When I was in grad school I took an Advanced Geometry course and one of the first things we did was look at non-euclidean geometries, specifically Taxicab Geometry. The goal was to have us think about why the Euclidean axioms we take for granted are actually so important. The basic premise of Taxicab Geo is that distance is measured by the sum of the horizontal and vertical distance rather than the Pythagorean Theorem. It was really interesting to see how just changing our definition of distance changed some pretty substantial things.
Euclidean Distance = 5
Taxicab Distance = 7
A few weeks back 90% of our freshman class took a trip out of state for three school days and we were left to find something for those left behind, so I decided to adapt the activity. I made some worskheets (first and second) and let kids work through them. The third day we build on taxicab day 2 and had them investigate Pi a little bit.
Overall I think the activity was scaffolded well, and I like the worksheets we made. I think the biggest problem was that the kids that stayed behind didn’t really want to do any work, so it was like pulling teeth to get them through it. I also think they saw it as busy work so never really stopped and thought “WHAT?! Circles are Squares?! CRAY!!!” like I wanted them to. I have given some thought to opening next year with this activity right when we talk about the axioms to help reinforce why that whole thing is important.
PS – Let me know if the Dropbox links don’t work, I’m still figuring out how to share things.