Which of the following cubes can be made from these nets?

Make some celtic knot patterns using tiling techniques

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. . . .

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?

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

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

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.

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

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

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

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

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

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

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?

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.

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

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?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outline of this plaque design?

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?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the workmen?

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.

Turn through bigger angles and draw stars with Logo.

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

Learn about Pen Up and Pen Down in Logo

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.

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

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

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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