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. . . .

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

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

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 some celtic knot patterns using tiling techniques

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.

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.

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

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

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

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

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

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

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.

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.

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.

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?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

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

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?

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?

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?

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

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.

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

Learn about Pen Up and Pen Down in Logo

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

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

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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

Turn through bigger angles and draw stars with Logo.

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?