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

Use the interactivities to complete these Venn diagrams.

Can you complete this jigsaw of the multiplication square?

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

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

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.

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

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?

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

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?

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

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!

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

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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

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

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

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in 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?

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

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?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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.

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

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?

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

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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?

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

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

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

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