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

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

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

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

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

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

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

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

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!

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

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

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?

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....?

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?

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?

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

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 complete this jigsaw of the multiplication square?

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

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

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?

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. . . .

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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?

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.

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?

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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!

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?

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

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

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

Use the interactivities to complete these Venn diagrams.

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

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.

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