In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.
A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown below. How many of the 1-cm cubes do not have red paint on any face?
Create Your Own Math
And then he challenges us as teachers:
- Do you have any ideas for extending the problem?
- If so, then jot them down.
People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math. 
Denise Gaskins' Let's Play Math 