Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
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?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
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.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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?
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?
Number problems at primary level that may require resilience.
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Resources to support understanding of multiplication and division through playing with number.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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?
What is the sum of all the three digit whole numbers?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
This number has 903 digits. What is the sum of all 903 digits?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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!
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Number problems at primary level that require careful consideration.
Using the statements, can you work out how many of each type of rabbit there are in these pens?