Following up to my previous post:
I have a couple of observations on this.
The first is that the populations we teach can strongly affect how we think about developing lessons. My students are poor estimators – In class discussion they’ll yell out numbers without any thought, hoping that they just guess right. I’ve made it part of my daily program, and many of them are starting to get better at it, but it’s still not a reliable enough skill that I can build another lesson on it. So while I appreciate the “how much is it worth” question, it would turn into just another guessing game in my class.
Secondly, I’m starting to buy into the idea that a good image can be a starting point for a number of different discussions. The way I took it reduces it to a 2d problem, but it could just as easily serve as an introduction to finding volumes of rotated curves for a calculus class, 5 years down the road from where the lesson above is aimed at. Or, an earlier level question could be “How big does the roll need to be before one bill will fit exactly all the way around?” for an exploration of what pi means.