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

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

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

If you can sketch y=f(x), there are several related functions you can also sketch...

Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.

When you're on trial for murder, it can be crucial that the court understands probability...

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

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.

Which of these triangular jigsaws are impossible to finish?

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

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

How can you quickly sort a suit of cards in order from Ace to King?

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

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

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

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.

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

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

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?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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?

"Statins cut the risks of heart attacks and strokes by 40%"

Should the Professor take statins? Can you help him decide?

Take a look at the video showing areas of different shapes on dotty grids...

Take a look at the video showing rhombuses and their diagonals...

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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

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?

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

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?

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