Number problems at primary level that may require resilience.
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?
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?
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?
This task combines spatial awareness with addition and multiplication.
Can you work out what a ziffle is on the planet Zargon?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
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.
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.
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.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This challenge combines addition, multiplication, perseverance and even proof.
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?
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?
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.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
If the answer's 2010, what could the question be?
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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
What is happening at each box in these machines?
Resources to support understanding of multiplication and division through playing with number.
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!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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.
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Number problems at primary level that require careful consideration.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?