56 406 is the product of two consecutive numbers. What are these two numbers?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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 activity focuses on doubling multiples of five.
Use the information to work out how many gifts there are in each pile.
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.
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?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
Here is a chance to play a version of the classic Countdown Game.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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.
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
Are these statements always true, sometimes true or never true?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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!
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?
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.
This task combines spatial awareness with addition and multiplication.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
What is happening at each box in these machines?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
This number has 903 digits. What is the sum of all 903 digits?
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?