Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]
Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
Stage: 4 Challenge Level:
Time playing with the balance is important. It would be easy to just tell students about "moments" as a formula, but finding this relationship for themselves through practical investigation is of much higher value.
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.