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

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?

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

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

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

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

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....?

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?

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?

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?

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

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

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

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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

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?

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

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

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

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

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

Sort the houses in my street into different groups. Can you do it in any other ways?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

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.

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.

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?

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.

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

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

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

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

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

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?

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

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

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?

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