I can tell whether two expressions are equivalent and explain why or why not.

I know and can identify the moves that can be made to transform an equation into an equivalent one.

I understand what it means for two equations to be equivalent, and how equivalent equations can be used to describe the same situation in different ways.

I can explain why some algebraic moves create equivalent equations but some do not.

I know how equivalent equations are related to the steps of solving equations.

I know what it means for an equation to have no solutions and can recognize such an equation.

Given an equation, I can solve for a particular variable (like height, time, or length) when the equation would be more useful in that form.

I know the meaning of the phrase “to solve for a variable.”

I can write an equation to describe a situation that involves multiple quantities whose values are not known, and then solve the equation for a particular variable.

I know how solving for a variable can be used to quickly calculate the values of that variable.

I can describe the connections between an equation of the form $ax+by=c$, the features of its graph, and the rate of change in the situation.

I can graph a linear equation of the form $ax+by=c$.

I understand that rewriting the equation for a line in different forms can make it easier to find certain kinds of information about the relationship and about the graph.

I can find the slope and vertical intercept of a line with equation $ax+by=c$.

I can take an equation of the form $ax+by=c$ and rearrange it into the equivalent form $y=mx+b$.

I can use a variety of strategies to find the slope and vertical intercept of the graph of a linear equation given in different forms.

I can explain the meaning of the term “constraints.”

I can tell which quantities in a situation can vary and which ones cannot.

I can use letters and numbers to write expressions representing the quantities in a situation.

I can tell which quantities in a situation can vary and which ones cannot.

I can use letters and numbers to write equations representing the relationships in a situation.

I can use words and equations to describe the patterns I see in a table of values or in a set of calculations.

When given a description of a situation, I can use representations like diagrams and tables to help make sense of the situation and write equations for it.

I can explain what it means for a value or pair of values to be a solution to an equation.

I can find solutions to equations by reasoning about a situation or by using algebra.

I can use graphing technology to graph linear equations and identify solutions to the equations.

I understand how the coordinates of the points on the graph of a linear equation are related to the equation.

When given the graph of a linear equation, I can explain the meaning of the points on the graph in terms of the situation it represents.

I can explain what we mean by “the solution to a system of linear equations” and can explain how the solution is represented graphically.

I can explain what we mean when we refer to two equations as a system of equations.

I can use tables and graphs to solve systems of equations.

I can solve systems of equations by substituting a variable or an expression.

I know more than one way to perform substitution and can decide which way or what to substitute based on how the given equations are written.

I can solve systems of equations by adding or subtracting them to eliminate a variable.

I know that adding or subtracting equations in a system creates a new equation, where one of the solutions to this equation is the solution to the system.

I can explain why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution.

I can solve systems of equations by multiplying each side of one or both equations by a factor, then adding or subtracting the equations to eliminate a variable.

I understand that multiplying each side of an equation by a factor creates an equivalent equation whose graph and solutions are the same as that of the original equation.

I can tell how many solutions a system has by graphing the equations or by analyzing the parts of the equations and considering how they affect the features of the graphs.

I know the possibilities for the number of solutions a system of equations could have.

I can get more information about a problem in order to write and solve a system of linear equations.

I can solve linear equations algebraically.

I can write linear equations to create a pattern.