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

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?

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?

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?

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

An interactive activity for one to experiment with a tricky tessellation

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.

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?

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.

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.

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. . . .

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

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

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

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?

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

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

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?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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

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

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

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

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

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

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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

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

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?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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