Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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....?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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?

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

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?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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

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

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

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

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

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?

An interactive activity for one to experiment with a tricky tessellation

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

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?

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?

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?

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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 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.

Use the interactivity or play this dice game yourself. How could you make it fair?

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.