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. . . .

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

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

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

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.

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

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?

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 some celtic knot patterns using tiling techniques

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

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

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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.

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

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

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.

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

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

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

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

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.

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?

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

Surprise your friends with this magic square trick.

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

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.

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

Make a mobius band and investigate its properties.

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.

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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

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.

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

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

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

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

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.

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

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