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

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

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?

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

Can you lay out the pictures of the drinks in the way described by the clue cards?

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

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

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.

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

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?

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.

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

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

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?

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

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

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

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?

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?

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

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?

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?

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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

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

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

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

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

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

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 the candle and sundial?

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 these clocks?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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

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 outline of Little Ming playing the board game?

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

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

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

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

The challenge for you is to make a string of six (or more!) graded cubes.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?