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?

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

This task combines spatial awareness with addition and multiplication.

Are these statements always true, sometimes true or never true?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

Number problems at primary level that may require determination.

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Use the information to work out how many gifts there are in each pile.

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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?

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.

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.

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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

This challenge combines addition, multiplication, perseverance and even proof.

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

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?

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.

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?

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?

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

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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

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

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

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

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

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