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 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?

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

Use Excel to explore multiplication of fractions.

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

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?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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

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

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

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

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

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.

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?

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?

A metal puzzle which led to some mathematical questions.

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

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

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

Use an Excel spreadsheet to explore long multiplication.

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

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

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.

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. . . .

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

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

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

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?

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?

Use an interactive Excel spreadsheet to investigate factors and multiples.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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.

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. . . .

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.

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?

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?

Have you seen this way of doing multiplication ?

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

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.

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 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. . . .

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?

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. . . .

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

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?

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.

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

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