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!

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

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?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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 activity for one to experiment with a tricky tessellation

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.

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. . . .

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

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?

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?

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

Can you complete this jigsaw of the multiplication square?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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

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

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.

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?

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?

Here is a chance to play a version of the classic Countdown Game.

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Use the interactivities to complete these Venn diagrams.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.