To avoid losing think of another very well known game where the
patterns of play are similar.
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?
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.
Square It game for an adult and child. Can you come up with a way of always winning this game?
Can you discover whether this is a fair game?
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. . . .
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.
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
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?
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. . . .
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.
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!
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?
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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. . . .
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
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.
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?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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 many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
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?
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
Find the vertices of a pentagon given the midpoints of its sides.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
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?
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
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
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. . . .
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.
Use Excel to explore multiplication of fractions.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Identical discs are flipped in the air. You win if all of the faces
show the same colour. Can you calculate the probability of winning
with n discs?
Here is a chance to play a fractions version of the classic
Here is a chance to play a version of the classic Countdown Game.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.