You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Can you make the birds from the egg tangram?

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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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?

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?

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?

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

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

Here is a version of the game 'Happy Families' for you to make and play.

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

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

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

Can you make five differently sized squares from the tangram pieces?

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

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.

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

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?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

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

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

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

Can you deduce the pattern that has been used to lay out these bottle tops?

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?

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

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

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

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?

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

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?

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?

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

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