I know that by now, most schools have started. I think I’m one of the last that still starts after Labor Day – not that I’m complaining. A popular blog post out there is a first day activity, and I wanted to share the one that I’ve done the past few years. Yes, it’s a debate, but a totally informal debate, one that works at any level of mathematical background, students have a lot of fun with, that builds both competition and teamwork in a low stress way, and tells me a surprising amount about my students.

After normal introductions, I give students a simple task – to come up with a number. It could be a favorite number, or a really interesting number, or a number that has some personal meaning. I then ask them, once they’ve decided on a number, to come up with as many interesting things about that number as they can, and give them a couple of minutes. They can use calculators, they can use the Internet, they can draw, and if they get stuck they can ask me for help (though, to be honest, they rarely ask for help with this).

After a few minutes, when at least some of the students are feeling like they’re done, I have them get into pairs, and then in the pair they decide which number is better. They are given about one minute to make their cases and decide, and once each pair has decided, I have each pair find another pair, and decide which of the two numbers is better. It’s interesting to me that I never actually describe this to students as a debate, and in theory they are working together, but they do have something invested in the number that they came with. Inevitably, groups start to argue, but generally nicely, and the whole idea of comparing the best and worst qualities of numbers becomes a source of passion.

The process of finding another group and then discussing, then finding another group and discussing, continues until you have (hopefully) two halves of the class shouting at each other about whether 32 is a better number than 360 (because powers of 2 are more important than having lots of factors and describing the degrees of a circle), or whether 12 is better than 18 (but of course 12 is better).

In listening to conversations that happen, I can get to know an amazing amount about student interests, as well as which students feel very comfortable with what numbers mean and how they can be manipulated and described mathematically. On top of it all, having an entire class passionately engaged in a meaningless debate about which number is best, where you can catch every student having fun playing with math from day one, is a pretty great way to start the year in my opinion.

So, what’s your favorite number? Why?