I finished up my unit on isometries today with my geometry classes and with the few extra minutes that I had, I began showing them how to predict where a ball will bounce after it hits something. At first, they kind of looked at me and wondered why I was explaining this to them, but once they made the connection to reflections and what we had been doing in class, they were hooked. I explained to them that the angle in incidence is equal to the angle of reflection (which was something I assumed they knew) and I actually had a student raise his hand and say "I actually didn't know that before just now and I can use that the next time I play pool." In the past when I taught this, my students blew me off and didn't really care. This year was different: they wanted to learn more. After we went through a few 'nice' examples of bouncing balls off walls that were perfectly straight, someone asked me about what if the wall was curved; could you still make a similar prediction as to where the ball would end up? This goes a little beyond the scope of the course, but I figured if they're asking I'm certainly not going to stop them. I explained to them all about tangent lines and points of tangency and everyone learned something.
Throughout the entire unit, students were asking me, 'Why do I need to know this?' I told them we were getting there and I wouldn't let them down, to which most of them went back to not caring. Perhaps next year I should start with this lesson. Thinking in terms of a 3 Acts-type format, I could show them a video of someone playing pool, bouncing a ball off a wall and stop it before it stops asking, 'Will it go in?' Or I could show a clip of a Dennis Rodman jumping up for a rebound and just before the ball bounces off the rim, 'Is he in the right spot at the right time?' (by the way, my students are always in disbelief when I tell them that Rodman holds the rebound record because he analyzed the angle the ball came in and he figured out where it would bounce to). This might catch their interest, we can dive into the material, and then come back to it in the end to calculate an answer.