What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

56 406 is the product of two consecutive numbers. What are these two numbers?

Find a great variety of ways of asking questions which make 8.

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?

This number has 903 digits. What is the sum of all 903 digits?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

This problem is designed to help children to learn, and to use, the two and three times tables.

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

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

Have a go at balancing this equation. Can you find different ways of doing it?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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

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?

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

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?

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

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?

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?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

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

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

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

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

This task combines spatial awareness with addition and multiplication.

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

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

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

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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