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 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?

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. . . .

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.

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.

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.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

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

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?

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. . . .

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

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.

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.

Can you beat the computer in the challenging strategy game?

A metal puzzle which led to some mathematical questions.

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?

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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?

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

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

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

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. . . .

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Can you work through these direct proofs, using our interactive proof sorters?

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?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

An Excel spreadsheet with an investigation.

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 explore multiplication of fractions.

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.

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

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.

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

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

This resource contains interactive problems to support work on number sequences at Key Stage 4.

How good are you at finding the formula for a number pattern ?

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?

Can you locate these values on this interactive logarithmic scale?

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.

A tool for generating random integers.