Module 1: In this module students analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They reason abstractly and quantitatively by choosing and interpreting units in the context of creating equations in two variables to represent relationships between quantities. They master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations. They learn the terminology specific to polynomials and understand that polynomials form a system analogous to the integers.
Unit 1: Introduction to Functions

M1.U1 Lessons: 
In unit 1, students explore the main functions that they will work with in Grade 9: linear, quadratic, and exponential. The goal is to introduce students to these functions by having them make graphs of situations (usually based upon time) in which the functions naturally arise. As they graph, they reason abstractly and quantitatively as they choose and interpret units to solve problems related to the graphs they create. 
M1.U1.L1

Unit 2: The Structure of Expressions

M1.U2 Lessons: 
In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Topic B, students use the structure of expressions to define what it means for two algebraic expressions to be equivalent. In doing so, they discern that the commutative, associative, and distributive properties help link each of the expressions in the collection together, even if the expressions look very different themselves (ASSE.2). They learn the definition of a polynomial expression and build fluency in identifying and generating polynomial expressions as well as adding, subtracting, and multiplying polynomial expressions (AAPR.1). The MidModule Assessment follows Topic B.

M1.U2.L6

Unit 3: Solving Equations and Inequalities (A.CED.3, 4, A.REI.1) 
M1.U3 Lessons: 
Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Topic C, instead of just solving equations, they formalize descriptions of what they learned before (variable, solution sets, etc.) and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear and nonlinear equations (AREI.1, AREI.3, ACED.4). Students take their experience solving systems of linear equations further as they prove the validity of the addition method, learn a formal definition for the graph of an equation and use it to explain the reasoning of solving systems graphically, and graphically represent the solution to systems of linear inequalities (ACED.3, AREI.5, AREI.6, AREI.10, AREI.12).

M1.U3.L10

Unit 4: Creating Equations to Solve Problems (N.CN.1, 2, 7)In Topic D, students are formally introduced to the modeling cycle (see page 61 of the CCLS) through problems that can be solved by creating equations and inequalities in one variable, systems of equations, and graphing (NQ.1, ASSE.1, ACED.1, ACED.2, AREI.3). The EndofModule Assessment follows Topic D.

M1.U4 Lessons:M1.U4.L25
