This activity challenges you to make collections of shapes. Can you give your collection a name?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

Complete the squares - but be warned some are trickier than they look!

Sort the houses in my street into different groups. Can you do it in any other ways?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Use the interactivity to sort these numbers into sets. Can you give each set a name?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

Can you fit the tangram pieces into the outline of the child walking home from school?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Move just three of the circles so that the triangle faces in the opposite direction.

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

An interactive activity for one to experiment with a tricky tessellation

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

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

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

How many different rhythms can you make by putting two drums on the wheel?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Use the interactivities to complete these Venn diagrams.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?