Can you expand on why you found the print textbooks “inadequate”?

Also, how do you imagine your applet being used by students? It seems possible to me that a student would just alter the point of reflection bit by bit until the shot was successful.

First of all, I find it frustrating that the first two books just state that the angle of incidence and angle of reflection will be the same, and CPM seems to just expect students to know that. (In fairness, maybe it was covered in an earlier CPM lesson.) As a student, I’d find this believable, but I’d be completely derailed and distracted by wondering why that is true. I think you could explain that the ball will keep traveling in the x direction at the same rate and will travel at the same speed, but with the opposite sign in the y direction, and have students work out the similar triangles and therefore know that the angles are the same. Admittedly, this is still asking students to take some physics on faith, but it seems like less of a jump and gives them some interesting and relevant math to reach that conclusion.

Aside from that…

Discovering Geometry: the problems seem clear enough mathematically, but as someone who doesn’t know much about pool, I feel really confused about why we are solving them. Why should I care about hitting the center of the 8 ball or not hitting the CP cushion? It seems completely arbitrary, which makes me feel like I’m missing the point.

CME Project: Ugh!!! My least favorite by far. The double reflection thing is insane. After staring at it a while, I see how it works, but I feel like if I sat down and solved the problem that follows their explanation, I’d be copying their steps rather than really thinking it out for myself in a way that would make sense of it. And it doesn’t connect well to my understanding of what the path of the pool ball actually looks like or how the bouncing off the walls works. Very procedural/monkey see monkey do.

CPM: I really like that they’ve basically introduced a reasonable coordinate system (the diamonds) that I could refer to instead of slapping down letters to mark points. The single ball is less distracting, too. Aside from some worry that students who don’t know angle of incidence=angle of reflection will be stuck, and my usual eye-rolling at CPM for boldfacing “tools,” I like the first page. 6-42b is flat out ridiculous and distracts from the new ideas, but the rest of 6-42 is clear, interesting, and varied.

Otherwise, I had the same reaction as Lisa: Fawn wore it best! I even Googled for the same lesson before realizing Lisa had already pointed to it. It’s memorable for sure, since I recalled it even though reading it (as part of Jo Boaler’s online course How to Teach Math) was the first time I ever heard of Fawn.

One way to start would be plotting shots on a piece of paper and seeing if you could replicate them with your marbles/pool balls. How perfect are the bounces really? With the use of slo-mo you could find a way to introduce percent error.

I think the elliptical pool table is relevant to this discussion: https://www.youtube.com/watch?v=4KHCuXN2F3I

The math says the ball goes in the hole every time, but practically that’s not true.

You could even scaffold the time at the pool hall, so that they record a few shots, then use mirrors as Björn suggested and keep building the concepts. I think that having them draw the scenarios afterward is key.

I love Fawn Nguyen’s task linked above – having students record their own pool shots is similar to having them draw their own mini-golf scenario. It becomes their own problem, which is always much more interesting than a textbook problem.

http://fawnnguyen.com/let-problem/

pool. golf. same thing.