Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
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?
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?
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 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?
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?
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!
A number game requiring a strategy.
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Use the information to work out how many gifts there are in each pile.
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.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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.
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?
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.
Choose a symbol to put into the number sentence.
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.
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.
Can you work out what a ziffle is on the planet Zargon?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
How would you count the number of fingers in these pictures?
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?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require resilience.
This number has 903 digits. What is the sum of all 903 digits?