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 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?

Here's a simple way to make a Tangram without any measuring or ruling lines.

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.

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?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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

What is the greatest number of squares you can make by overlapping three squares?

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Can you cut up a square in the way shown and make the pieces into a triangle?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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?

Can you fit the tangram pieces into the outline of this junk?

Can you fit the tangram pieces into the outline of Mai Ling?

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

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

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

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

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

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

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

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. . . .

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

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

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

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

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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

Make some celtic knot patterns using tiling techniques

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.

Surprise your friends with this magic square trick.

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

Can you fit the tangram pieces into the outline of this telephone?

Make a mobius band and investigate its properties.

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

Make a flower design using the same shape made out of different sizes of paper.

Can you visualise what shape this piece of paper will make when it is folded?

Delight your friends with this cunning trick! Can you explain how it works?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Can you fit the tangram pieces into the outline of Granma T?

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!