Prove Pythagoras' Theorem using enlargements and scale factors.
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?
Match pairs of cards so that they have equivalent ratios.
An environment that enables you to investigate tessellations of regular polygons
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.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
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?
Can you find a way to turn a rectangle into a square?
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
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?
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. . . .
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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. . . .
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 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.
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Match the cards of the same value.
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
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.
How good are you at finding the formula for a number pattern ?
Here is a chance to play a fractions version of the classic Countdown Game.
A tool for generating random integers.
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. . . .
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Use Excel to explore multiplication of fractions.
A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
Use Excel to investigate the effect of translations around a number grid.
An Excel spreadsheet with an investigation.
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to investigate factors and multiples.
An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.
Use an Excel spreadsheet to explore long multiplication.
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 an interactive Excel spreadsheet to explore number in this exciting game!
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
A group of interactive resources to support work on percentages Key Stage 4.
Can you find triangles on a 9-point circle? Can you work out their angles?
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 collection of resources to support work on Factors and Multiples at Secondary level.
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
How good are you at estimating angles?
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.
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...
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?