What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
56 406 is the product of two consecutive numbers. What are these
Find a great variety of ways of asking questions which make 8.
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.
What is the sum of all the three digit whole numbers?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This activity focuses on doubling multiples of five.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?