In this section, students work with linear expressions and justify whether they are equivalent. Having learned to perform arithmetic with rational numbers, students are now prepared to examine more complex expressions.

First, students see that rewriting subtraction as adding the opposite makes it possible to apply properties of addition, such as the associative or commutative property, to generate equivalent expressions....

In this section, students investigate situations that can be represented by tape diagrams and equations in the form and .

Students begin by recognizing that new structures are needed to represent situations that are not proportional (not in the form ). They then examine correspondences between descriptions of such situations and the tape diagrams that represent them. This examination is...

In this section, students solve inequalities of the forms and including any of the four inequality symbols, , , , or . First, students consider inequalities of the form or and determine which values make the inequality true. Next, they compare equations and inequalities that represent the same situation. They see that solving the related equation gives the boundary point...

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.

In this section, students build fluency with solving equations of the forms and . They begin by using balanced hanger diagrams to represent equations. They see that doing the same operation on each side keeps the hanger balanced and keeps the equation true. For example, an efficient process for solving an equation of the form involves subtracting from each side,...