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So, I’ve been trying to teach Algebra this year by modeling. I needed a good way to build the quadratic function model, so I started (about two weeks ago) by having the students analyze a basketball shot video. They used Logger Pro and found that vertical position vs. horizontal position made a nice curve. Like this:

But then I was lost as to how to get them to come up with the equation for the curve. They could get Logger Pro to tell them the equation, but that wouldn’t really help them. So, how can they come up with the equation when they’ve never seen one like this before?

I decided to take a different approach. We started by examining the function y=x^2 and then examining different ways to shift the function around (using Desmos). The handout I used had them graph different shifts (like shift y=x^2 up 3 units). Then I asked them to find the equation for that shift using Desmos. They had to figure out which piece of the equation to change.

Then after doing the activity (and a bunch of practice with it, making whiteboards, etc) they knew how to build a quadratic function from scratch. I think now it’s time to go back and find the equation of the original basketball shot we analyzed (BTW, I also teach these kids physics, so we’ve been studying why the ball behaves this way as well).

When I started writing this blog post, it was going to be about a failure to stick to teaching with modeling. As I typed it though, I realized that this was still a modeling unit. The kids recognize that the shape of the basketball graph is a symmetrical curve. We just didn’t have the appropriate skills yet to write the equation for the curve. Now we do, so it’s time to complete the model. I’ll let you know how it goes!