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?
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.
Match pairs of cards so that they have equivalent ratios.
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
Find the vertices of a pentagon given the midpoints of its sides.
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.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
An environment that enables you to investigate tessellations of
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
A collection of our favourite pictorial problems, one for each day
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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?
Match the cards of the same value.
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
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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.
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
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. . . .
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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.
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. . . .
Have you seen this way of doing multiplication ?
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?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to investigate factors and
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Use an interactive Excel spreadsheet to explore number in this
Use an Excel spreadsheet to explore long multiplication.
An Excel spreadsheet with an investigation.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you beat the computer in the challenging strategy game?
Can you find all the 4-ball shuffles?