7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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
Can you work out which spinners were used to generate the frequency charts?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
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 the interactivity or play this dice game yourself. How could
you make it fair?
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?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Match the cards of the same value.
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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
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 find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
Can you set the logic gates so that the number of bulbs which are
on is the same as the number of switches which are on?
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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.
Work out how to light up the single light. What's the rule?
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. . . .
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...
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.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
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?
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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.
Can you fit the tangram pieces into the outline of the child walking home from school?
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.
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.
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.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.