Lesson 2

Discover

 

As you saw in Lesson 1, rates can be represented in many different ways, including as a ratio and pictorially. The representation you choose depends on your purpose. A graph can also be used to represent and compare rates.

 

Try This 1

 

You should place your completed Try This activities in your course folder. Your teacher may ask to see your completed Try This activities.

 

Use the “Distance-Time Graphs” gizmo to investigate graphs of a runner’s position versus time for a 40-m dash.

 

Ensure that the number of points is set to 2. Working with Runner 1, the “Show graph” and “Show animation” boxes should be checked. Drag the green arrow on the graph to the left. Look at the animation of the runner at the bottom. What do you notice about the position of the runner in the race and the time on the stopwatch as the green line is moved?

1. What does the slope of the graph of Runner 1 represent?
   
   
2. Add in a second runner by clicking on the “New” button next to Runner 2. Again, make sure the “Show graph” and “Show animation” boxes are checked. You can click on the new button several times to see different lines plotted on the graph for this runner. What does it mean when the second runner’s line does not start at (0, 0)? Hint: Look at the position of the runner in the animation below the graph.
   
   
3. Now move the green line to the left again and watch the animation. What happens? Compare the graphs of each runner to their respective positions during the race. From the graph, identify the following:
   
   
   • Who will finish the race first? How can you tell this from the graph?
     
     
   • Who is the slower runner? How can you tell this from the graph?
     
     
   • What is happening in the race when the graphs of the two runners intersect?
     
     
4. Complete the “Assessment Questions” located below the race track. Choose “Check Your Answers” when you have finished answering the questions.