Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

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?

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?

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

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?

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

Prove Pythagoras Theorem using enlargements and scale factors.

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

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

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

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

Match pairs of cards so that they have equivalent ratios.

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.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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.

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?

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.

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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.

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?

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

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.

Use an Excel spreadsheet to explore long multiplication.

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

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?

Use Excel to explore multiplication of fractions.

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

A tool for generating random integers.

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

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

The classic vector racing game brought to a screen near you.

A metal puzzle which led to some mathematical questions.

Use Excel to practise adding and subtracting fractions.

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

An Excel spreadsheet with an investigation.

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

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

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. . . .

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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. . . .

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