Integers include all positive whole numbers, their negative counterparts, and zero. Understanding integers is essential for representing real-world quantities like temperature, elevation, debt, and direction.

The number line is the key tool for understanding integers. Positive numbers extend to the right, negative numbers to the left, and zero sits in the middle. This visual model helps students see that -3 is less than -1, even though 3 is greater than 1.

Adding and subtracting integers follows logical rules. Adding a positive moves right on the number line; adding a negative moves left. Subtracting a negative is the same as adding a positive. These rules make sense when connected to real-world contexts like gaining and losing money.

Multiplying and dividing integers follows the sign rules: positive × positive = positive, negative × negative = positive, and positive × negative = negative. These rules extend to division as well. Understanding why these rules work deepens mathematical reasoning.