A game in which players take it in turns to choose a number. Can you block your opponent?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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 use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Can you complete this jigsaw of the multiplication square?

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?

Use the interactivities to complete these Venn diagrams.

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

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

Can you fit the tangram pieces into the outline of Little Ming?

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?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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

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. . . .

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 set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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

An interactive activity for one to experiment with a tricky tessellation

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

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

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

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!

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

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

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

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

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.

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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.

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

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?

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

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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.

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.

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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

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?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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?