Odd Numbers
(KS2, Year 6)

The Lesson

An odd number is a whole number that cannot be divided exactly by 2.

Dictionary Definition

The Oxford English Dictionary defines an even number as a number "having one left over as remainder when divided by two. Opposed to even."

Examples of Odd Numbers

Some examples of odd numbers are given below:

Odd Numbers on a Number Line

The image below shows the odd numbers on the number line.

How to Check if a Number Is an Odd Number

A number is odd if it cannot be divided exactly by 2. If it is divided by 2, the answer will not be a whole number. There will be a remainder of 1.

Question

Is 25 an odd number?

Step-by-Step:

1

Divide the number by 2.
25 ÷ 2 = 12.5 = 12 r 1

2

Check if the answer from Step 1 is a whole number. If it is not, and there is a remainder of 1, the original number is odd. Else it is even. In our example, 12.5 is not a whole number.

Answer:

25 is an odd number.

A Formula to Generate Odd Numbers

The formula below generates odd numbers:

If k takes a whole number (1, 2, 3...), then n will always be odd.
k = 0 ∴ n = 2k + 1 = 2 × 0 + 1 = 1 k = 1 ∴ n = 2k + 1 = 2 × 1 + 1 = 3 k = 2 ∴ n = 2k + 1 = 2 × 2 + 1 = 5 k = 3 ∴ n = 2k + 1 = 2 × 3 + 1 = 7 k = 4 ∴ n = 2k + 1 = 2 × 4 + 1 = 9

Interactive Game on Odd Numbers

Here is an interactive game to help you learn about odd numbers.

Lesson Slides

The slider below shows a real example of odd numbers. Open the slider in a new tab

Top Tip

A Quick Way to See If a Number Is Odd

A number is odd if its last digit is 1, 3, 5, 7 or 9.
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See Also

What is an even number What is a number line? Play our "bubble pop" game on even numbers. Play our "bubble pop" game on odd numbers. Play our "whack-a-mole" game on odd numbers. Play our "bubble pop" game on prime numbers. Play our "bubble pop" game on composite numbers. Play our "bubble pop" game on square numbers. Arithmetic with even and odd numbers