Students should realize that not all situations can be modeled by positive numbers. Many situations require numbers that indicate the opposite direction of another number, such as distances above and below sea level, moving forward or backward, and depositing and withdrawing money.
Students are in the process of making the transition from arithmetic to algebra.
A good understanding of negative numbers and integers is needed to be successful in algebra. Use a number line to demonstrate the meanings of addition and subtraction. On a number line, negative numbers are to the left and positive numbers to the right. After having done several examples, students should generalize that the sum of two positive integers will be positive and that the sum of two negative integers will be negative. It will probably be more difficult for them to guess the sum when adding two numbers opposite in sign.