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" .
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
There are six numbers written in five different scripts. Can you sort out which is which?
Can you replace the letters with numbers? Is there only one solution in each case?
What is the sum of all the digits in all the integers from one to
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?
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?
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 may require determination.
Can you work out some different ways to balance this equation?
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?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Explore the relationship between simple linear functions and their
Number problems at primary level to work on with others.
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?
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?
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?
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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
How many six digit numbers are there which DO NOT contain a 5?
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.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Number problems for inquiring primary learners.
Who said that adding couldn't be fun?
There are nasty versions of this dice game but we'll start with the nice ones...
This activity involves rounding four-digit numbers to the nearest thousand.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Follow the clues to find the mystery number.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
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?
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
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?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
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?
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.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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. . . .