# Runners Activity - Worksheet

I would like to thank my colleagues of MathForum's Algebraic Reasoning Workshop - 3 - Winter07 for their activity ideas!

Getting Started

• Start Runners Activity*
• Click and drag popup window to right-hand side of your screen and resize this screen so that popup window and this screen do not overlap.

Directions for using Activity

Details

Runners Section:

• Click and drag runner to set starting position
• Click on runner to change direction

Activity Controls Section:

• Reset (use pause to stop activity in current position)
• Start or continue
• Go one step (stride)
• Pause

Runner Controls Section:

• Click on Runner to turn off/on
• Use arrow keys to set step size (length of stride)
• Note: To set position - click and drag runner in runners section

Graph Section

• Graph of (x,y)=(time, position of runner)
Activity 1: Exploring One Runner
• Turn off Emil (boy runner): in Runner Control Section, click on
• Set Lisa (girl runner): starting position=20' with step size=2

• Click on the play button.
• Look carefully at the generated graph. What can you say?

• Where on the graph does it show Lisa's starting position?
• Where on the graph does it show Lisa's ending position?
• How do we know the direction that Lisa is running?
Is she running forwards (towards 100' position) or backwards (towards 0' position)?
• How long did it take Lisa to finish the race?
• Where on the graph do you see Lisa's step size?
Activity 2: Exploring Two Runners
• Turn on both Troy (boy) and Singla (girl).
• Set the parameters in the Activity to match the graph below.

Parameters - ARGH, What's that??

• Parameters means the things you can change in an activity.
• So the parameters are: starting position, direction, and step size of each runner.
• So there are 6 parameters to check from the graph, fill in the table below and then set in the activity.
 Runner Starting Position Direction Step Size Singla (girl -blue line) Troy (boy -red line)
• Click on the play button to check your answers. If the graphs don't match, try again!
1. Where did Singla start the race?
2. Where did Troy start the race?
3. How long did it take Troy to finish the race?
4. How long did it take Singla to finish the race?
5. Who ran faster?
6. Where do the lines cross and what does it mean?
7. Steve says that Singla ran a longer distance because her line (the blue one) is longer. Is he correct?  If not, explain why.
Activity 3: Match the Pictures!

Directions: Match the Graphs to the Descriptions. Feel free to try them on the Activity!

 Four Graphs Four Descriptions 1. Sue and David are running in a race. Sue has a 20 foot head start. Their speed is the same. 2. Sue and David are running toward each other. They are running at the same speed. 3. Sue and David are running toward each other. David is faster than Sue. 4. Sue and David are running in a race. David has a 40 foot head start. Sue is running faster.
Activity 4: Tables & Graphs & Parameters - Oh my!
• The race-master recorded the following data.
 Rachel (girl) time position 20 40 30 60 40 80
 Mario (boy) time position 10 50 20 40 30 30
• Think about the following questions.
1. What can you tell about the direction(s) they are running?
2. Where did each runner start?
3. What are the parameters of the runners? Make a table of parameters as in Activity 2.
• Make an Activity that matches the tables.
• Set the parameters.
• Test your Activity. (Check that the points on the graph match the table data!)
• A few more questions.
1. Do their paths cross?
2. Which runner is running faster?