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?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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!

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

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.

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

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?

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

Use the interactivities to complete these Venn diagrams.

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?

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

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 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. . . .

An interactive activity for one to experiment with a tricky tessellation

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?

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?

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

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

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

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

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?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

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.

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

Can you complete this jigsaw of the multiplication square?

Can you fit the tangram pieces into the outline of Granma T?

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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

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.

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

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?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

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.

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?