I was driving to the grocery store. This particular trip took me down Cedar Street. I drove past this manhole cover. It caught my eye in such a way that I decided to pull into a nearby parking lot and, when the traffic cleared, tiptoe out to the middle of the five lane road and snap a photo of it.
So, my mind instantly went straight to rotations. (Which is on my mind because transformations are Unit 1 of the Geometry Course that I start teaching in, like, two weeks.)
What if I started out rotations by showing this picture and simply asking the students how much of a rotation would fix the yellow lines.
My goals would be for the students to explore how to investigate an apparent rotation, learn how to visually represent a rotation, and struggle through the task of explaining it out loud to another person.
It would be okay with me if we made it to the convenience of using degrees as a descriptor of how much something is rotated. That would be up to them. I do suspect that after a short time of “about this far” and “about that much” they’ll like to find something to ease the trouble of explaining the transformation.
If you can think of a way to frame this learning opportunity better, please make me a suggestion. I feel like this is a good opportunity that I don’t want to waste.