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

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?

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

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

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.

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

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?

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?

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?

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

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

Surprise your friends with this magic square trick.

Follow these instructions to make a five-pointed snowflake from a square of paper.

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

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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.

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

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

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

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

Make a mobius band and investigate its properties.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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

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?

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

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

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

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?

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 fit the tangram pieces into the outline of this telephone?

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

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

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

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

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 Mai Ling 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 outlines of the lobster, yacht and cyclist?

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

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?