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

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?

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!

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

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

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 game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

An interactive activity for one to experiment with a tricky tessellation

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

Can you complete this jigsaw of the multiplication square?

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.

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.

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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?

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

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

If you have only four weights, where could you place them in order to balance this equaliser?

Here is a chance to play a version of the classic Countdown Game.

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

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

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Work out the fractions to match the cards with the same amount of money.

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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

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

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

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.

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.

Find out what a "fault-free" rectangle is and try to make some of your own.

Use the number weights to find different ways of balancing the equaliser.

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.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Can you find all the different ways of lining up these Cuisenaire rods?

Use the interactivity or play this dice game yourself. How could you make it fair?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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