I taught a lesson about slope and systems of linear equations after the style of Dan Meyer’s “What Can You Do With This” series. I videotaped a footrace between myself and some of my students, and showed it in class.
I tried to follow several of Dan’s ideas about a good video segment like this. There is no clear focal point specified by the video, and no imposed frame of reference. I decided not to show the beginning or end of the race in the initial video with the hopes that the omission would incite interesting questions.
The startup question was simply, “who wins?” Some students immediately identified the runners that hit the right edge of the screen as the winners, and a few asked where the finish line was. My plan at this point was to let some controversy mount and then steer the conversation a little, but to my delight, in the midst of the conversation, a student in the back suggested we just figure out who is going faster. So, our question was narrowed. I took the opportunity to point out that this is what problem solving is about – figuring out what questions to ask. I somewhat artificially changed the student’s question to “how fast are the different runners going?” and challenged the class to figure it out.
Which is actually a pretty complicated task, given only the video above. I was using the quicktime player to show the video, which has a pretty great slider control that can practically move between individual frames. But when some students suggested that we need a timer, and another group said that we’d also need a frame of reference, I pulled up a new version.
I also had a video with just a timer and another with just the line ready in case they only asked for one of them.
From here, the conversation led itself at what felt like a fantastic pace. There was some controversy about whether or not we could really find a speed by just finding the slope between two points, and about what points to use, and whether or not it mattered. We checked with two different kinds of calculations, and got similar speeds, so the kids were convinced (though this sort of proof makes me feel a little dirty).
Somebody said, “OK, so who wins here?” and another student responded, “It depends on where the finish line was.” Again, I pointed out the great problem solving going on here (I like to emphasize that coming up with a question is just as important as being able to answer it). You can guess where this is going – we found the point at which it would be a tie using a system of linear equations.
I gave the video to the kids to play with themselves on individual computers. For an honors assignment I asked them to figure out how much of a head start I gave the other pack of racers, in feet, and several of them chose to tackle the problem. I considered the class a success because the students liked it, and I had everyone practicing solving systems of equations with interest and a purpose. And for those students that steered the conversation with narrowing questions (and many more with viable alternate questions) it was good practice problem solving. The lesson took 30 minutes.
There are several ways to improve this lesson. I didn’t have video of the finish or the start, to give the class closure, the proof that they were right. That’s not always bad, but it would have rounded this lesson off better, and I think it’s important to have kids leaving with as much satisfaction as possible. Also, some of the students in the race were also in my class. They knew the outcome of the race beforehand (to a finish line not specified in the video), and they knew that I had given them a head start, etc. I can’t wait to use this video next year (although I made the mistake of including a freshman who will probably be in my class eventually). This definitely affected our conversation in class a couple of times. Then again, maybe it’s worth it to have actual class members running in the video on screen.