I started class by holding up one cup and presenting the problem of stacking the cups high enough to reach my height. I worried about this. I was concerned that the students would want to know why I would want to do that, but no one word. Ok then! I think the challenge was enough of an interest that they didn't really care why.
We went through the whole activity and I want to share with you a few of the misconceptions that we uncovered during the lesson.
1) When I gave each group of students 10 cups to work with, some took the height of the 10 cups, and divided my height by that. What they failed to recognize was that when they placed the next 10 cups on the stack it wouldn't hover over the first 10, they would sick down.
2) Some groups realized that the height kept increasing my the size of the rim, so they divided my height by the rim height. Those students forgot to take in account the height of the body of the first cup.
3) Measuring was a small issue, most students measured the slant height of the cup rather than the vertical height. It didn't effect the results because there wasn't a huge different in the slant and vertical heights, and I'm short.
After they committed to a number and we stacked the cups to see how their numbers stacked up (pun intended!), I gave the groups this sheet:
For even more cup stacking fun check out this first act from Andrew Stadel.