These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Use the interactivities to complete these Venn diagrams.

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

Have you seen this way of doing multiplication ?

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

How good are you at finding the formula for a number pattern ?

Investigate matrix models for complex numbers and quaternions.

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.

Holly from Hermitage School sent a particularly well-explained solution to this problem.

Suryasnato, Bradley, Alex and Rhiannon all had a very logical way to solve this problem, each one slightly different to the others.

Simon and Trevor used the Newton Raphson method to solve this, Trevor using a spreadsheet and Simon a program in C. Andrei used interval halving and a graphical solution.

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.

This article for pupils explores what makes numbers special or lucky, and looks at the numbers that are all around us every day.

Some questions and prompts to encourage discussion about what experiences you want to give your pupils to help them reach their full potential in mathematics.

This article gives a proof of the uncountability of the Cantor set.

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.