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

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

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

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

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

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?

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

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

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

Can you deduce the pattern that has been used to lay out these bottle tops?

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

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

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

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

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?

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

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

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 fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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

Can you make the birds from the egg tangram?

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

Make a cube out of straws and have a go at this practical challenge.

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

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

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

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

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

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

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?

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

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

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 fit the tangram pieces into the outline of this junk?

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

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

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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.

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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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?