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.

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

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

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.

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?

Surprise your friends with this magic square trick.

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

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.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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. . . .

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.

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

Make a mobius band and investigate its properties.

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

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

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

Make some celtic knot patterns using tiling techniques

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

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?

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

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

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?

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

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.

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?

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.

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

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

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

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

Turn through bigger angles and draw stars with Logo.

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

Learn about Pen Up and Pen Down in Logo

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

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

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

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

A jigsaw where pieces only go together if the fractions are equivalent.

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