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?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
An animation that helps you understand the game of Nim.
Work out how to light up the single light. What's the rule?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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?
Meg and Mo still need to hang their marbles so that they balance,
but this time the constraints are different. Use the interactivity
to experiment and find out what they need to do.
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
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.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
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.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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?
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.
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. . . .
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.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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 a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Can you coach your rowing eight to win?
Here is a chance to play a version of the classic Countdown Game.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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. . . .
To avoid losing think of another very well known game where the
patterns of play are similar.
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. . . .
Can you explain the strategy for winning this game with any target?