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

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

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.

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

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

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?

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?

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

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

Make some celtic knot patterns using tiling techniques

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

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

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

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

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

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?

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

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

Use the tangram pieces to make our pictures, or to design some 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.

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.

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.

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

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

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.

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.

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.

Learn about Pen Up and Pen Down in Logo

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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?

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

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.

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

A description of how to make the five Platonic solids out of paper.