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

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?

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.

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

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.

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

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. . . .

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?

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.

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.

Use Excel to practise adding and subtracting fractions.

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. . . .

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.

An Excel spreadsheet with an investigation.

Match pairs of cards so that they have equivalent ratios.

Can you beat the computer in the challenging strategy game?

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?

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?

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

Use Excel to explore multiplication of fractions.

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.

Match the cards of the same value.

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

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.

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?

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.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

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. . . .

The classic vector racing game brought to a screen near you.

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!

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

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. . . .

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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 spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

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?

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?

A metal puzzle which led to some mathematical questions.

A collection of our favourite pictorial problems, one for each day of Advent.

Give your further pure mathematics skills a workout with this interactive and reusable set of activities.