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?

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?

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?

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

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. . . .

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

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?

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.

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

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?

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.

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

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

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.

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

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

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

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.

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?

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?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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.

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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.

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

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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

A tool for generating random integers.

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

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...

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

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

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

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?

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

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

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?

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.

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

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