Reflection: Complex Tasks The Stolen Car and Keys: An Introduction to Parametric Equations - Section 2: Share

One of the most challenging parts of the stolen car problem was how to graph since there were three quantities (time, feet east, and feet north). This really stumped my students but there were three options they came up with (two are shown in this image).

#1 - The feet east and feet north could represent the legs of a right triangle and we could find the hypotenuse to show the distance from the house. Thus, the two quantities would become a single quantity. Some students pointed out that this would work but we would not be able to see where the car was in relation to the house.

#2 - A common idea was to make two line - feet east v. time and feet north v. time. Again, the class decided that some important information would be missing, mainly that we would not be able to see the path of the car.

#3 - Finally, a few students thought about using a three-dimensional coordinate plane with time on the z-axis. This was hard to visualize, but students understood how this would work. One student noticed how if we looked at this graph with an overhead view, it would show us the path of the car but would not show time. This was a good transition to how we actually graphed these parametric equations.

Complex Tasks: How to Graph Three Variables?

The Stolen Car and Keys: An Introduction to Parametric Equations

Unit 11: Parametric Equations and Polar Coordinates
Lesson 1 of 12

Big Idea: A car and set of keys have been stolen - what does this have to do with parametric equations?

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50 minutes