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Many results can be explained by applying lower secondary school algebraic techniques, and many can also be explained using pictorial representations.

problem

### Number rules - OK

Can you produce convincing arguments that a selection of statements about numbers are true?

problem

### Take Three From Five

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

problem

### Always Perfect

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

*We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.*