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?

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.

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?

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.

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

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

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

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

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

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?

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

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

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

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?

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?

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 outlines of these people?

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?

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 clocks?

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?

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

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 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 candle and sundial?

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 the child walking home from school?

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 the chairs?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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

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.

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?