Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?

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?

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Video showing how to use the Number Plumber

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Steve has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Which of these triangular jigsaws are impossible to finish?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Design and test a paper helicopter. What is the best design?

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.

Watch the video to see how Charlie works out the sum. Can you adapt his method?

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

The Enigma Project's James Grime has created a video code challenge. Watch it here!