How do scores on dice and factors of polynomials relate to each
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Can you work through these direct proofs, using our interactive
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Which dilutions can you make using only 10ml pipettes?
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
Can you fill in the mixed up numbers in this dilution calculation?
Which dilutions can you make using 10ml pipettes and 100ml
Which exact dilution ratios can you make using only 2 dilutions?
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.
Can you discover whether this is a fair game?
Can you break down this conversion process into logical steps?
Prove Pythagoras' Theorem using enlargements and scale factors.
Give your further pure mathematics skills a workout with this interactive and reusable set of activities.
This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
This is an interactivity in which you have to sort into the correct
order the steps in the proof of the formula for the sum of a
Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!
Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
Make and prove a conjecture about the cyclic quadrilateral
inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Explore displacement/time and velocity/time graphs with this mouse
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
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. . . .
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
What is the quickest route across a ploughed field when your speed
around the edge is greater?
A tool for generating random integers.
How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with
the solutions x and y being integers? Read this article to find
Play countdown with matrices
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
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. . . .
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?
A spherical balloon lies inside a wire frame. How much do you need
to deflate it to remove it from the frame if it remains a sphere?
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.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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.
Six circles around a central circle make a flower. Watch the flower
as you change the radii in this circle packing. Prove that with the
given ratios of the radii the petals touch and fit perfectly.
The classic vector racing game brought to a screen near you.
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. . . .
Play countdown with vectors.
Play a more cerebral countdown using complex numbers.
A weekly challenge concerning prime numbers.
With red and blue beads on a circular wire; 'put a red bead between
any two of the same colour and a blue between different colours
then remove the original beads'. Keep repeating this. What happens?
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.
Can you beat the computer in the challenging strategy game?
Can you work out which spinners were used to generate the frequency charts?
Balancing interactivity with springs and weights.