This problem shows that the external angles of an irregular hexagon add to a circle.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Can you describe this route to infinity? Where will the arrows take you next?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Just look at the many solutions that were sent in, and the reasoning behind them all.

Can one example help us to perceive the generality?

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?