An environment that enables you to investigate tessellations of regular polygons

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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?

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?

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

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?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Can you find triangles on a 9-point circle? Can you work out their angles?

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.

An Excel spreadsheet with an investigation.

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 make a right-angled triangle on this peg-board by joining up three points round the edge?

Use an Excel spreadsheet to explore long multiplication.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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?

Can you find a way to turn a rectangle into a square?

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?

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Use Excel to explore multiplication of fractions.

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?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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. . . .

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.

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

Here is a chance to play a fractions version of the classic Countdown Game.

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. . . .

Match pairs of cards so that they have equivalent ratios.

Prove Pythagoras' Theorem using enlargements and scale factors.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

A collection of resources to support work on Factors and Multiples at Secondary level.

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 practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Use Excel to investigate the effect of translations around a number grid.

A group of interactive resources to support work on percentages Key Stage 4.

Use an interactive Excel spreadsheet to explore number in this exciting game!

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

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. . . .

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?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Can you explain the strategy for winning this game with any target?