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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

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?

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

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?

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Make a mobius band and investigate its properties.

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

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.

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.

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

What do these two triangles have in common? How are they related?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

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?

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 brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

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 lobster, yacht and cyclist?

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

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 outlines of the candle and sundial?

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

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

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?

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

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

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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

Can you logically construct these silhouettes using the tangram pieces?

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

What shape is made when you fold using this crease pattern? Can you make a ring design?

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