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 tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

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

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

Match pairs of cards so that they have equivalent ratios.

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

Use Excel to practise adding and subtracting fractions.

Use Excel to explore multiplication of fractions.

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

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.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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?

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

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

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?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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

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

Match the cards of the same value.

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

Which dilutions can you make using only 10ml pipettes?

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

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?

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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. . . .

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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 game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

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

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

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?

An Excel spreadsheet with an investigation.

Use an Excel spreadsheet to explore long multiplication.

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

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?