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?

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.

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

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.

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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?

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

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

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

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?

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

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?

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

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

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.

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

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

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

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

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

Surprise your friends with this magic square trick.

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

Make a mobius band and investigate its properties.

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?