56 406 is the product of two consecutive numbers. What are these two numbers?
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?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
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?
Resources to support understanding of multiplication and division through playing with number.
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.
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?
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?
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?
Number problems at primary level that may require resilience.
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?
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.
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?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
What is happening at each box in these machines?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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.
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!
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.
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.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Use the information to work out how many gifts there are in each pile.
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
How would you count the number of fingers in these pictures?
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?
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 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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?