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?

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

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

Make a mobius band and investigate its properties.

Surprise your friends with this magic square trick.

Make a clinometer and use it to help you estimate the heights of tall objects.

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

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

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

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

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 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?

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

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

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?

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?

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

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

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

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

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?

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

Can you make the birds from the egg tangram?

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.

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

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

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

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

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

Learn about Pen Up and Pen Down in Logo

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

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

This activity investigates how you might make squares and pentominoes from Polydron.

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

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.

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?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

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?

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

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

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

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