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

Make some celtic knot patterns using tiling techniques

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

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

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?

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

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. . . .

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.

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

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

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.

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?

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

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

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Follow these instructions to make a five-pointed snowflake from a square of paper.

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.

Surprise your friends with this magic square trick.

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?

Make a mobius band and investigate its properties.

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

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

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.

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.

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

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

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

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

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.

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

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.

Turn through bigger angles and draw stars with Logo.

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

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

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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