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. . . .

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?

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?

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.

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?

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

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

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.

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.

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

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.

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

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?

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.

Surprise your friends with this magic square trick.

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?

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

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

Learn about Pen Up and Pen Down in Logo

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?

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

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

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?

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

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

Delight your friends with this cunning trick! Can you explain how it works?

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

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

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

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?

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

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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.