It began with one student. I noticed pretty early in the semester that grade 9 math was old hat for him and that he needed a challenge, so we started to meet once a week or so to talk math and work on some interesting problems. (During our first meeting, we proved that the square root of 2 is irrational.)
Then, he brought a friend. Who eventually brought two more friends. (If you’ve been doing the math, you might expect 8 students at our next meeting; alas, there were only 5. But wait, that’s five students who want to do math outside of math class!) We did a few problems, but mostly spent time discussing the idea of doing independent projects that the students would present to the class on the last day before Christmas break.
They solved it in all of 3 minutes. Good thing I had another one in my pocket. It goes like this (I don’t have a reference for this one, so my wording is probably not ideal):
You and 8 of your friends are sitting in a circle and passing around a ball. In the first round, you pass the ball to the person to the right of you, who passes it to the person to the right of them, etc., until the ball gets passed back to you. This is when the round ends.
In the second round, the ball gets passed to every second person until the ball gets passed back to you. In the third round, the ball gets passed to every third person; etc. You play the game until you end up “passing” the ball to yourself, which does not count as a round.
How many passes are made in total before the game ends?
(Big thanks to Nat Banting for sharing this one!) Once the students solved the problem for 9 people, they solved it for 10, then for the general case. It’s an excellent problem and it did take them most of the lunch hour, but they got it in the end. Their persistence was extraordinary, and I could feel their satisfaction when they solved it in the end!
It was a great lunch hour, and you can imagine how I felt when I overheard the students saying “This is really fun!”
We spent the remaining time talking about pi, different kinds of infinities, abacuses (abaci?), and other fun things (the students are still thinking of ideas for their independent projects), and decided to meet again next week. I’m thinking of calling it Pi Club: Come for the (pizza) pie, stay for the math!
The only downside? My internship is over in December. But – but – but – we’re only getting started! I guess I’ll just have to be sure to make the most of the next four weeks. (P.S. Have a cool problem? Send it my way!)
This must be how teachers feel every year before the summer holidays when they have to say goodbye to their students, some for ever. And I suppose that part of internship is learning just how hard that can be.