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?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Number problems at primary level that may require resilience.
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?
This number has 903 digits. What is the sum of all 903 digits?
What is the sum of all the three digit whole numbers?
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.
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
If the answer's 2010, what could the question be?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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 the next number in this pattern: 3, 7, 19, 55 ...
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
What is happening at each box in these machines?
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?
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?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the information to work out how many gifts there are in each pile.
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 task combines spatial awareness with addition and multiplication.
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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!
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?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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!
Number problems at primary level that require careful consideration.
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
How would you count the number of fingers in these pictures?
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?