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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
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.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Resources to support understanding of multiplication and division through playing with number.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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.
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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.
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?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This task combines spatial awareness with addition and multiplication.
What is happening at each box in these machines?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Use the information to work out how many gifts there are in each pile.
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 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.
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Can you work out what a ziffle is on the planet Zargon?
What is the sum of all the three digit whole numbers?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?