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.
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?
Number problems at primary level that require careful consideration.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
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.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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.
What is happening at each box in these machines?
This number has 903 digits. What is the sum of all 903 digits?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Number problems at primary level that may require determination.
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?
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?
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. . . .
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?
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?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Can you complete this jigsaw of the multiplication square?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
There were 22 legs creeping across the web. How many flies? How many spiders?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
Can you replace the letters with numbers? Is there only one solution in each case?
This activity focuses on doubling multiples of five.
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?
56 406 is the product of two consecutive numbers. What are these
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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?