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?
56 406 is the product of two consecutive numbers. What are these two 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.
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.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Number problems at primary level that may require resilience.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he 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?
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?
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?
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?
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
A number game requiring a strategy.
Can you work out what a ziffle is on the planet Zargon?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the information to work out how many gifts there are in each pile.
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
What is happening at each box in these machines?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find different ways of creating paths using these paving slabs?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
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?
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 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!
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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 number has 903 digits. What is the sum of all 903 digits?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
How would you count the number of fingers in these pictures?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.