A Random Walk

Eight years ago my colleagues and I were looking to create a series of lessons about probability that would build upon each other across middle and high school. We wanted to create an engaging activity that would inspire students to ask lots of questions about probability, and be one that students would remember years later.

Being a Geometer’s Sketchpad enthusiast, I had been playing around with a sketch that allowed a point to take a random walk on the number line.  The students quite liked watching the point dance back-and-forth, sometimes off the screen to the left or right, and had lots of questions about random behavior.

So I thought, for reasons I can’t currently recall, that it would be cool to have the whole class do what that point was doing, en masse, out in the hallway.  Students would end up at different locations on the number line, and then we could form a human histogram of our final locations by stacking ourselves together down at the end of the hallway.

This was a big hit. The students enjoyed watching the dance (a pre-made sequence of coin flips or a scientific calculator  generated our steps to the left of right) and had even more questions. The lesson, for 7th graders, centered around determining probabilities and generating the different possible ways of landing on any particular location in the number line.  It was definitely memorable the next year when we followed up with more analysis of the probabilities and got into Pascal’s Triangle.

When I presented the lesson at NCTM in 2010, an attendee went home and tried it with a group of 100 teachers at a summer workshop.

Last year I decided to bring this lesson to my new school, and made some modifications – the students stand shoulder-to-shoulder and walk forward and backwards rather than left or right. This allows them to more easily see the motion of their classmates and feel like they are moving like a point on a number line. I submitted this lesson for the National Museum of Mathematics’ Rosenthal Prize – and it won. (!)  I have found the lesson to be very engaging for students and hope to see more teachers try it out.

Here’s how the lesson starts:

We’re going to go for a walk today. But it’s going to be a funny kind of walk… we’re going to let coin flips be your guide.

Select a volunteer walker and another student to flip a coin. With the walker standing in a suitable location, explain to the class that the student will take one step forward when the coin lands heads, and one step back when the coin lands tails. With each flip, have the volunteer take a step forward or back. Repeat 6-10 times to interest students in the randomness of the student’s motion.

If you were feeling random one day, and were to take a walk with coin flips as your guide like our volunteer just did, what would you wonder about? What would you be curious about?

More about the lesson in my next post!