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?
What is the sum of all the three digit whole numbers?
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?
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.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
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?
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.
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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 the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
There were 22 legs creeping across the web. How many flies? How many spiders?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This problem is designed to help children to learn, and to use, the two and three times tables.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Resources to support understanding of multiplication and division through playing with number.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the information to work out how many gifts there are in each
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?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Here is a chance to play a version of the classic Countdown Game.
If the answer's 2010, what could the question be?