Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 8, Part B:
Inverse Proportions

In This Part: Splitting a Prize | Ms. Anwar's Backyard | Another Inverse Porportion

The following Interactive Activity demonstrates the graph of another inverse proportion. Ms. Anwar is considering renting a house that has a large rectangular backyard. She wants to figure out if there will be room for her children's play equipment. The owner told her, "The backyard has an area of 2,000 square feet." Ms. Anwar thought about what he said and tried to imagine what the actual dimensions of the yard might be. In the Interactive Activity, you control one dimension of the yard, and the other dimension changes so that the area remains constant.
Note: You can also change the area of the yard (to 1,000 square feet) to see how this affects the dimensions.

Problem B4

Fill in the table below to show some possibilities for the dimensions of the yard if the area is 2,000 square feet.

 Length Width Area = length * width 50 40 2000 25 2000 100 2000 2 2000 2000 2000 2000 2000

 Length Width Area = length * width 50 40 2000 25 80 2000 100 20 2000 1,000 2 2000 40 50 2000 80 25 2000 2000 1 2000 0.5 4,000 2000

 Problem B5 Find an equation relating the length (x) and the width (y) in the table above.

 Problem B6 Graph the length vs. width in the table above.

Problem B7

As x changes, what happens to y? Try to describe this relationship as clearly as possible. These problems may help you:
Note 6

 a. Complete the table below. Round values for y to one decimal place, or use the exact fractional value.

 x y Decrease in y 20 100 -- 30 66.7 33.3 40 50 60 70 80 90 100

 x y Decrease in y 20 100 -- 30 66.7 33.3 40 50 16.7 50 40 10 60 33.3 6.7 70 28.6 4.7 80 25 3.6 90 22.2 2.8 100 20 2.2