Unit Activity
Unit: Rules of Exponents and Polynomials
This activity will help you meet these educational goals:
Mathematical Practices—You will make sense of problems and solve them, reason abstractly and quantitatively, use mathematics to model real-world situations, and look for and express regularity in repeated reasoning.
Introduction
In this unit, you used different methods to create and solve linear equations. You modeled scenarios using linear inequalities and solved them with the help of graphs. In this activity, you will analyze real-world situations by modeling them as equations and looking at their graphs.
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Directions and Analysis
Task 1: Tiles
Paulina is remodeling her bathroom. The tile she has chosen is shown below. There are squares and trapezoids in the tile. The side length of each square in the tile is x centimeters. The height and the length of one of the bases of each trapezoid is x centimeters. The other length is 2x centimeters.
a. Write a simplified equation to solve for x in terms of AT, the area of the tile. If necessary, use rational coefficients instead of root symbols.
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b. If the tile is a square with a length of b centimeters, what would AT be in terms of b?
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c. Using the result from part b, rewrite the equation for x in terms of b and explain how you simplify it. What does this equation really represent?
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d. Using the equation from part c, solve for x if the side length of the tile is 6 centimeters.
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e. After seeing her remodeled bathroom, Paulina’s friend Sabrina also wants to remodel her bathroom. The tile she has chosen is shown below.
If each of the smaller squares have sides c centimeters long, write an expression for the area of the whole tile, AT, and find the area of the tile if the length of the squares is 2.5 centimeters.
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f. Once she completes a wall, Sabrina notices that the number of squares along each side of the wall is equal to the number of square centimeters in each tile’s area. Write an equation for ...
