Use the interactivities to complete these Venn diagrams.

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

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?

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

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

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

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

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

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?

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?

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!

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?

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?

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.

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 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. . . .

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

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

Can you complete this jigsaw of the multiplication square?

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

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.

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?

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?

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

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

These interactive dominoes can be dragged around the screen.

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

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

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?

Can you fit the tangram pieces into the outlines of the chairs?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

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