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?

To avoid losing think of another very well known game where the patterns of play are similar.

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.

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!

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

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

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?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

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. . . .

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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.

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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

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

Can you locate these values on this interactive logarithmic scale?

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

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

Can you beat the computer in the challenging strategy game?

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

Play a more cerebral countdown using complex numbers.

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. . . .

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

Use Excel to explore multiplication of fractions.

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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

Use an Excel spreadsheet to explore long multiplication.

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

Match pairs of cards so that they have equivalent ratios.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

An environment that enables you to investigate tessellations of regular polygons

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

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.

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?