I find it interesting (and a bit depressing) that I still sometimes am surprised but which problems my students find hard. I recently made up a 3D geometry problems solving exercise that I thought was kind of interesting and not too challenging. I mean, I knew some students would have trouble with it, but I fully expected the majority of the class to get it, especially since it was group work. Boy was I wrong.

To be fair, the actual math content of the problem was not difficult for them. It was being organized enough to find a way to see the pattern that they had trouble with. The ones who did solve it made a table starting with smaller numbers and quickly saw the pattern.

Here is the problem. I would be interested in any comments any readers might have about it:

You have a large number of small identical cubes in front of you. The surface area of all of these cubes together is 23328 cm2. You start playing with the small cubes and realize you can put them together to build one giant cube with no small cubes left over. The surface area of the big cube is 1944 cm2.

  1. How many small cubes do you have?

  2. What is the area of one face of one of the small cubes?

  3. How long are the edges of each small cube?

  4. What is the volume of the big cube?

  5. What is the volume of each small cube?