I got quite a surprise last night when I asked my younger son what he wanted to learn about in today’s math project. The answer – random walks.

Not quite the answer I was expecting (!) but it turns out that he’d learned about them in this book:

I really didn’t have any ideas at all about how to introduce random walks to kids, so we just starting by playing around with a simple 1-D example. It was fascinating to hear what they boys thought a random walk would look like. I’m not sure they even know the words or ideas that you would normally use to describe one.

Net we moved to Mathematica. I wrote a short program that kept track of left and right moves in a random walk. We looked at how far left and how far right you go (and also where you end up) after a certain number of steps. In this video we looked at 100 and 1000 step random walks.

The main focus (not counting a mysterious little glitch with Mathematica) was trying to get them to describe what they were seeing with the various numbers.

For the last part of the project we looked at a random walk with 10,000 steps. It was fun to hear the boys try to guess at what some of the max / min numbers would be. We’ll have to revisit the random walk idea a few more times to explore the ideas in a bit more depth. They boys were really interested to learn more after we finished up!