Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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?

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

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

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

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

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?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

Can you sort these triangles into three different families and explain how you did it?

An environment which simulates working with Cuisenaire rods.

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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

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

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

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.

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

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

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

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?

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

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

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?

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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!

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

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

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?