Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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!
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What is happening at each box in these machines?
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Use the information to work out how many gifts there are in each
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?
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?
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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.
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This problem is designed to help children to learn, and to use, the two and three times tables.
This task combines spatial awareness with addition and multiplication.
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?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
This number has 903 digits. What is the sum of all 903 digits?
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?
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
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?