In Module 2, Topic C, students problem-solve with rational numbers and draw upon their work from Grade 6 with expressions and equations (6.EE.A.2, 6.EE.A.3, 6.EE.A.4, 6.EE.B.5, 6.EE.B.6, 6.EE.B.7). They perform operations with rational numbers (7.NS.A.3), incorporating them into algebraic expressions and equations. They represent and evaluate expressions in multiple forms, demonstrating how quantities are related (7.EE.A.2). The Integer Game is revisited as students discover “if-then” statements, relating changes in player’s hands (who have the same card-value totals) to changes in both sides of a number sentence. Students translate word problems into algebraic equations and become proficient at solving equations of the form px + q = r and p(x + q) = r, where p, q, and r, are specific rational numbers (7.EE.B.4a). As they become fluent in generating algebraic solutions, students identify the operations, inverse operations, and order of steps, comparing these to an arithmetic solution. The use of algebra to represent contextual problems continues in Module 3.
In Module 3, Topic B, students use linear equations and inequalities to solve problems. They continue to use bar diagrams from earlier grades where they see fit but will quickly discover that some problems would more reasonably be solved algebraically (as in the case of large numbers). Guiding students to arrive at this realization on their own develops the need for algebra. This algebraic approach builds upon work in Grade 6 with equations (6.EE.B.6, 6.EE.B.7) to now include multi-step equations and inequalities containing rational numbers (7.EE.B.3, 7.EE.B.4). Students solve problems involving consecutive numbers, total cost, age comparisons, distance/rate/time, area and perimeter, and missing angle measures. Solving equations with a variable is all about numbers, and students are challenged with the goal of finding the number that makes the equation true. When given in context, students recognize that a value exists, and it is simply their job to discover what that value is. Even the angles in each diagram have a precise value, which can be checked with a protractor to ensure students that the value they find does indeed create a true number sentence.