Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
Can you work out what a ziffle is on the planet Zargon?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
56 406 is the product of two consecutive numbers. What are these two numbers?
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.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This problem is designed to help children to learn, and to use, the two and three times tables.
What is the sum of all the three digit whole numbers?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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.
Resources to support understanding of multiplication and division through playing with number.
Number problems at primary level that may require determination.
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?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Number problems at primary level that require careful consideration.
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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 the information to work out how many gifts there are in each pile.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
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?
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?