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

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

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!

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

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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

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

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

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.

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

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

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?

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

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?

Surprise your friends with this magic square trick.

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 practical challenges are all about making a 'tray' and covering it with paper.

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

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?

Make a mobius band and investigate its properties.

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?

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

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?

Can you visualise what shape this piece of paper will make when it is folded?

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?

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

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

Can you deduce the pattern that has been used to lay out these bottle tops?

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?

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

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

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

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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

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?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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.

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

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

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

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