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 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 make a right-angled triangle on this peg-board by joining
up three points round the edge?
Cellular is an animation that helps you make geometric sequences composed of square cells.
Can you beat the computer in the challenging strategy game?
Take any parallelogram and draw squares on the sides of the
parallelogram. What can you prove about the quadrilateral formed by
joining the centres of these squares?
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.
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. . . .
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
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
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
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?
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.
Re-arrange the pieces of the puzzle to form a rectangle and then to
form an equilateral triangle. Calculate the angles and lengths.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Square It game for an adult and child. Can you come up with a way of always winning this game?
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. . . .
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?
Use Excel to explore multiplication of fractions.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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.
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?
Here is a chance to play a fractions version of the classic
The classic vector racing game brought to a screen near you.
Can you work through these direct proofs, using our interactive
A collection of our favourite pictorial problems, one for each day
A tool for generating random integers.
A weekly challenge concerning prime numbers.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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.
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.
Discover a handy way to describe reorderings and solve our anagram
in the process.
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.
Match the cards of the same value.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
How good are you at finding the formula for a number pattern ?
A metal puzzle which led to some mathematical questions.
Play countdown with matrices
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Triangle ABC has equilateral triangles drawn on its edges. Points
P, Q and R are the centres of the equilateral triangles. What can
you prove about the triangle PQR?
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Can you discover whether this is a fair game?
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
An Excel spreadsheet with an investigation.