I began by watching Vi Hart’s videos about hexaflexagons. Of course, Vi is fond of speeding things up, but I still thought I should be able to fold a strip of paper into equilateral triangles and make a hexaflexagon. Vi didn’t seem to be doing any measuring, like other websites recommend, so I was resistant to using a ruler. But after a bunch of mangled paper strips, I knew I needed a different strategy.
I found some pre-made, printable PDFs of hexaflexagon patterns. Some of the best are on a website called Aunt Annie’s crafts, on her Flexagons page. Print them, preferably in color. My brother and I were going to drive all the way down to Thetford, so I packed up some flexagon patterns, a scissor, and some double-sided tape for the trip.
I had plenty of time in the car to cut, tape, and fold several hexaflexagons, but I still didn’t know how to get them to do their special flip. I handed one to my brother while we stood around watching the Thetford cross country races, and he was able to figure it out.
These hexaflexagons are really cool. It’s worth trying one yourself. They were discovered by Arthur H. Stone in 1939, then popularized by Martin Gardner in his Scientific American column called “Mathematical Games” in 1956. Try pre-made patterns at first. I think starting students this way, then asking them how they might create their own if given a blank piece of paper, pencil, ruler, glue, and scissors, would be an excellent math activity, perfect for differentiation. We'll see how it goes at Math Night!