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

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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

Can you put these shapes in order of size? Start with the smallest.

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?

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

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

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?

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

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

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 make the birds from the egg tangram?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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?

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

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

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

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...?

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

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

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

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?

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?

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

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

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

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

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

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?

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

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?

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

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 clocks?

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

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

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?

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

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?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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?

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?

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

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