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
A java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
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
Can you work through these direct proofs, using our interactive
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you discover whether this is a fair game?
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
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.
Prove Pythagoras Theorem using enlargements and scale factors.
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
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. . . .
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.
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?
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?
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
Use Excel to explore multiplication of fractions.
A right-angled isosceles triangle is rotated about the centre point
of a square. What can you say about the area of the part of the
square covered by the triangle as it rotates?
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
To avoid losing think of another very well known game where the
patterns of play are similar.
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. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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.
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?
Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
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.
Match the cards of the same value.
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.
Give your further pure mathematics skills a workout with this interactive and reusable set of activities.
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!
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
A tool for generating random integers.
A weekly challenge concerning prime numbers.
Play a more cerebral countdown using complex 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. . . .
The classic vector racing game brought to a screen near you.
Play countdown with matrices
Play countdown with vectors.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
A metal puzzle which led to some mathematical questions.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Rotate a copy of the trapezium about the centre of the longest side
of the blue triangle to make a square. Find the area of the square
and then derive a formula for the area of the trapezium.
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.
How good are you at finding the formula for a number pattern ?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Practise your skills of proportional reasoning with this interactive haemocytometer.
Can you locate these values on this interactive logarithmic scale?
Can you work out which spinners were used to generate the frequency charts?