Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

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

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

Learn about Pen Up and Pen Down in Logo

What shape and size of drinks mat is best for flipping and catching?

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

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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.

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

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

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

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.

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

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

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?

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. . . .

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

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

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

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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.

What happens when a procedure calls itself?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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.

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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

Use the tangram pieces to make our pictures, or to design some 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?

Turn through bigger angles and draw stars with Logo.

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