This course begins with a discussion of the relationship between positive and negative numbers, and the concept of an opposite.  Examples of positive and negative numbers in the real world are explored.  The set of integers is then defined as the set of whole numbers,  , and their opposites.  This leads to a discussion of the relationship between the number line and the set of integers, including the meaning of addition and subtraction in terms of the number line.

The addition and subtraction of integers is then performed, away from the number line, and rules for adding and subtracting two integers are discussed.  The multiplication and division of two integers is also studied.  Rules for multiplying or dividing integers are then developed.  The concept of positive and negative is revisited in terms of the rules for operations on integers.  It is emphasized that while multiplying or dividing two negative integers gives a positive integer, this is not true for addition and subtraction.  A variety of examples are given to justify this conclusion.

The end of this unit begins a theme that is studied throughout the course, namely the concepts of variable and unknown.  Variables are used to write expressions, and when values are assigned to those variables, the expressions can be evaluated.  The meaning of variable in this context is emphasized, namely that these expressions can be evaluated for a variety of numbers (at this level, usually any number) and thus can vary when different numbers are used.  On the other hand, an equation is a statement where one or both sides may have an unknown number, and when a number is used for the unknown, the truth of the statement is evaluated.  The process of solving an equation is introduced as the process of finding numbers (there may be more than one) that make the equation a true statement.  Throughout this discussion the difference between variable and unknown is emphasized, namely that an unknown is a particular value that makes an equation true, while a variable can be a choice of values that make an equation true, or a choice of values that are used to evaluate an expression.