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.

Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?

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

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.

Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence

Prove Pythagoras' Theorem using enlargements and scale factors.

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?

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?

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

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

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

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

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.

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

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

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

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?

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?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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.

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. . . .

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

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. . . .

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.

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.

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. . . .

Use Excel to explore multiplication of fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

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?

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

Use an Excel spreadsheet to explore long multiplication.

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!

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

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.

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!

Can you beat the computer in the challenging strategy game?

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?

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?

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

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.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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.

An environment that enables you to investigate tessellations of regular polygons

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

A game in which players take it in turns to choose a number. Can you block your opponent?