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

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

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?

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.

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

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

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?

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

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 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.

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!

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?

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?

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

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

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

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?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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?

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

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

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?

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

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

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

Use the interactivities to complete these Venn diagrams.

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

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?

Can you fit the tangram pieces into the outlines of the candle and sundial?

What is the greatest number of squares you can make by overlapping three squares?

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.

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

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

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

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.

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....?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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