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My honors kids were a bit thrown by homework assignment 1B, which asked them to decide when the constant velocity model applied and solve for the one piece of information they didn’t know. A couple wrote me saying they didn’t understand what the CVPM was, which got me to thinking that perhaps in the past, they were more used to just memorizing formulas and plugging in numbers, rather than thinking about a connected set of ideas used to model a system. I then gave back the first mini-assessment of the year, and we talked about grading again. I know this is a conversation we’ll need to have a lot before students really get it, but I think they are beginning to recognize the fairness that SBG offers. And from there, we launched into a discussion about when to have the next test, using a metaphor of the best way to learn golf is to go to the driving range asap, and get a coach to watch you swing. The worst way is to continue to “study” golf by reading books and watching videos when you aren’t really sure what you are doing in the first place. Now that students were pretty solid on CVPM, it was time for the big payoff, using this model to really approach perplexing problem. Here are the problems I gave the kids, borrowed from Frank Nosschese and Dan Meyer. It was great to watch the kids launch themselves into an exploration without a detailed step by step guide, and see just how quickly they are improving in the ability to take data (all of the kids predicted the buggy collision perfectly–well not perfectly, but within the uncertainty of a piece of masking tape), and then took off on trying to find a mathematical solution, which caused one student to exclaim “This is so cool” as she saw how to solve a system of two equations. Surely, this was one of the first times a high school student has been genuinely stoked by solving a system of equations. The answer itself, was quite beautiful. For two trains, $a$, and $b$, the time collide will be $t'= \frac{x_b-x_a}{v_a-v_b}$ which allowed us to see that if the trains have the same velocity, they will never collide. It was a good day.