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?
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?
Who said that adding couldn't be fun?
Number problems at primary level to work on with others.
Find the sum of all three-digit numbers each of whose digits is
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?
Follow the clues to find the mystery 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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you substitute numbers for the letters in these sums?
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 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?
What is the sum of all the digits in all the integers from one to
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
How many six digit numbers are there which DO NOT contain a 5?
Number problems at primary level that may require determination.
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.
Number problems at primary level that require careful consideration.
Can you work out some different ways to balance this equation?
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.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This activity involves rounding four-digit numbers to the nearest thousand.
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" .
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?
Have a go at balancing this equation. Can you find different ways of doing it?
There are six numbers written in five different scripts. Can you sort out which is which?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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 for inquiring primary learners.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
What happens when you round these numbers to the nearest whole number?
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
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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?
Replace each letter with a digit to make this addition correct.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.