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

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Can you hang weights in the right place to make the equaliser balance?

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

Move just three of the circles so that the triangle faces in the opposite direction.

Twenty four games for the run-up to Christmas.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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.

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

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Complete the squares - but be warned some are trickier than they look!

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

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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....?

How many right angles can you make using two sticks?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Can you complete this jigsaw of the multiplication square?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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 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.

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

Use the number weights to find different ways of balancing the equaliser.

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?

If you have only four weights, where could you place them in order to balance this equaliser?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you fit the tangram pieces into the outline of the child walking home from school?