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.
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. . . .
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.
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 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.
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
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?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you discover whether this is a fair game?
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.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Use Excel to explore multiplication of fractions.
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.
Rotate a copy of the trapezium about the centre of the longest side
of the blue triangle to make a square. Find the area of the square
and then derive a formula for the area of the trapezium.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
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. . . .
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
A collection of our favourite pictorial problems, one for each day
Can you find all the 4-ball shuffles?
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?
Find the vertices of a pentagon given the midpoints of its sides.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Use Excel to investigate the effect of translations around a number
How good are you at finding the formula for a number pattern ?
The classic vector racing game brought to a screen near you.
Here is a chance to play a fractions version of the classic
An Excel spreadsheet with an investigation.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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 explore number in this
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
A tool for generating random integers.
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