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

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?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

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

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

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

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

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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?

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!

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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.

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

An interactive activity for one to experiment with a tricky tessellation

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.

Calculate the fractional amounts of money to match pairs of cards with the same value.

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

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 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?

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

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

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

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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....?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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?

The 2012 primary advent calendar features twenty-four of our posters, one for each day in the run-up to Christmas.