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

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?

What happens when a procedure calls itself?

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

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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

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

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

Turn through bigger angles and draw stars with Logo.

Learn about Pen Up and Pen Down in Logo

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

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?

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

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.

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. . . .

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 some celtic knot patterns using tiling techniques

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

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

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

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

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

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

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?

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

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

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

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.

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

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

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

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

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

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

Surprise your friends with this magic square trick.

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.

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

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

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Here's a simple way to make a Tangram without any measuring or ruling lines.

The challenge for you is to make a string of six (or more!) graded cubes.

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Make a mobius band and investigate its properties.