I don’t feel that my presentation of the problem did anything to make it any more interesting for the students. I think what interested my students was them doing the following: 1) discovering on their own that it’s not 5 inches, 2) each taking a guess at what the actual length was, 3) understanding that THEY could figure out if their guess was correct or not.
Check out Alex’s third entry. On the challenge / rigor side, every student is working on the same mathematical operations. On the investment / engagement side, every student is performing those operations on a guess to which she is personally attached. Who loses here? Nobody.
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