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

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

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

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?

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

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. . . .

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?

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.

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

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

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

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

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

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

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

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

Follow these instructions to make a three-piece and/or seven-piece tangram.

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.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Make a mobius band and investigate its properties.

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Surprise your friends with this magic square trick.

Did you know mazes tell stories? Find out more about mazes and make one of your own.

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

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

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

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

What happens when a procedure calls itself?

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

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?

Learn about Pen Up and Pen Down in Logo

Turn through bigger angles and draw stars with Logo.

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

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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

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

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?

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

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

How can you make a curve from straight strips of paper?