{"id":1255,"date":"2015-06-15T09:00:46","date_gmt":"2015-06-15T14:00:46","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=1255"},"modified":"2015-06-14T19:34:51","modified_gmt":"2015-06-15T00:34:51","slug":"math-warm-ups","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2015\/06\/15\/math-warm-ups\/","title":{"rendered":"Getting Warmer…"},"content":{"rendered":"

I\u2019m 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\u2019ve 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\u2019m highlighting here are just the tip of the iceberg.<\/span><\/p>\n

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An element of {cats}\u2229{math}. Thanks, Internet! Image: Jimmie, via Flickr.<\/p><\/div>\n

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\u2019s<\/span><\/a> \u201cpersonality coordinates<\/span><\/a>\u201d activity. Meyer write the must-read math teacher blog dy\/dan (which, by the way, I can\u2019t decide how to pronounce, but I suppose that\u2019s 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\u2019t use that activity but one I found in the comments: break people up into groups of size 2n<\/sup> 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.<\/span><\/p>\n

Sam Shah\u2019s blog Continuous Everywhere but Differentiable Nowhere<\/span><\/a> has some nice problems and puzzles, including the sack problem<\/span><\/a> that nerdsniped me a while ago<\/span><\/a>. Math Munch<\/span><\/a>, \u201ca weekly digest of the mathematical internet,\u201d has also been featured on this blog before<\/a>. It doesn\u2019t just focus on puzzles and games. There\u2019s 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<\/span><\/a>, who just sounded so enthusiastic about abstract algebra that I wanted to go find some symmetry groups.<\/span><\/p>\n

A new-to-me blog that\u2019s been a good puzzle source is Math=Love<\/span><\/a> by high school math teacher Sarah Hagan. Don\u2019t tell my students, but I think I\u2019ll be using the 1-4-5 square puzzle<\/span><\/a> challenge next week, and I might talk about happy numbers<\/span><\/a> 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\u2019ve been reading the blog for a few months, I\u2019m a bit embarrassed that I didn\u2019t 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.<\/span><\/p>\n

Futility Closet<\/a><\/span> isn\u2019t strictly a math blog, but it has tons of fun puzzles. The jeweler\u2019s observation<\/span><\/a> 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.<\/span><\/p>\n

I\u2019ve found some activities in other places as well. Last Thursday, we made a level one Menger sponge using leftover supplies<\/a> from MegaMenger<\/a> 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<\/i> by Jim Henle was fun (my review of the book is here<\/a>), and I\u2019ll be using Matt Parker\u2019s Things to Make and Do in the Fourth Dimension<\/i> later in the program (see my review here<\/a>). I might even try to make a domino circuit<\/span><\/a> (pdf), but I\u2019m not sure if I have enough patience or dominoes.<\/span><\/p>\n

Do you have a favorite source for math puzzles, games, or activities?<\/span><\/p>\n

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I\u2019m 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 … Continue reading →<\/span><\/a><\/p>\n

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