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'.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Can you work out what a ziffle is on the planet Zargon?
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 combines spatial awareness with addition and multiplication.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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.
Given the products of adjacent cells, can you complete this Sudoku?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
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?
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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
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?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
This challenge combines addition, multiplication, perseverance and even proof.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
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.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
Number problems at primary level that require careful consideration.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.