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?

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

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

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

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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

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

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?

Can you make the birds from the egg tangram?

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

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

A game to make and play based on the number line.

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?

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?

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.

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?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

How many models can you find which obey these rules?

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?

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?

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?

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 outline of Little Fung at the table?

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 these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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

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 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 outline of this plaque design?

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 the workmen?

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 Mai Ling and Chi Wing?

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 junk?

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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

Use the tangram pieces to make our pictures, or to design some of your own!

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