Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you replace the letters with numbers? Is there only one solution in each case?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
56 406 is the product of two consecutive numbers. What are these two numbers?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Here is a picnic that Chris and Michael are going to share equally. Can you tell us what each of them will have?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
Use the information to work out how many gifts there are in each pile.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Can you work out what a ziffle is on the planet Zargon?
This problem is designed to help children to learn, and to use, the two and three times tables.
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
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?
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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!
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
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 game that tests your understanding of remainders.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?