Section	Teacher-facing learning goals
Writing and Modeling with Equations	Lesson 1 Comprehend the term “constraint” to mean a limitation on the possible or reasonable values a quantity could have. Use variables and the symbols =, <, and > to represent simple constraints in a situation. Write expressions with numbers and letters to represent the quantities in a situation. Lesson 2 Given a description of a situation or an equation, identify quantities that vary and quantities that don’t. Understand that letters can be used to represent both quantities that vary and those that are constant. Write equations with numbers and variables to describe relationships and constraints. Lesson 3 Identify and describe (orally and in writing) patterns in tables of values and in calculations. Use observed patterns to generalize the relationships between quantities and to write equations. Lesson 4 Explain (orally and in writing) the meaning of solutions to equations in one variable and two variables. Find solutions to equations in one variable and in two variables by reasoning about the relationships in context. Interpret solutions to equations in one variable and in two variables. Lesson 5 Comprehend that the graph of a linear equation in two variables represents all pairs of values that are solutions to the equation. Interpret points on a graph of a linear equation to answer questions about the quantities in context. Use graphing technology to graph linear equations and identify solutions to the equations.
Manipulating Equations and Understanding Their Structure	Lesson 6 Comprehend that “equivalent equations” are equations that have exactly the same solutions, and that multiple equivalent equations can represent the same relationship. Determine and explain (orally and in writing) whether two equations are equivalent. Identify operations that can be performed on an equation to create equivalent equations. Lesson 7 Explain (orally and in writing) why performing certain operations on an equation may create equivalent equations but performing other operations may not. Understand that dividing by a variable is not used in solving equations because it can lead to equations that have fewer solutions than the original equation. Understand that equations that are not true for any value of the variable(s) do not have solutions. Lesson 8 Comprehend that “to solve for a variable” is to rearrange an equation to isolate a variable of interest. Rearrange multi-variable equations to highlight a particular quantity. Lesson 9 Practice writing equations in two or more variables and solving for a particular variable. Solve for a variable by performing acceptable operations, including when the values of other quantities in a multi-variable equation are not known. Lesson 10 Analyze how the numbers in an equation \(ax+by=c\) are reflected on its graph and are related to the rate of change in the relationship. Graph linear equations of the form \(ax+by=c\) and interpret points on the graph in context. Understand that different forms of a linear equation can give different insights about the relationship it represents and about the graph. Lesson 11 Determine the slope and vertical intercept of the graphs of linear equations by making use of structure or by rearranging the equations. Given an equation of the form \(ax+by=c\), write an equivalent equation of the form \(y=mx+b\).
Systems of Linear Equations in Two Variables	Lesson 12 Solve systems of linear equations by reasoning with tables and by graphing, and explain (orally and in writing) the solution method. Understand that the solution to a system of equations in two variables is a pair of values that simultaneously make both equations true, and that it is represented by the intersection point of the graphs of the equations. Understand that two (or more) equations that represent the constraints on the same quantities in the same situation form a system. Lesson 13 Recognize that a system can be efficiently solved by substitution if one variable is already isolated or can be easily isolated. Recognize that there are multiple ways to perform substitution to solve a system of equations. Solve systems of linear equations by substituting a variable with a number or an expression, and check solutions by substituting them back into the equations. Lesson 14 Recognize that adding or subtracting equations in a system creates a new equation with a solution that coincides with that of the original system, so the new equation can be used to solve the original system. Solve systems of equations by adding or subtracting the equations strategically to eliminate a variable. Use graphing technology to graph the sums and differences of the equations in a system, and analyze and describe (orally and in writing) the behaviors of the graphs. Lesson 15 Explain (orally and in writing) why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution. Practice solving systems of linear equations by adding or subtracting equations to eliminate a variable. Use a context to make sense of an equation that is the sum of two equations in a system, and to reason about why this equation shares a solution with the system. Lesson 16 Recognize that multiplying an equation by a factor creates an equivalent equation whose graph is the same as that of the original equation. Solve systems of equations by multiplying one or both equations by a factor and then adding or subtracting the equations to eliminate a variable. Understand that solving a system by elimination or by substitution entails creating one or more equivalent systems that would enable us to solve the original one. Lesson 17 Determine whether a system of equations will have 0, 1, or infinitely many solutions by analyzing their structure or by graphing. Recognize that a system of linear equations can have 0, 1, or infinitely many solutions. Use the structure of the equations in a linear system to make sense of the properties of their graphs.
Linear Inequalities in One Variable	Lesson 18 Interpret and write inequalities that represent the constraints in a situation. Lesson 19 Find the solution to a one-variable inequality by reasoning and by solving a related equation and testing values greater than and less than that solution. Graph the solution to an inequality as a ray on a number line and interpret the solution in context. Understand that the solution to an inequality is a range of values that make the inequality true. Lesson 20 Analyze and use the structure in inequalities to determine whether the solution is greater or less than the solution to a related equation. Write and solve inequalities in one variable to represent the constraints in situations and to solve problems.
Linear Inequalities in Two Variables	Lesson 21 Given the graph of a related equation, determine the solution region to an inequality in two variables by testing the points on the line and on either side of the line. Understand that the solutions to a linear inequality in two variables are represented graphically as a half-plane bounded by a line. Lesson 22 Find the solution to a two-variable inequality by graphing a related two-variable equation and determining the correct region for the solution. Interpret, in context, points on the graphs of equations and in the solution region of inequalities in two variables. Write inequalities in two variables to represent the constraints in a situation and identify possible solutions by reasoning. Lesson 23 Identify an inequality, a graph, an ordered pair, and a description that represent the constraints and possible solutions in a situation. Understand that a constraint on two variables can be represented by an inequality, a graph (a half-plane), and a verbal description. Write inequalities in two variables to represent the constraints in a situation and use technology to graph the solution set to answer questions about the situation.
Systems of Linear Inequalities in Two Variables	Lesson 24 Given descriptions and graphs that represent two constraints, identify values that satisfy each constraint and those that satisfy both constraints simultaneously. Understand that the solution set of a system of inequalities in two variables is comprised of any pair of values that make both inequalities true, and that it is represented graphically by the region where the graphs overlap. Write systems of inequalities in two variables, use technology to graph the solutions, and interpret the solutions in context. Lesson 25 Analyze given information about a situation involving multiple constraints and determine what additional information is needed to solve problems. Given a system of inequalities and their graphs, explain (orally and in writing) how to tell if a pair of values is a solution to the system. Practice writing systems of inequalities in two variables and finding the solution sets by reasoning or by graphing. Lesson 26 Define the constraints in a situation and create a mathematical model to represent them. Interpret a mathematical model, presented as inequalities and graphs, that represents a situation.

Alg1.2: Linear Equations, Inequalities and Systems