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.

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 cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Make an equilateral triangle by folding paper and use it to make patterns of your own.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Can you visualise what shape this piece of paper will make when it is folded?

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?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

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

Make a mobius band and investigate its properties.

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?

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?

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Make some celtic knot patterns using tiling techniques

Surprise your friends with this magic square trick.

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

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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

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

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?

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

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

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

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

Can you make the birds from the egg tangram?

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

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

What shape and size of drinks mat is best for flipping and catching?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

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?

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 Wai Ping, Wah Ming and Chi Wing?

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?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

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?

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