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

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

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

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.

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.

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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 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.

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

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

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!

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

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?

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

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?

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

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

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

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

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.

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

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

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

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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

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?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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?

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?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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

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

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?

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.

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