Replace each letter with a digit to make this addition correct.
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
Find the sum of all three-digit numbers each of whose digits is
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
There are six numbers written in five different scripts. Can you sort out which is which?
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 is the sum of all the digits in all the integers from one to
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Using balancing scales what is the least number of weights needed
to weigh all integer masses from 1 to 1000? Placing some of the
weights in the same pan as the object how many are needed?
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 numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. 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?
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?
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?
Who said that adding couldn't be fun?
Number problems at primary level that may require determination.
Number problems for inquiring primary learners.
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 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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many six digit numbers are there which DO NOT contain a 5?
Can you substitute numbers for the letters in these sums?
How many solutions can you find to this sum? Each of the different letters stands for a different 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
Carry out cyclic permutations of nine digit numbers containing the
digits from 1 to 9 (until you get back to the first number). Prove
that whatever number you choose, they will add to the same total.
Can you create a Latin Square from multiples of a six digit number?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
There are nasty versions of this dice game but we'll start with the nice ones...
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.
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
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
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Have a go at balancing this equation. Can you find different ways of doing it?
Four strategy dice games to consolidate pupils' understanding of rounding.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?