Can you each work out the number on your card? What do you notice? How could you sort the cards?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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

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?

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?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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?

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?

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

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

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

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

How many models can you find which obey these rules?

Can you make the birds from the egg tangram?

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?

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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

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

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?

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

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

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

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

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

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

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 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 the child walking home from school?

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

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 Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of this goat and giraffe?

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

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 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 outline of this telephone?

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

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?

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