Odd numbers are integers that cannot be evenly divided by 2. When you divide an odd number by 2, you will always get a remainder of 1. The sequence of odd numbers starts from 1 and goes on infinitely: 1, 3, 5, 7, 9, 11, and so on.

Characteristics of Odd Numbers:

1. Not divisible by 2: An odd number divided by 2 leaves a remainder of 1.
2. Ends in 1, 3, 5, 7, or 9: The last digit of an odd number is always one of these.
3. Alternate with even numbers: If you list the integers in order, odd numbers alternate with even numbers (which are divisible by 2).

Examples of Odd Numbers:

• 1: 1 ÷ 2 = 0 with a remainder of 1.
• 3: 3 ÷ 2 = 1 with a remainder of 1.
• 5: 5 ÷ 2 = 2 with a remainder of 1.
• 7: 7 ÷ 2 = 3 with a remainder of 1.

Visual Representation:

Imagine a set of objects that you want to divide into two equal groups. If the objects can’t be divided equally, you have an odd number of objects. Here’s a visual representation:

Grouping Objects

1. 5 Stars: When you try to group these stars into two equal parts, one star will always be left out, showing that 5 is an odd number.
2. 7 Circles: Similarly, dividing these circles into two equal groups leaves one circle out, indicating that 7 is an odd number.

Counting by Odd Numbers

If you count by odd numbers, you add 2 each time, starting from 1: 1, 3, 5, 7, 9, 11, 13, …

You can see that every time, the numbers are increasing by 2, and none of them can be evenly divided by 2 without a remainder.

Real-Life Examples:

• Counting Apples: If you have 3 apples and you try to divide them equally between two people, one apple will be left over.
• Stair Steps: If a staircase has 11 steps, you can’t divide it into two equal halves without having an extra step.

Understanding odd numbers is fundamental in arithmetic and helps build a foundation for more complex mathematical concepts.