Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 5, Part C:
Rates (40 minutes)

A rate describes how much one variable changes with respect to another. Rates are often used to describe relationships between time and distance. When an object or person moves at a constant rate, the relationship between distance and time is linear. Note 11

Problem C1

Achilles runs at a constant rate of 9 miles per hour. Note 12

 a. Write an equation describing the relationship between the distance Achilles covers and the time he runs. b. How far will Achilles travel in 1.5 hours? c. If you graphed the relationship between the distance Achilles covers and the time he runs, what would the graph look like? d. Enter your equation in a spreadsheet, and use the spreadsheet to draw the graph. Is the graph what you expected? Explain why or why not.

 Would a closed-form or a recursive rule be easier to work with in this situation?   Close Tip Would a closed-form or a recursive rule be easier to work with in this situation?

Problem C2

Achilles is going to race against a tortoise, who moves at only 1 mile per hour. To make the race fair, the tortoise gets a head start of 32 miles.

 a. Write an equation describing the relationship between distance and time for the tortoise. b. Enter the tortoise's equation into a spreadsheet. c. How long will it take for Achilles to catch up to the tortoise?

 Video Segment In this video segment, participants use a spreadsheet program to answer Problem C2. Watch this segment after you have completed Problem C2. If you get stuck on the problem, you can watch the video segment to help you. Could the participants have answered Problem C2 using a recursive rule? You can find this segment on the session video, approximately 17 minutes and 56 seconds after the Annenberg Media logo.

 Problem C3 Make a single graph that shows the progress of Achilles and the tortoise. Where do the two lines cross?

 Problem C4 What is the relationship between the points where the lines cross and Achilles passing the tortoise?

 Problem C5 Which of the two lines in Problem C3 represents a proportional relationship? How do you know?

 If you need more help with proportional relationships, refer to Session 4, Part C.    Close Tip If you need more help with proportional relationships, refer to Session 4, Part C.

 Problem C6 Suppose that two people were traveling a distance of 100 miles at the same speed, and the first person got a head start of 25 miles. When would you expect them to be at the same point? What does this tell you about their distance graphs? Note 13

 Session 5: Index | Notes | Solutions | Video