Creating and manipulating expressions and formulae

problem
Pythagoras proofs

Age

11 to 16

Challenge level

Can you make sense of these three proofs of Pythagoras' Theorem?
problem
What does it all add up to?

Age

11 to 18

Challenge level

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

Age

14 to 18

Challenge level

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

Age

7 to 14

Challenge level

The Number Jumbler can always work out your chosen symbol. Can you work out how?
problem
Regular hexagon loops

Age

11 to 14

Challenge level

Make some loops out of regular hexagons. What rules can you discover?
problem
Square number surprises

Age

14 to 16

Challenge level

There are unexpected discoveries to be made about square numbers...
problem
Fibonacci surprises

Age

11 to 14

Challenge level

Play around with the Fibonacci sequence and discover some surprising results!
problem
Puzzling place value

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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