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. . . .

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 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.

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

Make some celtic knot patterns using tiling techniques

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

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

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

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

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?

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

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 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.

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

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.

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

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

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.

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 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.

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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

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.

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

Surprise your friends with this magic square trick.

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?

A game in which players take it in turns to choose a number. Can you block your opponent?

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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?

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

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.

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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.

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

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Turn through bigger angles and draw stars with Logo.