This problem is designed to help children to learn, and to use, the two and three times tables.
56 406 is the product of two consecutive numbers. What are these two numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Number problems at primary level that may require determination.
What is the sum of all the three digit whole numbers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Resources to support understanding of multiplication and division through playing with number.
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?
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?
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.
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?
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'.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
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.
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?
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?
On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?
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?
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?
If the answer's 2010, what could the question be?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
This number has 903 digits. What is the sum of all 903 digits?
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?
What is happening at each box in these machines?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Number problems at primary level that require careful consideration.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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.