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.
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 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. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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 discover whether this is a fair game?
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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.
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.
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
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"
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
Can you find all the 4-ball shuffles?
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
How good are you at finding the formula for a number pattern ?
An Excel spreadsheet with an investigation.
Use Excel to practise adding and subtracting fractions.
An animation that helps you understand the game of Nim.
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.
A collection of our favourite pictorial problems, one for each day
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Find the vertices of a pentagon given the midpoints of its sides.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
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.
Use an interactive Excel spreadsheet to explore number in this
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.
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
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Use this animation to experiment with lotteries. Choose how many
balls to match, how many are in the carousel, and how many draws to
make at once.
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.
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. . . .
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?