Teaching Students About Whole Numbers

What is a Whole Number?

A whole number is a positive number that does not contain a fractional or decimal part. This means that, for example, the numbers 0, 1, 2, 3, 4, 5, 6, and 7 are whole numbers.

Numbers such as -3, 2.7, or 3 ½ are not whole numbers.

How can I tell if a number is a whole number?

There are 3 main factors to take into account when working out whether or not a number is a whole number:

  1. A whole number has to be positive, not a negative number, also known as a minus number. This means it has to be of a value of 0 or higher. For example, 0, 1, 2, and 3 are all whole numbers. However, -1, -2, and -3 are not.
  2. A whole number cannot include any fractional element. That means that numbers 1 ½, 3 ¼, and 7 ⅚ are not whole numbers, but 1, 3, and 7 are.
  3. A whole number cannot include any decimal element. This means that numbers such as 3.4, 7.9, and 11.234 are not whole numbers, but 3, 7, and 11 are.

As long as a number meets these criteria, a whole number can be any number from 0 to however high you (or anyone else) can count!

What are counting numbers?

Counting numbers are whole numbers that are used to count things. These could be 1, 2, 3, 4, etc. They’re a type of number you can use to say how much you have counted off something. They are any positive number. However, you cannot have negative counting numbers. This is because you can’t have minus 1 or 2 or any other negative number of something. This also doesn’t include fractions or decimals. So counting numbers can only ever be whole numbers. See if you can count some objects and find out which counting number you get.

Regarding counting numbers, there’s been some debate around whether the number zero is classed as a counting number. While you can’t have a negative amount of something, you can have none. Which would be a zero amount of whatever you’re counting. For this reason, some think zero should be classed as a counting number. However, there is no specific rule declaring that zero isn’t a counting number, but it depends on each person individually. So what do you think about zero? It could be a class discussion to decide if zero is a counting number.

Rounding to the Nearest Whole Number

In year 4, students must learn how to round to the nearest whole number. This means finding the whole number that is most similar in value to a given non-whole number.

Here are some examples:

  • The nearest whole number to 3.2 is 3
  • The nearest whole number to 5.7 is 4
  • The nearest whole number to 2 ¼ is 2
  • The nearest whole number to 8 ⅚ is 9

This can get tricky with numbers such as 2.5 or 4 ½ because they are strictly between two whole numbers. In this case, either of the two nearest whole numbers is acceptable, but rounding up rather than down is generally the best practice.

Visual Aids to Explain Whole Numbers

When explaining the difference between whole numbers and non-whole numbers, visual aids such as counters and shapes can be helpful.

For example, you can show a whole counter representing a whole number and a part of a counter showing non-whole numbers.

You could also do this with money. Try using whole pounds to represent whole numbers and pence to represent decimal values between whole numbers. For example, £3 would represent a whole number, whereas £3.20, for instance, would represent a non-whole number.

A number line can also be a helpful tool.

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