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?
Prove Pythagoras Theorem using enlargements and scale factors.
Find the vertices of a pentagon given the midpoints of its sides.
Can you work through these direct proofs, using our interactive
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
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
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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.
Practise your skills of proportional reasoning with this interactive haemocytometer.
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.
Can you locate these values on this interactive logarithmic scale?
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?
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?
Discover a handy way to describe reorderings and solve our anagram
in the process.
An environment that enables you to investigate tessellations of
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.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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.
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.
Match the cards of the same value.
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. . . .
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?
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?
Can you beat the computer in the challenging strategy game?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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?
How good are you at finding the formula for a number pattern ?
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 metal puzzle which led to some mathematical questions.
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.
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
Here is a chance to play a fractions version of the classic
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
A collection of our favourite pictorial problems, one for each day
Play countdown with vectors.
A weekly challenge concerning prime numbers.
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 Excel to investigate the effect of translations around a number
A group of interactive resources to support work on percentages Key
Play countdown with matrices
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?