Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 8, Part B:
Inverse Proportions (60 minutes)

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

Imagine that the teachers in your school decide to play the lottery together. If they win, the prize is \$800,000. Problem B1 is a table that shows how much each teacher will get, depending on how many of them contribute to buy the tickets. Note 4

Problem B1

Fill in the rest of this table: Note 5

 Number of teachers Amount each will receive 1 800,000 2 400,000 3 4 80,000 53,333.33

 Number of teachers Amount each will receive 1 800,000 2 400,000 3 266,666.66 4 200,000 10 80,000 15 53,333.33 20 40,000 100 8,000

 Problem B2 Describe a rule that fits the table. Try to find more than one rule. Explain why your rule will work if the table is continued.

 Problem B3 Graph the rule that shows how much each teacher will receive. Describe how this graph is different from other functions you've seen.

 Make sure you distinguish this function from all the other functions you've seen -- linear, exponential, quadratic, and cyclic.   Close Tip Make sure you distinguish this function from all the other functions you've seen -- linear, exponential, quadratic, and cyclic.

 Video Segment In this video segment, the class discusses the shape of the graph for the lottery problem. Then they discuss whether or not the graph crosses the line y = 0. Watch this segment after you've completed Problem B3. If you get stuck on the problem, you can watch the video segment to help you. What would a value of y = 0 mean in terms of the lottery problem? There is an important difference between this type of function -- a decreasing curve -- and a decreasing line. You can find this segment on the session video, approximately 10 minutes and 15 seconds after the Annenberg Media logo.

Functions like this are called inverse proportions. The relationship between the two variables in this function is called inverse variation. Inverse proportions are another example of nonlinear functions.

You can think of inverse proportions in two ways:

 • output = some constant / input, or • input * output = some constant

There are many applications of these kinds of functions. If you're getting paid a fixed amount of money to do a job, for example, your hourly rate depends on how quickly you complete the work. The shorter the time, the larger the hourly rate.

 Session 8: Index | Notes | Solutions | Video