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

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?

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. . . .

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

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

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.

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?

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

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

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

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

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

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.

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?

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

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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.

Match the cards of the same value.

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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

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.

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?

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...

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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

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

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

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

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

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.

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

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?

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?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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.

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.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.