Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
56 406 is the product of two consecutive numbers. What are these
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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.
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
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.
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is 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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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!
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use the information to work out how many gifts there are in each
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
What is happening at each box in these machines?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
How would you count the number of fingers in these pictures?
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?