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.
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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?
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. . . .
Use an interactive Excel spreadsheet to investigate factors and
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?
Use Excel to practise adding and subtracting fractions.
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?
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use Excel to investigate the effect of translations around a number
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Use an interactive Excel spreadsheet to explore number in this
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
A group of interactive resources to support work on percentages Key
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.
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?
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 collection of our favourite pictorial problems, one for each day
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.
An animation that helps you understand the game of Nim.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Match pairs of cards so that they have equivalent ratios.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Use Excel to explore multiplication of fractions.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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.
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
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
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.
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
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
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you fill in the mixed up numbers in this dilution calculation?
Can you break down this conversion process into logical steps?
Which dilutions can you make using 10ml pipettes and 100ml
Which exact dilution ratios can you make using only 2 dilutions?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?