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?

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?

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?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

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

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

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

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

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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?

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

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

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

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

Here is a chance to create some Celtic knots and explore the mathematics behind them.

Try out some calculations. Are you surprised by the results?

Play this game to learn about adding and subtracting positive and negative numbers

Imagine a very strange bank account where you are only allowed to do two things...

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

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

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?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

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

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

Video showing how to use the Number Plumber

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

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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

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

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

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

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?

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

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.

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?