### Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

### Odd Differences

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.

### Peeling the Apple or the Cone That Lost Its Head

How much peel does an apple have?

This problem was designed to explore equivalence of change (ie. if a $10\%$ decrease isn't the opposite of a $10\%$ increase, what is? ) and to move students towards the important Stage 5 concept: exponential growth and decay.