What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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.

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?

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

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

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

Learn about Pen Up and Pen Down in Logo

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

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

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?

Surprise your friends with this magic square trick.

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.

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

Make a mobius band and investigate its properties.

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

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

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?

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

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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?

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

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

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

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

What happens when a procedure calls itself?

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

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?

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?

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

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

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.

A description of how to make the five Platonic solids out of paper.

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

Build a scaffold out of drinking-straws to support a cup of water

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?