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. . . .

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

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.

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.

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.

Make some celtic knot patterns using tiling techniques

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.

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

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

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 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.

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.

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.

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?

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?

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?

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

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.

Surprise your friends with this magic square trick.

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.

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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

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

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?

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?

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?

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?

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?

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

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

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

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

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?

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.

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