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?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
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.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This number has 903 digits. What is the sum of all 903 digits?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you find different ways of creating paths using these paving slabs?
Use the information to work out how many gifts there are in each pile.
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?
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?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
What is happening at each box in these machines?
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?
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'.
Number problems at primary level that may require resilience.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
Can you work out what a ziffle is on the planet Zargon?
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?
Resources to support understanding of multiplication and division through playing with number.
56 406 is the product of two consecutive numbers. What are these two numbers?
What is the sum of all the three digit whole numbers?
How would you count the number of fingers in these pictures?