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.

The last day for students to send us their solutions to the live problems is Monday 15 March. 

Dozens live

Age 7 to 14
Challenge Level
Can you select the missing digit(s) to find the largest number?

Take Three from Five live

Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Number Rules - OK live

Age 14 to 16
Challenge Level
Can you produce convincing arguments that a selection of statements about numbers are true?

Always Perfect live

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.

Seeing Is Believing 

Age 11 to 18
In this article for teachers we draw attention to the value of visual representations.