Fault-free Rectangles
This problem will encourage children to generalise and be systematic. It involves not just identifying a pattern but starting to explore why the pattern occurs. The possibilities for extension are endless. For example:
What happens if you take rods that differ in length by two?
Are there any rods which can't be made into fault-free rectangles?
Are there any combinations of rods which can't be made into fault-free rectangles?