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?
Here is a picnic that Chris 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.
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
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?
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
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.
Resources to support understanding of multiplication and division through playing with number.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
What is the sum of all the three digit whole numbers?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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 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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
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.
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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!
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
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 arrange 5 different digits (from 0 - 9) in the cross in the
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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?
What is happening at each box in these machines?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
How would you count the number of fingers in these pictures?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
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.
Can you work out what a ziffle is on the planet Zargon?