In geometry, we started a unit on angles and segments in circles. Since we are at the end of the softball season, I decided to use a situation that I’ve encountered to help them figure out how to calculate arc length.
I like to work out and run during the hour I have after school and before needing to be at softball to start pre-game warm ups. In order to save some time, I usually run around the school or on the softball field. So the question arises:
I define a pole as from the left field foul pole to the right field foul pole and back. My students immediately asked for some measurements and some sort of “proof” that the field was circular.
My students quickly figured out that the 90 degree angle made by the foul lines was a quarter of the circle and tied that to the idea that they were using a percentage of the circumference. As a group, we came up with a general formula and then worked some practice problems dealing with arc length.