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?
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
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?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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 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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
56 406 is the product of two consecutive numbers. What are these
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.
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?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
What is the sum of all the three digit whole numbers?
What is happening at each box in these machines?
How would you count the number of fingers in these pictures?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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!
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
This number has 903 digits. What is the sum of all 903 digits?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.