To begin Module 3, students will generate equivalent expressions using the fact that addition and multiplication can be done in any order with any grouping and will extend this understanding to subtraction (adding the inverse) and division (multiplying by the multiplicative inverse) (7.EE.A.1). They extend the properties of operations with numbers (learned in earlier grades) and recognize how the same properties hold true for letters that represent numbers. Knowledge of rational number operations from Module 2 is demonstrated as students collect like terms containing both positive and negative integers.
An area model is used as a tool for students to rewrite products as sums and sums as products and can provide a visual representation leading students to recognize the repeated use of the distributive property in factoring and expanding linear expressions (7.EE.A.1). Students examine situations where more than one form of an expression may be used to represent the same context, and they see how looking at each form can bring a new perspective (and thus deeper understanding) to the problem. Students recognize and use the identity properties and the existence of inverses to efficiently write equivalent expressions in standard form (2x + (-2x) + 3 = 0 + 3 = 3)(7.EE.A.2). By the end of the topic, students have the opportunity to practice Module 2 work on operations with rational numbers (7.NS.A.1, 7.NS.A.2) as they collect like terms with rational number coefficients (7.EE.A.1).
