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.

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?

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

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.

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?

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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

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?

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?

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.

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?

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

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?

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

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

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

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

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

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

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

Can you make the birds from the egg tangram?

Here's a simple way to make a Tangram without any measuring or ruling lines.

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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

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?

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?

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 fit the tangram pieces into the outlines of these people?

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 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 chairs?

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

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 Little Ming playing the board game?

An activity making various patterns with 2 x 1 rectangular tiles.

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

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?

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

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