Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

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

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?

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

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?

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

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

Take a look at the video and try to find a sequence of moves that will take you back to zero.

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 Charlie works out the sum. Can you adapt his method?

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

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?

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

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

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?

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

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

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

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

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

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

Video showing how to use the Number Plumber

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

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

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

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

A video clip of Jo Boaler talking about Complex Instruction.

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?

Look carefully at the video of a tangle and explain what's happening.

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.

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.