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?

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

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

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

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

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

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.

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.

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

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

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

A tool for generating random integers.

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?

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.

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

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.

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

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

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

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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 fit the tangram pieces into the outline of Granma T?

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

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

A collection of our favourite pictorial problems, one for each day of Advent.

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?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outlines of the chairs?

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

Can you fit the tangram pieces into the outlines of these people?

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

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

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?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Fung at the table?