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
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.
Can you discover whether this is a fair game?
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
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
Prove Pythagoras Theorem using enlargements and scale factors.
Can you work through these direct proofs, using our interactive
Find the vertices of a pentagon given the midpoints of its sides.
To avoid losing think of another very well known game where the
patterns of play are similar.
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?
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.
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
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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.
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?
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?
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 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. . . .
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.
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.
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 collection of our favourite pictorial problems, one for each day
A weekly challenge concerning prime numbers.
Play countdown with matrices
Square It game for an adult and child. Can you come up with a way of always winning this game?
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.
Here is a chance to play a fractions version of the classic
Practise your skills of proportional reasoning with this interactive haemocytometer.
Match the cards of the same value.
Can you beat the computer in the challenging strategy game?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
A metal puzzle which led to some mathematical questions.
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.
How good are you at finding the formula for a number pattern ?
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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
Use an Excel spreadsheet to explore long multiplication.
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
Use an interactive Excel spreadsheet to investigate factors and