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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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