Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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?

An interactive activity for one to experiment with a tricky tessellation

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?

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

What happens when you try and fit the triomino pieces into these two grids?

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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....?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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?

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

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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

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

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

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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.

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

Practise your number bonds whilst improving your memory in this matching pairs game.

Practise your tables skills and try to beat your previous best score in this interactive game.

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.

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.

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

This activity challenges you to make collections of shapes. Can you give your collection a name?

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.

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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?

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.

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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