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.

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

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

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

A metal puzzle which led to some mathematical questions.

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

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

Use Excel to explore multiplication of fractions.

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.

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?

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. . . .

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.

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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 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. . . .

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...

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Work out how to light up the single light. What's the rule?

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?

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

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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

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.

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.

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

Use an Excel spreadsheet to explore long multiplication.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?