Getting Started 
Misconception/Error The student does not understand how to solve linear equations. 
Examples of Student Work at this Level The student:
 Misinterprets algebraic expressions.
 Does not apply properties of equality correctly.
 Does not isolate the variable.

Questions Eliciting Thinking When you solve an equation, what are you trying to find?
Do you know what the properties of equality are and how to use them?
How do you begin the process of solving an equation? 
Instructional Implications Review what it means for a number to be a solution of an equation. Give an example of an equation and provide a set of numbers, some of which are not solutions. Demonstrate how to use substitution to test numbers to determine whether or not they are solutions. Ask the student to check the solution found for the equation on the worksheet to determine if it is actually a solution of the given equation.
Review the order of operations conventions, the Distributive Property, and the properties of equality. Explain how these properties can be used to solve equations of the form x + p = q and px = q (6.EE.2.7) and equations of the form px + q = r and p(x + q) = r (7.EE.2.4) with positive integer coefficients. Consider modelling the equation solving process using algebra tiles. Challenge the student to solve equations first with algebra tiles then on paper. Require the student to show all work completely and justify each step. Once the student is comfortable solving equations with integer coefficients, transition the student to equations with integer and rational coefficients. Provide additional opportunities to solve linear equations with rational coefficients.
If needed, provide additional instruction on operations with rational numbers. Consider implementing the MFAS tasks Rational Addition and Subtraction (7.NS.1.1) or Applying Rational Number Properties (7.NS.1.2) to provide additional review for students struggling with rational number operations. 
Moving Forward 
Misconception/Error The student is unable to correctly compute with rational numbers. 
Examples of Student Work at this Level The student correctly applies properties of equality but is unable to correctly calculate with rational numbers.

Questions Eliciting Thinking What is × 3? Is 3 equal to one?
Can you show me how you divided 3.5 by ? 
Instructional Implications Review operations with rational numbers and provide frequent opportunities to add, subtract, multiply, and divide rational numbers in a variety of forms. Consider implementing the MFAS tasks Rational Addition and Subtraction (7.NS.1.1) or Applying Rational Number Properties (7.NS.1.2) to provide additional review for students struggling with rational number operations.
Explain that dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction. Using the equation in this task, demonstrate how this idea can be used in the equation solving process. Suggest using two steps to multiply both sides of x = by (e.g., by first multiplying both sides of the equation by three; then dividing each side of the equation by two). As an alternative, guide the student to rewrite each fraction in the equation with a common denominator and then to multiply both sides of the equation by the common denominator. Allow the student to use the approach that makes most sense to him or her.
Remind the student to use substitution to check solutions in the original equation. Provide additional opportunities to solve linear equations with rational coefficients. 
Almost There 
Misconception/Error The student makes a minor computational error. 
Examples of Student Work at this Level The student makes a sign error.

Questions Eliciting Thinking You have a slight error in your solution. Can you find it?
Can you substitute the solution into the original equation in order to check it? 
Instructional Implications Provide direct feedback to the student concerning any minor error made. Allow the student to revise incorrect work. Then ask the student to substitute the solution into the original equation to determine if it makes the equation true. Provide additional opportunities to solve linear equations with rational coefficients and remind the student to check solutions. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly solves the equation clearly showing each step of work. The solution of the equation is given as , 5.25, or .

Questions Eliciting Thinking Can you name the algebraic properties that justify each step of your equation solving process?
Is there a way that you can check to see if your answer is correct? 
Instructional Implications Challenge the student with more difficult equations to solve. Provide equations that include coefficients in a variety of forms and require use of the Distributive Property to both factor and combine like terms.
Consider implementing the MFAS tasks Linear Equations  2 and Linear Equations  3 (8.EE.3.7). 