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?

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 metal puzzle which led to some mathematical questions.

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

Use an Excel spreadsheet to explore long multiplication.

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

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

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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

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?

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 loci at Key Stage 4.

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.

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

A tool for generating random integers.

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

Use Excel to explore multiplication of fractions.

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.

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

An environment that enables you to investigate tessellations of regular polygons

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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

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

Match pairs of cards so that they have equivalent ratios.

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

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.

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

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

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. . . .

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

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. . . .

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

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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?

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

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...