We drew a circle and measured the diameter and radius. The diameter was 3 and radius was 1.5. The formula was C=2ΠR so we multiplied 2 x 3.14 x 1.5 and it equaled 9.42. Then we divided 9.42/3 (diameter) and it equaled 3.14. Which is C/D and was the info that was given to us. So we proved that circumference is C=2ΠR. -A student proof.

The proof I was expecting was something like “Since Π is defined as C/D, then C=ΠD, and since D=2R, then C=2ΠR.” What’s the feedback that will cause them to be concerned about thinking in circles? The best (only) idea I’ve come up with is: “If you had multiplied 2x7x1.5 to get 21, then divided C/D = 21/3 = 7, you would have shown that Π=7.” But I have ’till Jan 4th to find something better. Any suggestions?