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

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

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

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

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

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?

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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

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?

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

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

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?

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

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

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

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 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?

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 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 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 outline of Little Fung at the table?

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

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?

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.

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

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

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

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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?

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

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?

How many models can you find which obey these rules?

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

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?