Why do this problem?
This challenge is a good extension to the usual one of just finding the pentominoes. It also gives an opening for discussing further extensions to the challenge - eg what about where the front door to the houses would be?
Start with finding the shapes that are required for the rest of the challenge by presenting the pupils with interlocking cubes that can represent the squares.
Have you checked that no two are the same?
How did you go about finding all the different designs?
Suggestions from the pupils to the question that start ,"I wonder what would happen if we. . . . ?"
It would be helpful for some pupils to have squared paper that has the same size squares as the cubes they are using.