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# Numerical Explorations

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Take Three from Five

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Number Rules - OK

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Always Perfect

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Seeing Is Believing

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Number theory - the study of the natural numbers - does not typically feature in school curricula, but it is a rich source of interesting problems which can lead to surprising results. The problems in this feature will offer your students the opportunity to notice patterns, conjecture, generalise and prove results.

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

You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these problems.

Age 11 to 16

Challenge Level

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?

Age 14 to 16

Challenge Level

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

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.

Age 11 to 18

In this article for teachers we draw attention to the value of visual representations.

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