What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Benâ€™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?
56 406 is the product of two consecutive numbers. What are these
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?
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?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Visitors to Earth from the distant planet of Zub-Zorna were amazed
when they found out that when the digits in this multiplication
were reversed, the answer was the same! Find a way to explain. . . .
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
Resources to support understanding of multiplication and division through playing with number.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Number problems at primary level that may require determination.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Where will the point stop after it has turned through 30 000
degrees? I took out my calculator and typed 30 000 ÷ 360. How
did this help?
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.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
This problem is designed to help children to learn, and to use, the two and three times tables.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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 sum of all the three digit whole numbers?
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?
Find the highest power of 11 that will divide into 1000! exactly.
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
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?
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.
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?