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

Number problems at primary level that require careful consideration.

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

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

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

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

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?

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

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

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?

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

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

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

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

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

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

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

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

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

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?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

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.

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

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

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Can you complete this jigsaw of the multiplication square?

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

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?

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?

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?

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

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?

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

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. . . .

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 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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

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

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