What is the quickest route across a ploughed field when your speed around the edge is greater?

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.

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

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?

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. . . .

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?

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

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.

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!

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

Discover a handy way to describe reorderings and solve our anagram in the process.

An environment that enables you to investigate tessellations of regular polygons

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.

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

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

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

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

Can you beat the computer in the challenging strategy game?

Cellular is an animation that helps you make geometric sequences composed of square cells.

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.

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.

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.

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.

Practise your skills of proportional reasoning with this interactive haemocytometer.

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. . . .

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?

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

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

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 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 Excel to explore multiplication of fractions.

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

A tool for generating random integers.

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

Can you locate these values on this interactive logarithmic scale?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Match pairs of cards so that they have equivalent ratios.

Use Excel to practise adding and subtracting fractions.

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 an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

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.

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

Square It game for an adult and child. Can you come up with a way of always winning this game?

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