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?
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
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.
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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Number problems at primary level that may require resilience.
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Can you work out what a ziffle is on the planet Zargon?
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.
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
This task combines spatial awareness with addition and multiplication.
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 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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What is happening at each box in these machines?
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?
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.
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and 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?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Use the information to work out how many gifts there are in each pile.
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?
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. . . .
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
More resources to support understanding multiplication and division through playing with numbers
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
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?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
Number problems at primary level that require careful consideration.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Resources to support understanding of multiplication and division through playing with number.