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?

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

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 create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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

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?

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!

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

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

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.

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

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

Can you find all the different triangles on these peg boards, and find their angles?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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

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?

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?

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?

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

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

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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

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

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

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

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

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.

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

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

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....?

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

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

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

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

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 problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

How many right angles can you make using two sticks?

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