To be totally fair, my favorite day takes more than one day. But that’s not really that important. So we start our balanced forces unit. We get our idea of Newton’s 1st Law. We get some forces vocabulary. I show them the bare minimum in drawing system schemas and free body diagrams. And then we get this amazing problem from Matt Greenwolfe:
It’s actually the first of a set of very similar problems. Each problem has a small change (smoother floor, usually). Doing the first problem, though, is wonderful. The cognitive load is really high. They are drawing their first FBDs. They are drawing a velocity graph that shows speeding up and slowing down, even though they’ve only studied constant velocity so far. They are applying Newton’s 1st Law. And all of that has to work in concert for any of it to make sense.
I ask them to draw one big velocity-time graph on their whiteboards. They should divide it into 3 sections to show the three parts of the event. I also want them to line up FBDs with each part of their graph (a lot of them use system schemas to draw the FBDs, but we don’t need to share those with each other for the discussion). Finally, I tell them that it’s really important not to look at what other groups are doing before the discussion. It’s possible that no one will have a completely correct board. But we need lots of different ideas. If they all have different wrong answers, they will agree on the correct answer during the discussion, even if it’s different from every board at the start. If they all have the same wrong answer, they will just quickly agree about it (obviously).
Those first board are all over the place. Their ideas are fascinating and awesome. Sometimes you can’t even tell how wonderful their ideas are until they start talking during the discussion. I love everything about this. The level of thinking and creation is incredible. This is the very first problem they are doing in balanced forces. In some ways, this is really their first true physics problem (not just descriptive motion, but actually using a fundamental principle to reason and making multiple diagrams to represent the same thing in different ways). I can’t get enough of it.
We get together in a circle. I prep them a little for how to run the discussion and encourage them to take on the challenge of doing this with minimal support from me. We start by looking around and noticing similarities and differences. Then they start asking other groups questions about the choices they made that disagree with their own boards. And when they change their minds about something, they update their boards.
Our classroom is a little awkward for this discussion in a circle, so they suggested making one consensus board up at the front. We put the whiteboards on chairs up there, too, so we could see all of the ideas more easily. And every once in a while everyone would run up and start making changes to their own group’s board. One kid took the lead on being responsible for drawing the consensus.
After the first day, we had done 2/3 of the problem. Because of the school calendar, we actually had almost 2 weeks go by in between before the class met again. Today we got our boards back together, got our heads back in the problem, and went back at it. Here are some photos of how their consensus progressed today.
Okay, that’s really interesting! There was a lot of buzz that kept coming up, going away, and coming back up about whether the box reaches a maximum, constant speed. And whether it slows down as soon as you let go. You can see above both of those ideas—the third section shows the box slowing down a bit, then slowing down more rapidly. We got caught up (as always happens) in the idea of pushing with a constant FORCE versus pushing at a constant VELOCITY.
So I gave them a spring scale and something to pull and had them pull it across the table (and eventually floor) keeping the reading on the scale at a constant value (that I chose for them). The kid pulling realized that it keeps speeding up if you keep that value the same, and he took some time in explaining that (in many different ways) to the rest of the class.
Here’s where they landed at the end. I forgot to take a photo before I showed them how to make it a dashed line for our use in problem 2, but you get the idea. And in case you think they might let the details get washed over here, they spent at least 10 minutes debating how the two slopes should compare and basically deciding on the idea that the steepness of the slope on the velocity-time graph has to do with out unbalanced the FBD is.
Problem 2 is total cake after all of that (it’s the same problem, but on a polished floor), so we will also pick up a few more of the questions we put aside today when we discuss it next class (they made the whiteboards and are ready to go). The cognitive load significantly decreases after this first one, letting more kids into the discussion and letting the Newton’s 1st Law arguments resurface again and again as they become ready to have and answer those questions.
What a great set of questions—challenging, complex, requiring synthesis—and no numbers needed at all. When you start the unit by wrestling down these kinds of ideas, the stage has been set for some sophisticated work for the next couple of weeks. What a group of rock stars these kids are.