Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
Can you work out what a ziffle is on the planet Zargon?
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.
What is the sum of all the three digit whole numbers?
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
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 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.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Number problems at primary level that require careful consideration.
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.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Number problems at primary level that may require determination.
This number has 903 digits. What is the sum of all 903 digits?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Use the information to work out how many gifts there are in each
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
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?
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.
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?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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.