What is the sum of all the digits in all the integers from one to
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. . . .
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
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?
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Four strategy dice games to consolidate pupils' understanding of rounding.
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 that may require determination.
Number problems at primary level to work on with others.
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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?
Can you create a Latin Square from multiples of a six digit number?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Number problems at primary level that require careful consideration.
A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
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
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?
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.
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?
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?
Follow the clues to find the mystery number.
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
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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 show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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?
Replace each letter with a digit to make this addition correct.
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?
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!
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 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 substitute numbers for the letters in these sums?
Using balancing scales what is the least number of weights needed
to weigh all integer masses from 1 to 1000? Placing some of the
weights in the same pan as the object how many are needed?
Who said that adding couldn't be fun?
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
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. . . .