How will you work out which numbers have been used to create this multiplication square?
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?
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?
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.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you find different ways of creating paths using these paving slabs?
Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Number problems at primary level that require careful consideration.
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?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
What is happening at each box in these machines?
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 number has 903 digits. What is the sum of all 903 digits?
Use the information to work out how many gifts there are in each pile.
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?
How would you count the number of fingers in these pictures?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
If the answer's 2010, what could the question be?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
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.
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What is the sum of all the three digit whole numbers?
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?