A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
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
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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?
Number problems at primary level that may require determination.
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?
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
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?
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.
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?
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" .
Number problems at primary level to work on with others.
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.
What is the sum of all the digits in all the integers from one to
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
This activity involves rounding four-digit numbers to the nearest thousand.
Find the sum of all three-digit numbers each of whose digits is
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 work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What happens when you round these three-digit numbers to the nearest 100?
Four strategy dice games to consolidate pupils' understanding of rounding.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Explore the relationship between simple linear functions and their
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?
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. . . .
Number problems at primary level that require careful consideration.
Who said that adding couldn't be fun?
Can you replace the letters with numbers? Is there only one
solution in each case?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
There are six numbers written in five different scripts. Can you sort out which is which?
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?
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. . . .
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
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
Carry out cyclic permutations of nine digit numbers containing the
digits from 1 to 9 (until you get back to the first number). Prove
that whatever number you choose, they will add to the same total.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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?