I had a great time today, volunteering at the Julia Robinson Mathematics Festival. There were 16 tables. Each table had two volunteers helping kids with a page full of interesting problems, that generally started pretty easy, and ended up quite challenging.
Ours was the Multiplication Table - each participant's first job was to create a multiplication table, and look at the pattern of even and odd numbers. They were asked to describe the pattern, and explain why it turns out the way it does. The next few questions, about which numbers show up the fewest and most times, stretched kids a bit more. Which numbers show up an odd number of times? Some saw it immediately, and some weren't ready for that question. If we made the table bigger, what would be the first number with 10 factors? One girl I worked with saw it pretty quickly. What about 11 factors? I didn't even get that far...
The 3 hours were up before I knew it, and then we had a presentation by Karl Schaeffer, of Math Dance. It was fabulous! He had us get in groups of 3, and try to swap places with neighbors to make each permutation* just once. Then we tried it in groups of 4. Then we did windmills with our arms. You'd be surprised how many ways there are to do that (clockwise or counter, both arms the same or different, in phase or out). There was even more.
Check out their video:
I had just ordered his book last week. I can't wait to play with it.
*Permutation means arrangement. You can arrange the three letters A, B, and C in a bunch of ways: ABC, ACB, BAC, BCA, CAB, and CBA. How many ways could you arrange 4 letters?