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
Can you work through these direct proofs, using our interactive
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.
Can you discover whether this is a fair game?
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.
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 into the correct
order the steps in the proof of the formula for the sum of a
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
A collection of resources to support work on Factors and Multiples at Secondary level.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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.
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 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
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
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?
This set of resources for teachers offers interactive environments
to support work on graphical interpretation at Key Stage 4.
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 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.
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!
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.
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. . . .
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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?
A weekly challenge concerning prime numbers.
The classic vector racing game brought to a screen near you.
Use Excel to explore multiplication of fractions.
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 matrices
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Play a more cerebral countdown using complex numbers.
Play countdown with vectors.
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?
Investigate how logic gates work in circuits.
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?
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 good are you at finding the formula for a number pattern ?
Cellular is an animation that helps you make geometric sequences composed of square cells.
Can you locate these values on this interactive logarithmic scale?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
A metal puzzle which led to some mathematical questions.
Here is a chance to play a fractions version of the classic
Can you beat the computer in the challenging strategy game?
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.
A tool for generating random integers.
Match the cards of the same value.
A collection of our favourite pictorial problems, one for each day