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.

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.

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

Can you locate these values on this interactive logarithmic scale?

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

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

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. . . .

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?

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

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

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

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

Use Excel to explore multiplication of fractions.

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

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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.

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 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?

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?

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.

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

An environment that enables you to investigate tessellations of regular polygons

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

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 is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

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.

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

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?

A tool for generating random integers.

Use an Excel spreadsheet to explore long multiplication.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

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

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

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

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

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

An Excel spreadsheet with an investigation.