I'm very impressed by the commentary in the kick-off post. The default WCYDWT stance has the eager math teacher stroking his chin and musing that "we should really tie this into gas prices somehow … " while studiously avoiding the essential, practical details of constructing a framework for that learning. Instead, at freaking last, our commenters are starting to attack those logistics with a certain thrilling mania, developing full-bodied worksheets, manipulatives, and Geogebra applets1.
I'm not exactly sure of the best route through this problem. In fact, the one that interests me most is one I don't know how to solve. I hope you can help me with that. I only know one thing:
We can't learn much from an obscure background element of a video clip unless we drag it into the foreground. We need our own copy of that bouncing DVD screensaver. So I made one in AfterEffects. [download clip]
Your goal with these intro clips should be to infect your students with as much of PB&J's anticipation as you can:
Take bets: will it hit a corner with five minutes? Ten minutes? Put a few students on record.
Now ask your students, "what matters here?" There are nearly ten variables you can define together. Ask, "what are good ways to measure what matters?" Pixels, angles, speed, time, etc.
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Play this clip. It features information that should, ideally, surprise no one. Your students have abstracted all this information already. You're just taking their hard wor and pressing play. [download clip]
From there, take your pick. You could give them something fairly explicit like this [download image]:
Or you could just give them this grid, 720 by 480 with ten-pixel increments, go frame-by-frame through the movie, and pick out some data points together. [download image]
The awesome observation they should make, regardless of what route they take, is that, once that icon starts moving, the rest of its natural life is foretold. It's totally predictable in this frictionless environment.
By my count, we're still missing a clip.
We need video of the solution. It's one thing for you to consult your answer key (the full measure of your authority) and confirm a student's answer. (A: lower-left corner at 1:34.) It's another thing entirely to say, "It doesn't matter what I think. Let's check the tape."
So here are five minutes of the DVD screensaver.
Now will someone teach me how to solve this algebraically?