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?
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.
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.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
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?
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?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
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?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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 teachers looks at how teachers can use problems from the NRICH site to help them teach division.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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?
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.
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?
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
This task combines spatial awareness with addition and multiplication.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This challenge combines addition, multiplication, perseverance and even proof.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
What is happening at each box in these machines?
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!
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Resources to support understanding of multiplication and division through playing with number.
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?
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?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Given the products of adjacent cells, can you complete this Sudoku?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Play this game and see if you can figure out the computer's chosen number.
Number problems at primary level that require careful consideration.