56 406 is the product of two consecutive numbers. What are these two numbers?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Given the products of adjacent cells, can you complete this Sudoku?
Here is a chance to play a version of the classic Countdown Game.
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
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.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Number problems at primary level that may require resilience.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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.
Can you work out what a ziffle is on the planet Zargon?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
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.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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.
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?
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?
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.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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 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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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,. . . .
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?
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
What is the least square number which commences with six two's?
This task combines spatial awareness with addition and multiplication.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.