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!

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?

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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?

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.

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.

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

Can you complete this jigsaw of the multiplication square?

What happens when you try and fit the triomino pieces into these two grids?

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?

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

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

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

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

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

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

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

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

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?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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

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?

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

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

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?

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

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?

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

Exchange the positions of the two sets of counters in the least possible number of moves

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

Use the interactivities to complete these Venn diagrams.

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