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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find the next number in this pattern: 3, 7, 19, 55 ...
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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 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!
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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.
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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?
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 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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Have a go at balancing this equation. Can you find different ways of doing it?
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. . . .
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?
Can you work out some different ways to balance this equation?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
This number has 903 digits. What is the sum of all 903 digits?
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 do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?