This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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.
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.
Number problems at primary level that may require resilience.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Have a go at balancing this equation. Can you find different ways of doing it?
Resources to support understanding of multiplication and division through playing with number.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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 is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Use the information to work out how many gifts there are in each pile.
Number problems at primary level that require careful consideration.
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?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?