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

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

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?

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.

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....?

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.

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

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.

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

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

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.

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

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

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.

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

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.

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

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

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

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

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

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?

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

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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?

An environment which simulates working with Cuisenaire rods.

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

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

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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

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

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

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

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.

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