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

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

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?

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.

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

Twenty four games for the run-up to Christmas.

How many right angles can you make using two sticks?

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

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

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?

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 activity for one to experiment with a tricky tessellation

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?

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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

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?

Can you complete this jigsaw of the multiplication square?

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?

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?

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

What happens when you try and fit the triomino pieces into these two grids?

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?

Make one big triangle so the numbers that touch on the small triangles add to 10.

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

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!

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 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.

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

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?

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

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

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

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?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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?