sketch each rectangle on your paper, label its dimensions, and write an equivalence statement for the area as a product and a sum.
a. b.
[ a: , b: ]
Problem 219 Category 1: Multiplying polynomials
4
Your study team has a new student who does not understand the Distributive Property. Explain how and why the Distributive Property can help you find the product of . Include drawings of algebra tiles in your explanation.
[ ]
Problem 220 Category 1: Multiplying polynomials
5
Find the area of each part of the generic rectangles below and write the area of the whole as a product and a sum.
a. b.
[ a: ,
b: ]
Problem 221 Category 1: Multiplying polynomials
6
Find each of the following products by drawing and labeling a generic rectangle or by using the Distributive Property.
a. b.
[ a: , b: ]
Problem 222 Category 1: Multiplying polynomials
7
Solve the following equations for the indicated variable. Show all of your work.
a. Solve for x :
b. Solve for y :
c. Solve for m :
d. Solve for x :
[ a: , b: , c: , d: ]
Problem 226 Category 1: Solving for given variables
8
Solve the following equations for the indicated variable. Show all of your work.
a. Solve for x :
b. Solve for y :
c. Solve for w :
d. Solve for x :
[ a: , b: , c: , d: ]
Problem 228 Category 1: Solving for given variables
9
Using a set of Algebra Tiles, arrange the tiles pictured at right into one large rectangle.
a. On your paper, sketch your rectangle.
b. What are the dimensions (length and width) of the rectangle you made? Label your sketch with its dimensions.
c. Write a statement showing that .
[ b: , c: ]
Problem 247 Category 1: Factoring quadratics
10
Write the area of the rectangle below as a product and as a sum.
[ ]
Problem 252 Category 1: Multiplying polynomials