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?

Can you find a way to turn a rectangle into a square?

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?

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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

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.

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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.

Which dilutions can you make using only 10ml pipettes?

Can you fill in the mixed up numbers in this dilution calculation?

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?

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!

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

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

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. . . .

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.

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

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.

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.

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. . . .

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?

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.

Can you beat the computer in the challenging strategy game?

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.

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

Can you find the pairs that represent the same amount of money?

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

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

Can you work out which spinners were used to generate the frequency charts?

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

Can you locate these values on this interactive logarithmic scale?

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.

Use Excel to explore multiplication of fractions.

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. . . .

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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 interactive Excel spreadsheet to investigate factors and multiples.

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.

An environment which simulates working with Cuisenaire rods.

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

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?