Number problems at primary level that require careful consideration.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
What is the sum of all the three digit whole numbers?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Number problems at primary level that may require resilience.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Use the information to work out how many gifts there are in each pile.
This number has 903 digits. What is the sum of all 903 digits?
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.
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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?
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
What is happening at each box in these machines?
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?
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!
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
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?
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
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?
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?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Resources to support understanding of multiplication and division through playing with number.