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.

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

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?

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

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?

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

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

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!

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.

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

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

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?

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

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 put these shapes in order of size? Start with the smallest.

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

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

How many right angles can you make using two sticks?

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

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

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

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?

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?

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.

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

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?

Use the number weights to find different ways of balancing the equaliser.

Can you hang weights in the right place to make the equaliser balance?

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

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....?

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 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.

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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?

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?

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

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

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?

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

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.

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?

Here is a chance to play a version of the classic Countdown Game.