This problem starts with a 1 by 1 by 1 painted cube. Then builds to a 2 by 2 by 2 painted cube, then 3 by 3 by 3 painted cube, etc. Students are asked to count the number of 1 by 1 by 1 cubes that have paint on all six faces, three faces, two faces, one face and no faces. There is a table that has some of the information filled in to help the student find the needed information and then they are asked to try to generalize the patterns found.
This works really well if you have cubes to give the students to build at least the first three figures.
Answer key included.