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?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
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.
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?
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. . . .
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 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.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
An animation that helps you understand the game of Nim.
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?
A tool for generating random integers.
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.
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
Match pairs of cards so that they have equivalent ratios.
Use Excel to explore multiplication of fractions.
How good are you at finding the formula for a number pattern ?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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.
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
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
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
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?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you find all the 4-ball shuffles?
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
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
Use an interactive Excel spreadsheet to explore number in this
Use Excel to investigate the effect of translations around a number
A group of interactive resources to support work on percentages Key
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to investigate factors and
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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?