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.

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.

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?

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.

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

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

Match the cards of the same value.

An environment that enables you to investigate tessellations of regular polygons

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

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

Match pairs of cards so that they have equivalent ratios.

A metal puzzle which led to some mathematical questions.

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

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

A weekly challenge concerning prime numbers.

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.

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. . . .

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.

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?

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?

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

Can you beat the computer in the challenging strategy game?

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

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

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

Use an Excel spreadsheet to explore long multiplication.

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

A tool for generating random integers.

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

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

Can you locate these values on this interactive logarithmic scale?

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.

An Excel spreadsheet with an investigation.

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

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

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

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.

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!

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

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