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 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?
Given the nets of 4 cubes with the faces coloured in 4 colours,
build a tower so that on each vertical wall no colour is repeated,
that is all 4 colours appear.
Can you discover whether this is a fair game?
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you work through these direct proofs, using our interactive
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 be the first to complete a row of three?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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. . . .
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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
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?
Match pairs of cards so that they have equivalent ratios.
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.
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 the computer in the challenging strategy game?
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
Find the vertices of a pentagon given the midpoints of its sides.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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?
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. . . .
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
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.
Match the cards of the same value.
A mathematically themed crossword.
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!
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
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?
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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.
Which exact dilution ratios can you make using only 2 dilutions?
A metal puzzle which led to some mathematical questions.
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.
Can you locate these values on this interactive logarithmic scale?
Which dilutions can you make using 10ml pipettes and 100ml
Can you fill in the mixed up numbers in this dilution calculation?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Practise your skills of proportional reasoning with this interactive haemocytometer.
Can you break down this conversion process into logical steps?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.