Prove Pythagoras' Theorem using enlargements and scale factors.
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 moves.
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.
Can you discover whether this is a fair game?
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.
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?
Can you beat the computer in the challenging strategy game?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Match pairs of cards so that they have equivalent ratios.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
Can you find a way to turn a rectangle into a square?
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. . . .
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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 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 simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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 tool for generating random integers.
How good are you at finding the formula for a number pattern ?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
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?
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.
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
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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 Excel to explore multiplication of fractions.
An Excel spreadsheet with an investigation.
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
A collection of resources to support work on Factors and Multiples at Secondary level.
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A group of interactive resources to support work on percentages Key Stage 4.
Use Excel to investigate the effect of translations around a number grid.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Use Excel to practise adding and subtracting fractions.
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?