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

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

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?

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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.

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

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?

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.

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

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

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

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

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

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?

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

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?

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

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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?

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?

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 make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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

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?

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

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

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?

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

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

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

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

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

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