This article for teachers suggests ideas for activities built around 10 and 2010.

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Resources to support understanding of multiplication and division through playing with number.

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Can you work out some different ways to balance this equation?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

There were 22 legs creeping across the web. How many flies? How many spiders?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

How would you count the number of fingers in these pictures?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?