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?

Use the interactivities to complete these Venn diagrams.

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

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

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

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.

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

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?

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. . . .

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

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!

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?

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?

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?

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?

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

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

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?

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?

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

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

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?

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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

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

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!

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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.

Exchange the positions of the two sets of counters in the least possible number of moves

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?