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

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?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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?

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

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?

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

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

These practical challenges are all about making a 'tray' and covering it with paper.

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

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?

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

Here is a version of the game 'Happy Families' for you to make and play.

Can you make the birds from the egg tangram?

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

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

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

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

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?

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?

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?

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?

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.

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

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

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

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?

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

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.

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

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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 telephone?

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.

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