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?
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?
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 resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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?
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
An animation that helps you understand the game of Nim.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Work out how to light up the single light. What's the rule?
A tool for generating random integers.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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
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.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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.
Match pairs of cards so that they have equivalent ratios.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Use Excel to explore multiplication of fractions.
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?
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?
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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. . . .
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
An Excel spreadsheet with an investigation.
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.
Can you work out which spinners were used to generate the frequency charts?
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?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
A game in which players take it in turns to choose a number. Can you block your opponent?
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.