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?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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. . . .
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?
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
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
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 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 opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Use Excel to explore multiplication of fractions.
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
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.
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 resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
Match pairs of cards so that they have equivalent ratios.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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 tool for generating random integers.
A collection of our favourite pictorial problems, one for each day
Match the cards of the same value.
Use Excel to investigate the effect of translations around a number
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
How good are you at finding the formula for a number pattern ?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Here is a chance to play a fractions version of the classic
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
An animation that helps you understand the game of Nim.
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 find all the 4-ball shuffles?
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to investigate factors and
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Use an interactive Excel spreadsheet to explore number in this
An Excel spreadsheet with an investigation.
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.
Meg and Mo need to hang their marbles so that they balance. Use the
interactivity to experiment and find out what they need to do.