Properties of Numbers

The problems in this feature will give your students the chance to investigate the properties of numbers in a variety of contexts.  They will have the opportunity to explore, conjecture and develop convincing arguments for any general results that they discover.

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

Divisibility Tests 

Age 11 to 16
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.


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

Clock Arithmetic 

Age 11 to 18
Challenge Level
What happens if we change the rules and make the usual straight number line into a circle?


Age 11 to 14
Challenge Level
Can you work out what step size to take to ensure you visit all the dots on the circle?

Clock Squares 

Age 14 to 18
Challenge Level
Can you find a way of predicting the value of large square numbers with the help of our power modulo calculator?

More Adventures with Modular Arithmetic 

Age 14 to 18
Challenge Level
Investigate what happens when we add or multiply numbers using modular arithmetic.

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