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. . . .

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.

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

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?

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.

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

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

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

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

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

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

Make some celtic knot patterns using tiling techniques

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

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?

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

Surprise your friends with this magic square trick.

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

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

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

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

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.

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

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

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

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

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

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

Make a mobius band and investigate its properties.

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?

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?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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?

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

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

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

Learn about Pen Up and Pen Down in Logo