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?
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?
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?
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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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.
This problem is designed to help children to learn, and to use, the two and three times tables.
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'.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
56 406 is the product of two consecutive numbers. What are these
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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.
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
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 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.
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 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?
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 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?
Can you work out what a ziffle is on the planet Zargon?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
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.
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 challenge combines addition, multiplication, perseverance and even proof.
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?
This task combines spatial awareness with addition and multiplication.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge encourages you to explore dividing a three-digit number by a single-digit number.