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?

A metal puzzle which led to some mathematical questions.

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.

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?

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

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?

Use Excel to explore multiplication of fractions.

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.

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.

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

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

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

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

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

Use an Excel spreadsheet to explore long multiplication.

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

An environment which simulates working with Cuisenaire rods.

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.

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

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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

Work out the fractions to match the cards with the same amount of money.

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...

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

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?

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?

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.

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

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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.

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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.

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.

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?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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.

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. . . .

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

An Excel spreadsheet with an investigation.

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.

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