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

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

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

Learn about Pen Up and Pen Down in Logo

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

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

Surprise your friends with this magic square trick.

Make a mobius band and investigate its properties.

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

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.

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

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

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

Learn to write procedures and build them into Logo programs. Learn to use variables.

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

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.

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

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.

What happens when a procedure calls itself?

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

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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

Turn through bigger angles and draw stars with Logo.

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

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

A game to make and play based on the number line.

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

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

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

Make some celtic knot patterns using tiling techniques

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

Follow these instructions to make a five-pointed snowflake from a square of paper.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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

This article for students gives some instructions about how to make some different braids.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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

Use the tangram pieces to make our pictures, or to design some of your own!

Here are some ideas to try in the classroom for using counters to investigate number patterns.