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

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?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

Write a Logo program, putting in variables, and see the effect when you change the variables.

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

What happens when a procedure calls itself?

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

Learn about Pen Up and Pen Down in Logo

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Use the tangram pieces to make our pictures, or to design some of your own!

Build a scaffold out of drinking-straws to support a cup of water

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Learn to write procedures and build them into Logo programs. Learn to use variables.

More Logo for beginners. Now learn more about the REPEAT command.

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Turn through bigger angles and draw stars with Logo.

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

A game to make and play based on the number line.

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

Make a clinometer and use it to help you estimate the heights of tall objects.

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

A game in which players take it in turns to choose a number. Can you block your opponent?

Which of the following cubes can be made from these nets?

Make some celtic knot patterns using tiling techniques

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

A description of how to make the five Platonic solids out of paper.

This article for students gives some instructions about how to make some different braids.

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

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

What shape and size of drinks mat is best for flipping and catching?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

What shape would fit your pens and pencils best? How can you make it?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?