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

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.

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?

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

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.

What is the greatest number of squares you can make by overlapping three squares?

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?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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

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?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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?

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.

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?

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

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

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

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?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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.

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Make a flower design using the same shape made out of different sizes of paper.

Can you make the birds from the egg tangram?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

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

Exploring and predicting folding, cutting and punching holes and making spirals.

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

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Which of the following cubes can be made from these nets?

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

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?