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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This task combines spatial awareness with addition and multiplication.
Are these statements always true, sometimes true or never true?
Number problems at primary level that may require determination.
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
This number has 903 digits. What is the sum of all 903 digits?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
56 406 is the product of two consecutive numbers. What are these
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use the information to work out how many gifts there are in each
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 a great variety of ways of asking questions which make 8.
This problem is designed to help children to learn, and to use, the two and three times tables.
What is the sum of all the three digit whole numbers?
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?
Can you work out what a ziffle is on the planet Zargon?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
This challenge combines addition, multiplication, perseverance and even proof.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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.
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?