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

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?

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

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

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

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.

Make a mobius band and investigate its properties.

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

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?

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

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

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.

Surprise your friends with this magic square trick.

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

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.

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.

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

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?

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.

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

What happens when a procedure calls itself?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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

Learn about Pen Up and Pen Down in Logo

Write a Logo program, putting in variables, and see the effect when you change the variables.

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

Can you make the birds from the egg tangram?

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

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

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

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

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

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?

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?

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?

Turn through bigger angles and draw stars with Logo.

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