Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of 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?

Move just three of the circles so that the triangle faces in the opposite direction.

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

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

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

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.

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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?

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. . . .

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

Complete the squares - but be warned some are trickier than they look!

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

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

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

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.

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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.

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

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

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

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

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?

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!

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

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

What is the greatest number of squares you can make by overlapping three squares?