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?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Make a mobius band and investigate its properties.

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.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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.

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

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

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

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

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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?

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

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

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?

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

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

An activity making various patterns with 2 x 1 rectangular tiles.

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

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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

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

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?

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

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

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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 outline of this shape. How would you describe it?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

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 these people?

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

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