Probability and Falling Down

On Thursday we explored probability using ideas I got from a UMS workshop with Dr. Schaffer and Mr. Stern, founders of Math Dance.

First we warmed up by doing things like "make a shape with two hands on the floor but no feet."

We progressed from shapes to movements. Everyone had to make up a movement, which could be pretty much anything so long as it had a beginning and an end and didn't involve running into furniture or people. Several kids chose to fall down, because, hey, falling down is fun!

We voted on which movements we liked the best and settled on two: Lydia's, which involved running around like a horse, and Daniel's, which involved spinning around and then falling down. Everyone learned both movements.

Then came the probability. We flipped a coin 5 times. Heads meant Daniel's movement, Tails meant Lydia's movement. We ended up with a 5-move dance, which we were doing as Renata walked through the room and wondered what on earth this had to do with math! Then we made up another dance by doing another set of coin flips. Then we flipped coins some more because everyone wanted a turn to be the coin flipper.

Although there was a lot of falling down, yes, we really were doing math!

• Problem-solving: How do you get two hands on the floor and no feet? How do you make these different shapes with your body?
• Probability: Instead of just seeing that the coin comes up about half heads and about half tails, there's a physical understanding that the coin tells you to do one move about half the time and the other move about half the time.
• Collaboration: How do we all run around like horses in a small room without crashing into each other?

Today we concentrated on the coin-flipping aspect. Each kid flipped a coin 100 times and recorded the number of heads and tails. Most got about 45/55, one got 31/69, one got 50/50. Not everyone made it to 100 flips, but those that didn't still got about half one and half the other.

Everyone recognized 31/69 as being interesting, so we talked about what could have caused so many tails. The flipper of that coin suggested the head side was heavier. Someone else said that pennies are made like a sandwich, with a core of one metal inside and another metal on the outside, and suggested that the core of this coin could be off-center, which would mess with the balance.