Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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?

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

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?

Could games evolve by natural selection? Take part in this web experiment to find out!

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

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

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

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?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you fit the tangram pieces into the outlines of these clocks?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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.

Can you fit the tangram pieces into the outline of Little Fung at the table?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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.

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outlines of these people?

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?

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

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?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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.

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?

Can you fit the tangram pieces into the outline of the child walking home from school?

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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. . . .

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.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

An interactive activity for one to experiment with a tricky tessellation

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Exchange the positions of the two sets of counters in the least possible number of moves

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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.

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

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