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

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

Can you complete this jigsaw of the multiplication square?

Use the interactivities to complete these Venn diagrams.

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?

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

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

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

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?

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 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?

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

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

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

Work out the fractions to match the cards with the same amount of money.

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

An interactive activity for one to experiment with a tricky tessellation

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

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.

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?

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.

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 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.

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

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.

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

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

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.

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

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!

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

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

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

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

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

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

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

Train game for an adult and child. Who will be the first to make the train?

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

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?

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

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

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?