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?
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
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
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand. . . .
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.
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?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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 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.
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.
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.
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
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Work out how to light up the single light. What's the rule?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
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.
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
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?
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...
An animation that helps you understand the game of Nim.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
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
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.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Here is a chance to play a fractions version of the classic
A collection of our favourite pictorial problems, one for each day
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
A tool for generating random integers.