Bring ’em back to share ideas, then let them try to answer the question with their favorite model (which not be their own).

This approach is obviously not focussing on a particular field of math like vectors, and if that is tour interest, you would have to corral read in that direction. For me, though, each one of these open-ended questions is an opportunity to experience mathematical thought over any particular content criterion of a curriculum. This perspective also allows the question to be asked of nearly any age group.

I’d launch the class with the video. And, like Josh G’s “terse plan,” go the route of asking something on the order of where’s are any or all of the magical spots where a logo might start and never hit a corner.

Kids would get this sheet. Basically with the question and a grid. And they’d probably draw all over it before they leave the grid and start to generate some sort of formulas and rules. I’d need to figure out those a little more before teaching this, but I wanted to put it up before I went home.

http://www.scribd.com/full/26698404?access_key=key-v7s9wq8n9w5um5gnbgi

http://dl.dropbox.com/u/3450194/bounce.html

The initial velocity and the size of the box can be changed. Hit ‘stop’ at the bottom of the screento reset. The slider controls the animation speed.

I think something like this would be a good thing to put into kids’ hands. It’s just like drawing out paths on graph paper, but retains some of the dynamic of the original problem to it. I hope it helps you guys to think of other possibilities.

[Oh, I should throw in a button to show the trace of the ball.]

I’m not sure I can articulate why, but I’m having mixed feelings about this WCYDWT. Part of my unease has been expressed in the fact that posters have been making suggestions about lesson plans and activities that are related to the idea of the video, but that aren’t based on the video or use it in a central way.

The lesson plan that I’d expect to come out of this, based on what’s come out of previous WCYDWTs, would involve something like truncating the video before the question is resolved, ask kids whether or not they thought it would bounce into a corner, and get them to say what data they’d need to test their guesses. Then they’d make some measurements and rig up some models (either on paper or using software). (Very a la “throwing-balls-into-trashcan-modeled-with-parabolas”)

Two things. First, it seems to me that we’d want our kids to be in the mental state of the characters in the video. I don’t know if using the video is the best way to make that happen. The situation in the video is a distant instance of a phenomenon that we could present more intimately. That is, the opening prompt could be a DVD screen saver–that’s what the students would encounter, rather than the Office folk watching the same thing. Maybe a ball bouncing around like on my applet above, without the grid and without the arrow?

Second, I just want to say that if the actual clip is used and analyzed, more time is spent on digging the data out of screen shots and and building models, rather than exploring the mathematical structure that’s happening here. That is, there’s a trade-off: exploring more models and the questions they raise (more “pure math”y) versus creating the right model for a particular given situation (more “applied math”y). Both are super-important and fun. I just think there’s a balance there to be struck.

What’s driving me crazy is that I totally remember another activity I’ve done (as a student) which hit on the same kind of tiled-rectangle thinking. … oh wait I just remembered. The problem in question was, “if you draw a line on a co-ordinate plane between two points, how many “boxes” on the grid does the line pass through? How can you generalize that?”

Seems those two things are related but on opposite ends of the thought process – working out either gets you to the other end, but I don’t know if presenting both together would help.

Students can shift the size of the rectangle to experiment and gather data on which angles work with which sizes of rectangle.