To avoid losing think of another very well known game where the
patterns of play are similar.
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. . . .
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?
Can you discover whether this is a fair game?
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?
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 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!
Square It game for an adult and child. Can you come up with a way of always winning this 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.
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. . . .
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
Find the vertices of a pentagon given the midpoints of its sides.
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?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
Match pairs of cards so that they have equivalent ratios.
Can you be the first to complete a row of three?
Can you beat the computer in the challenging strategy game?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Match the cards of the same value.
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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.
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
Discover a handy way to describe reorderings and solve our anagram
in the process.
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?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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. . . .
The classic vector racing game brought to a screen near you.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Here is a chance to play a fractions version of the classic
A collection of our favourite pictorial problems, one for each day
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?
Can you find all the 4-ball shuffles?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Practise your skills of proportional reasoning with this interactive haemocytometer.
How good are you at finding the formula for a number pattern ?
A metal puzzle which led to some mathematical questions.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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.
An environment that enables you to investigate tessellations of