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.
If the answer's 2010, what could the question be?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Find the next number in this pattern: 3, 7, 19, 55 ...
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
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This number has 903 digits. What is the sum of all 903 digits?
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.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
This challenge combines addition, multiplication, perseverance and even proof.
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.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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 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 work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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.
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 task combines spatial awareness with addition and multiplication.
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
How would you count the number of fingers in these pictures?
Can you work out some different ways to balance this equation?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.