Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Which of these triangular jigsaws are impossible to finish?

Can you describe this route to infinity? Where will the arrows take you next?

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

There are lots of different methods to find out what the shapes are worth - how many can you find?

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

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?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Match the charts of these functions to the charts of their integrals.