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?
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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.
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?
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?
Can you work out what a ziffle is on the planet Zargon?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
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.
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?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Given the products of adjacent cells, can you complete this Sudoku?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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,. . . .
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?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Play this game and see if you can figure out the computer's chosen number.
Here is a chance to play a version of the classic Countdown Game.
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?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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 value of the circle changes in each of the following problems. Can you discover its value in each problem?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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. . . .
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
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.
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
What is the least square number which commences with six two's?
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.