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

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.

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

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

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

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

A metal puzzle which led to some mathematical questions.

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.

Prove Pythagoras Theorem using enlargements and scale factors.

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?

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

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

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

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

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

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 explore multiplication of fractions.

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?

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.

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

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

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?

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

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

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.

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.

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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?

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?

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

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

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

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

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.

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. . . .

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?

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 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?

Use an interactive Excel spreadsheet to investigate factors and multiples.

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.

An Excel spreadsheet with an investigation.

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?

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

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. . . .