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.

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

Can you make the birds from the egg tangram?

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?

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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 arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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?

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

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

Delight your friends with this cunning trick! Can you explain how it works?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

How many models can you find which obey these rules?

Our 2008 Advent Calendar has a 'Making Maths' activity for every 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?

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

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?

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 lobster, yacht and cyclist?

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?

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

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 brazier for roasting chestnuts?

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

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

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

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 this shape. How would you describe it?

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?

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

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

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

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

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?

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

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?

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?