Can you work out what a ziffle is on the planet Zargon?
Number problems at primary level that may require resilience.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these two numbers?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
More resources to support understanding multiplication and division through playing with numbers
Related resources supporting pupils' understanding of multiplication and division through playing with numbers.
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?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
Resources to support understanding of multiplication and division through playing with number.
If the answer's 2010, what could the question be?
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
Given the products of adjacent cells, can you complete this Sudoku?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
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 primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 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!
What is happening at each box in these machines?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This task combines spatial awareness with addition and multiplication.
Use the information to work out how many gifts there are in each pile.
Can you find different ways of creating paths using these paving slabs?
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
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.
These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Play this game and see if you can figure out the computer's chosen number.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Number problems at primary level that require careful consideration.
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?