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.

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

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

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

This article for students gives some instructions about how to make some different braids.

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.

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

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

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

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

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

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

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

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.

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

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?

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.

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?

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.

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?

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

Surprise your friends with this magic square trick.

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

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

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

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?

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

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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?

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.

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

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?