Number problems at primary level that may require resilience.
This task combines spatial awareness with addition and multiplication.
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.
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
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?
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?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Here is a chance to play a version of the classic Countdown Game.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
This challenge combines addition, multiplication, perseverance and even proof.
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
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.
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
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?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Use the information to work out how many gifts there are in each pile.
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
What is happening at each box in these machines?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Can you work out what a ziffle is on the planet Zargon?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Number problems at primary level that require careful consideration.
Given the products of adjacent cells, can you complete this Sudoku?
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" .