Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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.

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?

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

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.

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

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

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 the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

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

Can you find triangles on a 9-point circle? Can you work out their angles?

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

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

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.

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. . . .

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.

An interactive activity for one to experiment with a tricky tessellation

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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.

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.

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?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2?

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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

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.

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

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

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?

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

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

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

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?

Calculate the fractional amounts of money to match pairs of cards with the same value.

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?

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.