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

Surprise your friends with this magic square trick.

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

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

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

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

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

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

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.

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

Make a mobius band and investigate its properties.

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

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.

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

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

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 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?

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

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

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.

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.

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?

Turn through bigger angles and draw stars with Logo.

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

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

Learn about Pen Up and Pen Down in Logo

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?

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

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.

Can you make the birds from the egg tangram?

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?

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.

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?

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

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?

What happens when a procedure calls itself?

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

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

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