Making over another typical geometry problemJuly 11, 2013
It’s time to look at another typical geometry problem to make over. This time Dan Meyer (@ddmeyer) presented this problem for revision.
I like this problem’s basic core idea. Looking at the volume of a sphere (the meatball) and the volume of the cylinder (the cooking pot), in general, this is a pretty tasty set-up (pun intended). Especially considering that I am always a fan of problems that make use of food.
For this problem, food and cooking were actually more of a problem that a support.
First, the cooking pot is sitting on a hot burner and I’ll be the first to tell you, a cooking pot doesn’t have to be full to spill over. So, the question of whether or not sauce will spill over is a bit more complicated that it might seem at first.
Second, meatballs aren’t spheres. They are irregular and rarely are two of them congruent.
I know that I am probably picking knits, but the reason we use contexts in math problems is to use the context to enrich the problem. If we have to ignore basic parts of the context to solve the problem, then the context might be more of a distraction than a support.
So, how can we reconfigure the context to support the problem? Well, my first thought was to choose spherical objects that are all congruent: for example, baseballs. Coaches regularly carry baseballs around in 5-gallon buckets, so there is our cylindrical container.
And I figured I’d deliver the task in a video simply because videos tend to improve engagement on their own.
So, we have a pretty good match with the educational goals, except now we have a much more supportive context and the students have more freedom in modeling and designing the solution process. The answer isn’t “yes, because…” or ”no, because…” now, which increases the chance of meaningful student-to-student math talk and real interest in another person’s solution.