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.

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

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

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

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

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?

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!

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

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?

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

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

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

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?

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

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

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

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

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

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

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.

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....?

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

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

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.

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?

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.

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

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

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

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?

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?

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

NRICH December 2006 advent calendar - a new tangram for each 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?

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

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?

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.

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?

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