Lesson Name: Taxi-cab Metric B - Circle
Resources: Regular_city_2.gsp. Note: in order to view and use this file you need to have a Geometry Sketchpad installed in your computer.
Outline: Create a circle using the taxi-cab metric.
Begin with a discussion of definitions. What makes a circle a circle? What makes other geometric figures, those geometric figures. If the students are too attached to the visualizations of the figures they are working with they will have more trouble accepting a taxi-cab circle as an actual circle. (This may take a lesson in itself.)
Step 1: (~10 min) How are you going to approach the problem? Discuss different methods for figuring out how to graph the circle.
Step 2: (~15-20 min) Implement what you discussed in step 1.
Goals: Seeing the importance of definitions over visualizations.
Implementation: Draw various figures both geometric and otherwise and ask the students what shapes they are and why.
For graphing the circle discuss how to make a t-chart of points to get a general idea of what the circle looks like.