Getting Started 
Misconception/Error The student is unable to correctly solve the equation and provides no explanation or justification. 
Examples of Student Work at this Level The student makes an algebraic or computational error when solving the equation and provides no explanation or justification. The student:
 Multiplies only one side of the equation by four.
 Does not correctly subtract three from .

Questions Eliciting Thinking What are the properties of equality? How can they be used to solve equations?
What are you being asked to find? What does it mean to solve an equation? What is the goal in solving an equation?
Will you explain how you tried to solve the equation? 
Instructional Implications Review the properties of equality and the properties of operations. Explain the reasoning process used in solving linear equations and that each step follows from the equality asserted in the previous step. Emphasize that appropriate application of the properties of equality enables one to rewrite an equation in an equivalent form. Provide the student with the steps of the solution of an equation and ask the student to justify each step using properties of equality and operations.
If needed, review the application of the properties of equality and the properties of operations to the process of solving an equation. Provide a variety of equations for the student to solve. Begin with simple onestep equations, then twostep equations and finally, equations with rational expressions. Ask the student to justify each step of the process of solving and provide feedback as needed.
Consider using the MFAS tasks Justify the Process 1 (AREI.1.1) and Justify the Process 2 (AREI.1.1) if not used previously. 
Moving Forward 
Misconception/Error The student correctly uses algebraic properties to solve the equation but cannot fully explain nor justify the steps. 
Examples of Student Work at this Level The student correctly solves the equation but:
 Does not fully explain and justify the steps.
 Explains the solving process but does not justify the steps.

Questions Eliciting Thinking What does explain mean? What does justify mean?
How did you get 5x + 3 = 28? What did you do? What property allows you to do that? 
Instructional Implications Review the properties of equality and the properties of operations. Explain the reasoning process used in solving linear equations and that each step follows from the equality asserted in the previous step. Emphasize that appropriate application of the properties of equality enables one to rewrite an equation in an equivalent form. Provide the student with the steps of the solution of an equation and ask the student to justify each step using properties of equality and operations.
Consider using the MFAS tasks Justify the Process 1 (AREI.1.1) and Justify the Process 2 (AREI.1.1) if not used previously. 
Almost There 
Misconception/Error The student correctly solves the equation and justifies the solution process, but is unable to communicate confidence as following from mathematical reasoning. 
Examples of Student Work at this Level The student solves, explains, and justifies as follows:
The student writes that he or she is confident in the solution because the equation was easy to solve or because, â€śI know I solved it right.â€ť 
Questions Eliciting Thinking Can you give a mathematical reason for your confidence?
How do you know that each step of your solution process follows from the previous step? 
Instructional Implications Explain to the student that he or she correctly applied the properties of equality to rewrite the given equation in the form x = 5. It is the use of these properties and their correct application that should be the source of confidence. In addition, ask the student to verify that x = 5 satisfies the original equation. Explain that if it does, then the two equations, Â = 7 and x = 5, are equivalent which means that five must be a solution.
Consider using the MFAS tasks Justify the Process 1 (AREI.1.1) and Justify the Process 2 (AREI.1.1) if not used previously. 
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 solves, explains, and justifies as follows:
The student writes that he or she is very confident in his or her answer because:
 â€śI know that I correctly used the properties of equality in each step.â€ť
 â€śI know my solution is correct because I substituted five for x in the original equation and five made the resulting equation true.â€ťÂ

Questions Eliciting Thinking Another student used cross multiplication in the first step? How might you justify cross multiplying?
Is five the only solution of this equation? Could there be another solution? 
Instructional Implications Provide the student with the equation Â =Â . Assuming that this equation is true, ask the student to justify why it follows that ad = bc. 