Find a great variety of ways of asking questions which make 8.
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?
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?
56 406 is the product of two consecutive numbers. What are these
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received 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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
This problem is designed to help children to learn, and to use, the two and three times tables.
There were 22 legs creeping across the web. How many flies? How many spiders?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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?
What is happening at each box in these machines?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find the next number in this pattern: 3, 7, 19, 55 ...
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
This activity focuses on doubling multiples of five.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.