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.

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

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

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

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

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

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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?

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?

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

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

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

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?

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

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

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

Make a mobius band and investigate its properties.

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

Surprise your friends with this magic square trick.

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

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

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

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

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

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?

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

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

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

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

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

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

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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?

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

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

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

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

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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.

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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?

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?

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

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

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