Today was the last full day before Christmas break, and another teacher and I had talked about gathering up both of our classes to do some fun holiday geometry. In the end, the other teacher was absent this week and then very busy when they returned, so they trusted me to just plan the session by myself.
This is how I structured it.
First, we did this snowflake prediction activity in partners. Everybody folded the papers together for the first snowflake, drew out their predictions, and cut it out. Then, I monitored that each pair of partners finished predicting the next two before I gave them each one piece of paper to have them cut out a snowflake to verify their predictions. (They split up what they would cut up, both to save time and save paper.) Then they proceeded to make more predictions, followed by more testing by cutting out snowflakes. This took about 40 minutes. Meanwhile, both the other teacher and I circulated to make sure that kids were understanding how to apply the idea of symmetry to making appropriate predictions.
Then, with the remaining 40 minutes, the kids got to choose between either doing a tetrahedron origami (mostly unassisted; the exercise was in reading and deciphering diagrammed instructions... the hardest part is reading the earlier instructions on how to create the regular hexagons out of a rectangular sheet of paper), or making a geometric sequence/recursive pattern (see below).
This second activity, by the way, was one that I learned at PCMI. :) You keep cutting each segment into smaller thirds (or any fixed fraction), and folding up the middle part. In the end, you end up with a very intricate design. I'll post a photo when I get a chance!
It was awesome! We wrapped up the class by talking a bit about the rotational symmetry of the tetrahedron and also about why we could fold hexagons up into tetrahedrons (same base shape, the equilateral triangle). It was a lovely way to inject some last-minute holiday cheers after all the heavy-duty algebra we had been doing.