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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

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

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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?

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

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

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

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.

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

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

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. . . .

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?

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

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

An interactive activity for one to experiment with a tricky tessellation

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.

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?

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?

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?

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

Use the interactivities to complete these Venn diagrams.

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

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

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?

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

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

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.

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

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

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?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

These interactive dominoes can be dragged around the screen.

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.