What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you substitute numbers for the letters in these sums?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Number problems at primary level that require careful consideration.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Number problems at primary level that may require determination.
Number problems at primary level to work on with others.
Find the sum of all three-digit numbers each of whose digits is
Who said that adding couldn't be fun?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
What happens when you round these three-digit numbers to the nearest 100?
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole 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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
There are six numbers written in five different scripts. Can you sort out which is which?
What happens when you round these numbers to the nearest whole 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?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
This activity involves rounding four-digit numbers to the nearest thousand.
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?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
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.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Number problems for inquiring primary learners.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
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 show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
What is the sum of all the digits in all the integers from one to
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
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" .
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
How many solutions can you find to this sum? Each of the different letters stands for a different number.