Creating and manipulating expressions and formulae

Can you make sense of these three proofs of Pythagoras' Theorem?

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Make some loops out of regular hexagons. What rules can you discover?

There are unexpected discoveries to be made about square numbers...

Play around with the Fibonacci sequence and discover some surprising results!

Can you explain what is going on in these puzzling number tricks?

Where should you start, if you want to finish back where you started?

Can you figure out how sequences of beach huts are generated?