This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

This problem looks at how one example of your choice can show something about the general structure of multiplication.

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?

Watch the video to see how Charlie works out the sum. Can you adapt his method?

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

By proving these particular identities, prove the existence of general cases.

Have a look at this very detailed solution sent in to what some may have thought was quite an easy problem!

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

These students explained the cleverness of their code-breaking journeys very clearly, and should give many insights to all would-be code breakers.

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 one example help us to perceive the generality?

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

Third in our series of problems on population dynamics for advanced students.