I saw this problem on a sheet my son brought home from math team practice:

A couple of people point out on twitter than the problem isn’t worded so well. That’s my fault. The actual problem was a little longer but I was trying to capture the main point of the problem and did so in a slightly sloppy way.

Anyway, my son struggled with the problem at the math team tryouts, and the problem seemed so cool to me that I wanted to do a little more than just explain it to him.

Here’s our discussion. In the first part we just try to understand what’s going on – his first question was how you could get different shapes?

The second part of the discussion was about how to determine the largest difference in volume. This turned into a nice discussion about numbers and arithmetic. How could we tell which of the two numbers we had was bigger?

Fun little problem – and definitely a heck of a challenging problem for 6th graders!