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?

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

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

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 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?

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

Surprise your friends with this magic square trick.

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

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

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

Make a mobius band and investigate its properties.

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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

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

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 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?

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.

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

Can you make the birds from the egg tangram?

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

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?

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

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.

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

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?

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.

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

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?

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

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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?

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

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

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?

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

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

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

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