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?

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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.

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?

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

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

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

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

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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?

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

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

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

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

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

Can you make the birds from the egg tangram?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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

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

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 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 Ming playing the board game?

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

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

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

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

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?

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

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

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

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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

Can you lay out the pictures of the drinks in the way described by the clue cards?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?