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?

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

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

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

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

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

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?

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?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

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

Can you logically construct these silhouettes using the tangram pieces?

Can you make the birds from the egg tangram?

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

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

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of the workmen?

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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?

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

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

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.

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.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.