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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
Number problems at primary level that require careful consideration.
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Find the next number in this pattern: 3, 7, 19, 55 ...
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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.
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.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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 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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
Use the information to work out how many gifts there are in each
What is happening at each box in these machines?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
This number has 903 digits. What is the sum of all 903 digits?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 jigsaw of the multiplication square?
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. . . .
Can you score 100 by throwing rings on this board? Is there more
than way to do 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?
Number problems at primary level that may require determination.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Can you replace the letters with numbers? Is there only one solution in each case?
Have a go at balancing this equation. Can you find different ways of doing it?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
This problem is designed to help children to learn, and to use, the two and three times tables.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What is the sum of all the three digit whole numbers?
Can you work out what a ziffle is on the planet Zargon?