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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
56 406 is the product of two consecutive numbers. What are these two numbers?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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.
Play this game and see if you can figure out the computer's chosen number.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Given the products of adjacent cells, can you complete this Sudoku?
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. . . .
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?
Number problems at primary level that may require resilience.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
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.
These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
Here is a chance to play a version of the classic Countdown Game.
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.
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?
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?
This task combines spatial awareness with addition and multiplication.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
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?
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.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
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. . . .
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?
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you 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?
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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. . . .
Find the highest power of 11 that will divide into 1000! exactly.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?