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

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

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?

Use the interactivities to complete these Venn diagrams.

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

An interactive activity for one to experiment with a tricky tessellation

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

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. . . .

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

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

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.

These interactive dominoes can be dragged around the screen.

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?

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 how to light up the single light. What's the rule?

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!

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

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?

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?

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.

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

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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.

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....?

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 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?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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 or play this dice game yourself. How could you make it fair?

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. . . .

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

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?

Here is a chance to play a version of the classic Countdown Game.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.