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...

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

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.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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

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.

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

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

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

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

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

Use Excel to explore multiplication of fractions.

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.

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?

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.

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 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.

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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. . . .

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Can you beat the computer in the challenging strategy game?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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

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.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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.

Can you explain the strategy for winning this game with any target?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

These interactive dominoes can be dragged around the screen.

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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 find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?