Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Can you make five differently sized squares from the tangram pieces?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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.

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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.

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

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?

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

Make a mobius band and investigate its properties.

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

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Surprise your friends with this magic square trick.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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!

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

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?

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

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

These pictures show squares split into halves. Can you find other ways?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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

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

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

In this activity focusing on capacity, you will need a collection of different jars and bottles.

For this activity which explores capacity, you will need to collect some bottles and jars.

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

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Explore the triangles that can be made with seven sticks of the same length.

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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?

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