Patrick W. Thompson
Arizona State University
This assignment uses the sketch City Distances. There are two ways to use this sketch, the GSP 4.0 version or a Java version. For some reason the Java version insists on up being negative and down being positive, but it's not hard to adjust to that.
The sketch depicts a car on a stretch of road, passing between two cities named (somewhat uncreatively) City A and City B. The activities in this assignment are based on your use of that sketch.
The immediate objective is that you become able to imagine how the car's distances from the two cities vary with the car's location on the road. Subsequent objectives will be that you understand graphs with greater sophistication.
The activities in this assignment are structured in four levels. The levels begin at a level of engagement -- "making sense" of the simulation and building a strong sense of covariation (keeping track simultaneously of two quantities' values as they vary). Subsequent activities are aimed at having you be able to answer questions about covariation through your imagination.
You will be asked at times to observe, reflect, and respond to questions. When you are asked to write your answer, please include the question you are answering. This is so that when I read an answer, I know what question you are answering.
Watch the distances from City A and from City B as you vary the car's location
This is the set of axes on which the distances between the car and the two cities will be plotted.
For each arrangement:
Imagine the behavior of Distance from A relative to the car's position as you move the car from one end of the road to the other.
Imagine the behavior of Distance from B relative to the car's position as you move the car from one end of the road to the other.
Imagine the behavior of Correspondence Point as you move the car from one end of the road to the other.
Sketch your prediction of the graph that Correspondence Point will make with this arrangment.
Test your prediction.
Explain why you think each will be tricky.
After making all your predictions:
(After you have tested your prediction: Describe how the graph changes as you move point B parallel to the road. Why does the graph change as it does?)
(After you have tested your prediction: Describe how the graph changes as you move point A perpendicular to the road. Why does the graph change as it does?)