We would like to thank Geoff Faux for introducing us to the idea of 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?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.