How will you decide which way of flipping over and/or turning the grid will give you the highest total?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
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?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
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
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?
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?
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Resources to support understanding of multiplication and division through playing with number.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
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 at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Given the products of adjacent cells, can you complete this Sudoku?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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'.
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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!
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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.
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
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?