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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
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 what a ziffle is on the planet Zargon?
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?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Resources to support understanding of multiplication and division through playing with number.
Number problems at primary level that may require resilience.
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
Use the information to work out how many gifts there are in each pile.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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.
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
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 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?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Number problems at primary level that require careful consideration.
What is happening at each box in these machines?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
This number has 903 digits. What is the sum of all 903 digits?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
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?