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" .
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?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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.
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?
How many six digit numbers are there which DO NOT contain a 5?
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
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. . . .
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Replace each letter with a digit to make this addition correct.
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?
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?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Can you work out some different ways to balance this equation?
Number problems at primary level that may require determination.
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
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.
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)?
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. . . .
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Find the sum of all three-digit numbers each of whose digits is
Can you create a Latin Square from multiples of a six digit number?
There are six numbers written in five different scripts. Can you sort out which is which?
Explore the relationship between simple linear functions and their
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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 replace the letters with numbers? Is there only one
solution in each case?
This article, written for teachers, looks at the different kinds of
recordings encountered in Primary Mathematics lessons and the
importance of not jumping to conclusions!
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
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
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole 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?
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?
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. . . .
The number 3723(in base 10) is written as 123 in another base. What
is that base?
What happens when you round these three-digit numbers to the nearest 100?
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Follow the clues to find the mystery number.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?