Age 11 to 14
This problem demonstrates how a formula can be derived from the
context (rather than "pattern-spotting") in a variety of ways.
It also provides practice in the manipulation of algebraic symbols
and generates generalities that can promote discussions on
equivalent symbolic forms.
A teacher comments:
This was a good opportunity to practise
simple and more difficult sequences and generation of formulae,
ranging from linear to cubic. All pupils were able to access the
problem up to (and beyond) their own "natural" ability (Year 9 set