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" .
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
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?
Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
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.
Think of any three-digit number. Repeat the digits. The 6-digit
number that you end up with is divisible by 91. Is this a
What is the sum of all the digits in all the integers from one to
Number problems at primary level that may require determination.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Number problems at primary level to work on with others.
Explore the relationship between simple linear functions and their
There are six numbers written in five different scripts. Can you sort out which is which?
Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. . . .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
How many six digit numbers are there which DO NOT contain a 5?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Follow the clues to find the mystery number.
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
Number problems at primary level that require careful consideration.
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
Number problems for inquiring primary learners.
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Can you replace the letters with numbers? Is there only one
solution in each case?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Who said that adding couldn't be fun?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
There are two forms of counting on Vuvv - Zios count in base 3 and
Zepts count in base 7. One day four of these creatures, two Zios
and two Zepts, sat on the summit of a hill to count the legs of. . . .
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?
Four strategy dice games to consolidate pupils' understanding of rounding.
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Find the values of the nine letters in the sum: FOOT + BALL = GAME
What happens when you round these three-digit numbers to the nearest 100?