Session 8, Part B: Inverse Proportions

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.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. If you prefer, you can view the low-tech version of this acivity, which doesn't require the Flash plug-in.

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	80	2000
100	20	2000
1,000	2	2000
40	50	2000
80	25	2000
2000	1	2000
0.5	4,000	2000

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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	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

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b.	As x increases by 10, what happens to y? Does y go up a fixed amount? An increasing amount? A decreasing amount?
c.	As x doubles, what happens to y? As x triples, what happens to y?
d.	If x is very small, what can you say about y? What if x is very big?

"Ms. Anwar's Backyard" problem taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p.110. www.glencoe.com/sec/math

Next > Part B (Continued): Another Inverse Proportion

Session 8: Index | Notes | Solutions | Video