List

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.

article

Divisibility tests

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

problem

Favourite

Dozens

Age

7 to 14

Challenge level

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

problem

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?

problem

Favourite

Stars

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?

problem

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?

problem

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.