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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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'.
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.
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?
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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Resources to support understanding of multiplication and division through playing with number.
This problem is designed to help children to learn, and to use, the two and three times tables.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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
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?
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 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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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.
Can you work out some different ways to balance this equation?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Can you work out what a ziffle is on the planet Zargon?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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 the sum of all the three digit whole numbers?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house