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?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
What is the sum of all the three digit whole numbers?
Ben’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?
56 406 is the product of two consecutive numbers. What are these two numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Number problems at primary level that may require determination.
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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?
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?
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.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
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?
Resources to support understanding of multiplication and division through playing with number.
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.
Use the information to work out how many gifts there are in each pile.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
What is happening at each box in these machines?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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 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!
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 number has 903 digits. What is the sum of all 903 digits?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Can you work out what a ziffle is on the planet Zargon?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?