Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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

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

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.

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.

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

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?

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 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 shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

An interactive activity for one to experiment with a tricky tessellation

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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?

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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

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

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

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 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. . . .

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?

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

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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?

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

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

Can you fit the tangram pieces into the outline of Granma T?

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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