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 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.

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

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.

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

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?

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.

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

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

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?

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

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

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

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

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?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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.

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

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....?

An interactive activity for one to experiment with a tricky tessellation

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

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?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Try out the lottery that is played in a far-away land. What is the chance of winning?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .