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

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?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

Can you make five differently sized squares from the tangram pieces?

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

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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

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

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 ...

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?

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

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

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

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

Did you know mazes tell stories? Find out more about mazes and make one 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!

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?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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

Surprise your friends with this magic square trick.

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 see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Make a mobius band and investigate its properties.

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?

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.

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

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

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

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Explore the triangles that can be made with seven sticks of the same length.

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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?

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

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

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

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

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?

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?

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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