Can you sort these triangles into three different families and explain how you did it?

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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?

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

How many right angles can you make using two sticks?

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?

Can you hang weights in the right place to make the equaliser balance?

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.

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

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 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. . . .

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?

An interactive activity for one to experiment with a tricky tessellation

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.

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

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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

Use the number weights to find different ways of balancing the equaliser.

Twenty four games for the run-up to Christmas.

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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?

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

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?

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

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.

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

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

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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

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!

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