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

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

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

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

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

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

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?

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?

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

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

Surprise your friends with this magic square trick.

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

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

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

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

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.

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.

Make some celtic knot patterns using tiling techniques

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

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

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.

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?

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?

Learn about Pen Up and Pen Down in Logo

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

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

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

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

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

Turn through bigger angles and draw stars with Logo.

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

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

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.

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

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

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

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

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

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

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