Discover a handy way to describe reorderings and solve our anagram
in the process.
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Triangle ABC has equilateral triangles drawn on its edges. Points
P, Q and R are the centres of the equilateral triangles. What can
you prove about the triangle PQR?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to explore number in this
Use an Excel spreadsheet to explore long multiplication.
Use an interactive Excel spreadsheet to investigate factors and
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
Use Excel to investigate the effect of translations around a number
A group of interactive resources to support work on percentages Key
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?
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.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Use Excel to practise adding and subtracting fractions.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
An environment that enables you to investigate tessellations of
Can you find all the 4-ball shuffles?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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?
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
An Excel spreadsheet with an investigation.
A collection of our favourite pictorial problems, one for each day
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. . . .
A tool for generating random integers.
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.
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 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.
Can you beat the computer in the challenging strategy game?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
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.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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 red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
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.
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.