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

Can you put these shapes in order of size? Start with the smallest.

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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.

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?

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.

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

Make a mobius band and investigate its properties.

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

Surprise your friends with this magic square trick.

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!

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

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?

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

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.

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?

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

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

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

In this activity focusing on capacity, you will need a collection of different jars and bottles.

For this activity which explores capacity, you will need to collect some bottles and jars.

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

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

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

These pictures show squares split into halves. Can you find other ways?

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

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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?

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

Can you describe a piece of paper clearly enough for your partner to know which piece it is?