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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
56 406 is the product of two consecutive numbers. What are these two numbers?
Number problems at primary level that may require determination.
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?
What is the sum of all the three digit whole numbers?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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?
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 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?
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
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?
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?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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!
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'.
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?
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.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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 happening at each box in these machines?
Use the information to work out how many gifts there are in each pile.
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?
This problem is designed to help children to learn, and to use, the two and three times tables.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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 work out what a ziffle is on the planet Zargon?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?