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?
How many six digit numbers are there which DO NOT contain a 5?
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?
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. . . .
There are six numbers written in five different scripts. Can you sort out which is which?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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 is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Replace each letter with a digit to make this addition correct.
Number problems at primary level that may require determination.
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 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?
Can you work out some different ways to balance this equation?
Follow the clues to find the mystery number.
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?
Number problems at primary level to work on with others.
Number problems at primary level that require careful consideration.
Who said that adding couldn't be fun?
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?
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.
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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" .
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Have a go at balancing this equation. Can you find different ways of doing it?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
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
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?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
Four strategy dice games to consolidate pupils' understanding of rounding.
Find the sum of all three-digit numbers each of whose digits is
What is the sum of all the digits in all the integers from one to
What happens when you round these numbers to the nearest whole number?
32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50
x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if
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.
Can you substitute numbers for the letters in these sums?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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
What happens when you round these three-digit numbers to the nearest 100?