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?

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?

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

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!

Can you complete this jigsaw of the multiplication square?

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

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 interactivities to complete these Venn diagrams.

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

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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. . . .

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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.

An interactive activity for one to experiment with a tricky tessellation

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

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

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 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?

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....?

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. . . .

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!

Can you find all the different ways of lining up these Cuisenaire rods?

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

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?

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

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?

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

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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

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?

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