Session 4: Speeds, Rates, Steepness, and Lines (45 minutes)
In Parts B and C we examined the proportionality of mixtures and scale models. In this activity, we will take a close look at graphs to learn more about the relationships between distance and time, and between steepness and speed. Note 8
Suppose seven cars are all near an intersection. The graph below show the distances between cars and the intersection as time passes. Study this graph carefully and then try to answer the following questions.
In what direction is each car moving in relation to the intersection?
Compare the cars' speeds. How do their speeds relate to the steepness of the lines?
How could you approximate the cars' speeds using the labels on the axes? Close Tip
Does the distance vary directly with time for any of the cars? That is, is the relationship between distance and time proportional for any of the cars? How do you know?
Do any of the cars stop during their trips? If so, which cars?
Choose one of the seven cars, and describe your trip in this car. Use your imagination! Think of your observations as a passenger or driver in this car, and give the highlights of your trip for these 15 seconds. Include where and when you started the trip and what you saw going on around you -- in front of the car, to the sides, and through the rearview mirror.
Car problem taken from IMPACT Mathematics Course 2, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p. 328-329. www.glencoe.com/sec/math