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?
56 406 is the product of two consecutive numbers. What are these
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?
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.
If the answer's 2010, what could the question be?
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?
Number problems at primary level that may require determination.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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 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?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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.
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!
Use the information to work out how many gifts there are in each
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This problem is designed to help children to learn, and to use, the two and three times tables.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Can you work out what a ziffle is on the planet Zargon?
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?
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.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?