Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

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.

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!

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.

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

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?

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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?

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

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.

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.

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

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.

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

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

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

An interactive activity for one to experiment with a tricky tessellation

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?

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?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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

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?

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

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

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

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

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

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

Can you sort these triangles into three different families and explain how you did it?

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.

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

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?