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.
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?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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?
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.
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 find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
An animation that helps you understand the game of Nim.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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.
Use Excel to explore multiplication of fractions.
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
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?
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.
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.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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?
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 give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
A game in which players take it in turns to choose a number. Can you block your opponent?
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. . . .
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
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.
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?
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.
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?
Use Excel to practise adding and subtracting fractions.
Use Excel to investigate the effect of translations around a number
An Excel spreadsheet with an investigation.
Use an interactive Excel spreadsheet to explore number in this
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
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. . . .