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
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?
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.
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!
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.
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
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Find the vertices of a pentagon given the midpoints of its sides.
Can you be the first to complete a row of three?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Match the cards of the same value.
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.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Match pairs of cards so that they have equivalent ratios.
Can you beat the computer in the challenging strategy game?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
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.
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Use Excel to explore multiplication of fractions.
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?
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.
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?
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. . . .
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.
How good are you at finding the formula for a number pattern ?
A metal puzzle which led to some mathematical questions.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Can you find all the 4-ball shuffles?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Practise your skills of proportional reasoning with this interactive haemocytometer.
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
Here is a chance to play a fractions version of the classic
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?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Discover a handy way to describe reorderings and solve our anagram
in the process.