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

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

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?

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

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

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

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?

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

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

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

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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.

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

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

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?

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

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?

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?

Number problems at primary level that may require determination.

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?

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

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

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

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?

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?

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

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

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?

Number problems at primary level that require careful consideration.

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?

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

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?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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?

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

Can you replace the letters with numbers? Is there only one solution in each case?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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