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

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

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

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

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?

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

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

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

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

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

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

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.

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?

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

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 1 to 8 into the circles so that the four calculations are correct?

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?

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.

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?

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

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

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

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

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.

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

An interactive activity for one to experiment with a tricky tessellation

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.

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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

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

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

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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

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

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

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

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