I’m currently teaching a summer school for high school students. Our main focus is number theory and its applications to cryptology, but I like to start each morning with some kind of warm-up math puzzle or game. I know plenty of fun math stuff, but I’ve never worked with high schoolers before, so I took to the blogs to find some good activities for that age group. The Internet has almost as many puzzles and games as it has cat pictures, so the sites I’m highlighting here are just the tip of the iceberg.
An element of {cats}∩{math}. Thanks, Internet! Image: Jimmie, via Flickr.
For the first day, I wanted an activity that would get the kids working together a bit and introducing themselves to each other. A bit of searching, I came upon Dan Meyer’s “personality coordinates” activity. Meyer write the must-read math teacher blog dy/dan (which, by the way, I can’t decide how to pronounce, but I suppose that’s the point). His activity had students in a group label themselves on a coordinate axis by how much of two different traits they had. I didn’t use that activity but one I found in the comments: break people up into groups of size 2n and have them come up with yes-or-no questions so that each person in the group has a different set of answers. I only did it with groups of four students, and I had students mix up a couple of times to meet new people and come up with different traits. The next time I use this activity, I will probably ask them to get into groups of eight after playing once or twice in groups of four.
Sam Shah’s blog Continuous Everywhere but Differentiable Nowhere has some nice problems and puzzles, including the sack problem that nerdsniped me a while ago. Math Munch, “a weekly digest of the mathematical internet,” has also been featured on this blog before. It doesn’t just focus on puzzles and games. There’s a strong art component as well, and the curators usually include some web-based interactive activities. Periodically they run interviews with mathematicians, teachers, and artists. I especially enjoyed the Q&A with Carolyn Yackel, who just sounded so enthusiastic about abstract algebra that I wanted to go find some symmetry groups.
A new-to-me blog that’s been a good puzzle source is Math=Love by high school math teacher Sarah Hagan. Don’t tell my students, but I think I’ll be using the 1-4-5 square puzzle challenge next week, and I might talk about happy numbers at some point. Very helpfully, Hagan often includes logistical information about how she made the puzzles or games work in the classroom and ideas to make them go more smoothly in the future. She also shares links to other sites with math games and puzzles Now that I’ve been reading the blog for a few months, I’m a bit embarrassed that I didn’t start reading it earlier. Hagan is very well known in the math teacher blogging world. Aside from the puzzles and games, she shares a lot of helpful tips about running the classroom and reflections on her teaching practices.
Futility Closet isn’t strictly a math blog, but it has tons of fun puzzles. The jeweler’s observation caught my eye recently. Why must every convex polyhedron have at least two faces with the same number of sides? It’s a simple question with a short, clever answer, but I think students will have fun trying to figure it out.
I’ve found some activities in other places as well. Last Thursday, we made a level one Menger sponge using leftover supplies from MegaMenger in October. The students had heard about fractals from a guest speaker earlier in the week, so we talked a little more about how something could have a non-integer dimension and figured out the fractal dimensions of the Cantor set and the Menger sponge. The seven penny game from The Proof and the Pudding by Jim Henle was fun (my review of the book is here), and I’ll be using Matt Parker’s Things to Make and Do in the Fourth Dimension later in the program (see my review here). I might even try to make a domino circuit (pdf), but I’m not sure if I have enough patience or dominoes.
Do you have a favorite source for math puzzles, games, or activities?
“I didn’t use that activity but one I found in the comments: break people up into groups of size 2^n and have them come up with yes-or-no questions so that each person in the group has a different set of answers.” Though he didn’t sign it completely, that comment was from Jonah Ostroff (currently at U Washington) and the name of that version of the game is Orthogonal Questions. The Fano Questions variant is pretty difficult, though Jonah has made it work at least once.
Thank you very much for these links. I think some of these puzzles will be especially useful for me in the classroom.