Question 1(3 points)

1. You have a 5-foot-by-7-foot rectangular rug in your classroom. You also have a bunch of square-foot tiles and some tape measures.

a. What is the most primitive way to determine the area of the rug?

b. What is a less primitive way to determine the area of the rug, and why does this method work.

Question 2(3 points)

2. Draw a 3-cm-by-7-cm rectangle. Then discuss the difference in the units we attach to the 3 and the 7 in these two situations:

• When applying the rectangle area formula to determine the area of the rectangle.
• When viewing the rectangle as decomposed into equal groups of 1-cm-by-1-cm squares in order to apply the definition of multiplication.

Question 3 (3 points) a. Explain how to decompose the large rectangle in Figure 12.4 into 2% groups with 3% squares in each group, so as to describe the area of the rectangle as Explain why the area is (2% X 3%)cm 2 b. Calculate 2% X 3% without a calculator, showing your calculations. Then verify that this calculation has the same answer as when you determine the area of the rectangle in Figure 12.4 by counting squares