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.
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
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you discover whether this is a fair game?
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?
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 give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Match pairs of cards so that they have equivalent ratios.
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!
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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 interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
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.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Square It game for an adult and child. Can you come up with a way of always winning this game?
Can you beat the computer in the challenging strategy 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.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
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
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. . . .
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?
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 java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
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.
Have you seen this way of doing multiplication ?
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 set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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. . . .
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.
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?
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
A metal puzzle which led to some mathematical questions.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you find all the 4-ball shuffles?
Use Excel to explore multiplication of fractions.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Use an interactive Excel spreadsheet to investigate factors and
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
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. . . .
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.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?