Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
56 406 is the product of two consecutive numbers. What are these
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This problem is designed to help children to learn, and to use, the two and three times tables.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you work out what a ziffle is on the planet Zargon?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Number problems at primary level that require careful consideration.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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.
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
If the answer's 2010, what could the question be?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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
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?
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.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require determination.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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. . . .
What is happening at each box in these machines?
There were 22 legs creeping across the web. How many flies? How many spiders?
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.
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 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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you replace the letters with numbers? Is there only one solution in each case?
This activity focuses on doubling multiples of five.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Resources to support understanding of multiplication and division through playing with number.
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.