This problem is designed to help children to learn, and to use, the two and three times tables.
Number problems at primary level that may require determination.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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?
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?
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?
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Use the information to work out how many gifts there are in each pile.
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?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find the next number in this pattern: 3, 7, 19, 55 ...
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
Number problems at primary level that require careful consideration.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
What is happening at each box in these machines?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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!
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
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?