Section	Teacher-facing learning goals
Puzzle Problems	Lesson 1 Calculate a missing value for a number puzzle that can be represented by a linear equation in one variable, and explain (orally and in writing) the solution method. Create a number puzzle that can be represented by a linear equation in one variable.
Linear Equations in One Variable	Lesson 2 Calculate the weight of an unknown object using a hanger diagram, and explain (orally) the solution method. Comprehend that adding and removing equal items from each side of a hanger diagram or multiplying and dividing items on each side of the hanger by the same amount are moves that keep the hanger balanced. Lesson 3 Compare and contrast (orally and in writing) solution paths to solve an equation in one variable by performing the same operation on each side. Correlate (orally and in writing) changes on hanger diagrams with moves that create equivalent equations. Lesson 4 Calculate a value that is a solution for a linear equation in one variable, and compare and contrast (orally) solution strategies with others. Critique (in writing) the reasoning of others in solving a linear equation in one variable. Lesson 5 Calculate a value that is a solution to a linear equation in one variable, and explain (orally) the steps used to solve. Create an expression to represent a number puzzle, and justify (orally) that it is equivalent to another expression. Justify (orally) that each step used in solving a linear equation maintains equality. Lesson 6 Categorize (orally and in writing) linear equations in one variable based on their structure, and solve equations from each category. Describe (orally and in writing) features of linear equations that have one solution, no solution, or many solutions. Describe (orally) strategies for solving linear equations in one variable with different features or structures. Lesson 7 Compare and contrast (orally and in writing) equations that have no solutions or infinitely many solutions. Create linear equations in one variable that have either no solutions or infinitely many solutions, using structure, and explain (orally) the solution method. Lesson 8 Describe (orally) a linear equation as having “one solution”, “no solutions”, or “an infinite number of solutions”, and solve equations in one variable with one solution. Describe (orally) features of linear equations with one solution, no solution, or an infinite number of solutions. Lesson 9 Create an equation in one variable to represent a situation in which two conditions are equal. Interpret the solution of an equation in one variable in context.
Systems of Linear Equations	Lesson 10 Determine (in writing) a point that satisfies two relationships simultaneously, using tables or graphs. Interpret (orally and in writing) points that lie on one, both, or neither line on a graph of two simultaneous equations in context. Lesson 11 Create a graph that represents two linear relationships in context, and interpret (orally and in writing) the point of intersection. Interpret a graph of two equivalent lines in context. Lesson 12 Comprehend that solving a system of equations means finding values of the variables that makes both equations true at the same time. Coordinate (orally and in writing) graphs of parallel lines and a system of equations that has no solutions. Create a graph of two lines that represents a system of equations in context. Lesson 13 Coordinate (orally) the solution of an equation with variables on each side to the solution of a system of two linear equations. Create a graph of a system of equations, and identify (orally and in writing) the number of solutions of the system of equations. Lesson 14 Calculate values that are a solution for a system of equations, and explain (orally) the solution method. Generalize (orally) a process for solving systems of equations using substitution. Justify (orally and in writing) that a particular system of equations has no solutions using the structure of the equations. Lesson 15 Categorize (in writing) systems of equations, including systems with infinitely many or no solutions, and calculate the solution for a system using a variety of strategies. Create a system of equations that represents a situation and interpret (orally and in writing) the solution in context.
Let's put it to work	Lesson 16 Calculate the solution to a system of equations in context, and present (using words and other representations) the solution method. Create a system of equations to solve a problem in context. Critique (orally) peer solutions to a system of equations.

8.4 Linear Equations and Linear Systems