This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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.
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?
What is the sum of all the three digit whole 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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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.
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?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Number problems at primary level that may require resilience.
Find the next number in this pattern: 3, 7, 19, 55 ...
Here is a chance to play a version of the classic Countdown Game.
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?
What is happening at each box in these machines?
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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
A game that tests your understanding of remainders.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Use the information to work out how many gifts there are in each pile.
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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 work out what a ziffle is on the planet Zargon?
Resources to support understanding of multiplication and division through playing with number.
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?
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?
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?