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

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

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?

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

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....?

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.

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?

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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?

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

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

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?

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

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

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

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

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

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

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

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

Can you complete this jigsaw of the multiplication square?

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?

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

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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

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

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

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?

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?

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.

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

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

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

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.

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

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.