Number problems at primary level that require careful consideration.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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.
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?
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?
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.
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?
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?
Use the information to work out how many gifts there are in each pile.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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!
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?
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?
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?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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.
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
This task combines spatial awareness with addition and multiplication.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
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?
This challenge combines addition, multiplication, perseverance and even proof.
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
Find the next number in this pattern: 3, 7, 19, 55 ...
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?