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

Make a mobius band and investigate its properties.

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

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.

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

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.

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?

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

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.

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?

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

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

Learn about Pen Up and Pen Down in Logo

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.

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

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.

Can you fit the tangram pieces into the outline of Granma T?

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?

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

Turn through bigger angles and draw stars with Logo.

More Logo for beginners. Now learn more about the REPEAT command.

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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.

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

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

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.

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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

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?

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

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.

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?

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.