Nice! Let us know how it goes if you get a chance.

I may add an extension that asks students to prove whether we’ll, eventually, sink 2-3 of the shots. I’ll look to choose one that drops after 3-4 bounces, another that gets stuck in an endless loop, and another that may fall after far too many bounces. In debriefing the last one, we’ll have to speculate on the impact of striking a corner of the pocket.

http://www.pbslearningmedia.org/resource/lsps07.sci.phys.energy.lightreflect/light-and-the-law-of-reflection/

It explains what a photon is, and then it shows ball bearings and light bouncing off a flat surface.

l hodge:

Which of the questions, if any, require reasoning? Why not a question or two providing the destination and requesting the initial path?

The contrasting cases require an attention to structure and the ability to generate and defend a hypothesis. The initial exercise requires spatial intuition. The final exercise requires attention to precision. Your question is nice, though.

Chester:

After teaching about pool tables, I’m still going to have to cover the material more conventionally anyway, except I now have less time to do it in. I don’t see that helps.

I don’t mind you repeating yourself in every post, Chester. But clearly we come at the project of math education from very different angles. I tend to chalk your frustration with individual activities, lessons, and posts to those differences, not to the activities, lessons, and posts themselves.

That said, I am curious which material you’ll have to cover “more conventionally” anyway. The “material” I’ve focused on here is a particular understanding about angles and their application to pool. That material is “covered” in this activity already. It’s just sandwiched in between a couple of other productive and interesting activities.

One could make the argument that those extra activities are an unconscionable expense of time and I will shrug in response and move along. How a teacher spends her finite classroom time isn’t really my business.

One can’t argue that the material isn’t covered, though.

Just because I don’t subscribe to a program of straight explicit instruction, no chaser, doesn’t mean I subscribe to discovery learning, the usual boogeyman in your comments.

My question isn’t “should or shouldn’t we explain?” Rather, “What can we do before we explain, both to interest students in that explanation and prepare them to learn from it?”

OH YISSSS. Such a huge improvement on the originals!

I love this partly because the fake ones LOOK fake, and students have to think about why and are given materials to test their hypothesis. You’re making students refine their intuition to include mathematical precision, which they can then use to solve the rest. I feel like this honors and builds on the knowledge they already have in a way that’s far more motivational than throwing out some big-words statement about angles of incidence and reflection.

Actually, that last statement applies to the whole lesson.