Fast forward to last week. I was shopping, and I found these on clearance:
For decorative use only. I am such a rule-breaker.
I traced out the shape of the region I wanted to rotate.
Cut it out. Open it up. Voila!
You have to hold it a certain way or it will sort of fall apart, but I thought it was a nice visual and tactile representation of a volume of rotation.
This one fell apart when I opened it up. I learned that you have to make sure some of the original glue is left intact when you cut out your shape. I tried running a bead of glue along one side, but then it wouldn't open very well.
Still, my students were really intrigued to see what would happen as we cut and unfolded each one.
This one turned out really nice: