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 explain the strategy for winning this game with any target?

Triangular 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

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.

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.

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?

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.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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?

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.

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?

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

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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. . . .

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

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

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Use Excel to explore multiplication of fractions.

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

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

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

An Excel spreadsheet with an investigation.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Train game for an adult and child. Who will be the first to make the train?

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.

The 2012 primary advent calendar features twenty-four of our posters, one for each day in the run-up to Christmas.

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

A game in which players take it in turns to choose a number. Can you block your opponent?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

What is the greatest number of squares you can make by overlapping three squares?

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

A train building game for two players. Can you be the one to complete the train?

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

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...

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Can you beat the computer in the challenging strategy game?

Can you find the pairs that represent the same amount of money?