Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

Can you work out which spinners were used to generate the frequency charts?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Use the interactivity or play this dice game yourself. How could you make it fair?

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

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

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

A tool for generating random integers.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Work out how to light up the single light. What's the rule?

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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 1 person to play on screen. Practise your number bonds whilst improving your memory

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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

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

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?

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

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

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?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Can you fit the tangram pieces into the outline of the child walking home from school?

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

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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.