Vi Hart has a series of mind-blowing videos that explore intriguing math concepts in rapid, quirky, entertaining ways.
I love the little hexaflexagons. You can think of them as half nose-pincher (or fortune-teller, or origami basket– you know, that toy you made during church by ripping the program into a square and folding in its corners to the middle, then flipping it over and folding the corners in again) and half way-cool-math-avante garde concept art.
I made some short videos to simply explain how to make and use the two kinds of these tricky devices:
If you’re a teacher, feel free to check out my three lesson plans on hexaflexagons. I included links to the Vi Hart videos. The links are to her Vimeo videos, because you can download them from there (so you don’t have to rely on streaming them during class).