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?
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you work out what a ziffle is on the planet Zargon?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
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.
Number problems at primary level that may require determination.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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.
Are these statements always true, sometimes true or never true?
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?
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?
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?
This task combines spatial awareness with addition and multiplication.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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!
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!
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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
Use the information to work out how many gifts there are in each pile.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?