List

Numerical explorations

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.

problem

Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?

problem

Take three from five

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?

problem

Number rules - OK

Age

14 to 16

Challenge level

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

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.

article

Seeing is believing

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.