Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
How much peel does an apple have?
Invite ideas about possible directions for generalisation,
perhaps starting with the easier results like allowing 'plus one
more' to become plus two, plus three, and so on.
More able students will produce more extended generalisations
and have a motivation to account for what is observed, challenging
one another to communicate clear explanations or visualisations of
the fundamental processes.
Able students will sense the potential power of a spreadsheet
and should be encouraged to work collaboratively to become
proficient and confident in its use.