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

Work out how to light up the single light. What's the rule?

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

NRICH December 2006 advent calendar - a new tangram for each 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?

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

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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

A metal puzzle which led to some mathematical questions.

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!

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?

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

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 outline of this brazier for roasting chestnuts?

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 this telephone?

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

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.

Train game for an adult and child. Who will be the first to make the train?

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

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

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?

Square It game for an adult and child. Can you come up with a way of always winning this game?

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?

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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?

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

An interactive activity for one to experiment with a tricky tessellation

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

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

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.