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?

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

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

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

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

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 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?

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

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

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

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.

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?

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.

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

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

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

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!

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. . . .

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

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.

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 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?

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!

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?

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 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?

Can you complete this jigsaw of the multiplication square?

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.

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 fit the tangram pieces into the outline of this telephone?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Can you fit the tangram pieces into the outlines of the chairs?

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

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

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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.

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of these clocks?