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

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.

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?

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

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?

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

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?

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

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

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 fit the tangram pieces into the outline of Little Ming?

Use the interactivities to complete these Venn diagrams.

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?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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

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.

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.

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.

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

An interactive activity for one to experiment with a tricky tessellation

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

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!

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

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?

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

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

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?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Square It game for an adult and child. Can you come up with a way of always winning this game?