Getting Started 
Misconception/Error The student is not able to correctly use algebraic properties to solve the equation. 
Examples of Student Work at this Level The student does not understand how to solve the equation. Errors may include:
 Attempting to apply algebraic properties but not following order of operations.
 Failing to distribute completely and then dividing each side of the equation by different values.

Questions Eliciting Thinking How could you use the Distributive Property in this part of the equation?
What does it means to combine like terms?
What are the properties of equality? How can you use them to solve equations?
What are you being asked to find? What does it mean to solve an equation? 
Instructional Implications Be sure the student understands what it means to solve an equation. Review the order of operations conventions, the Distributive Property, and combining like terms.Â Provide opportunities to apply properties of operations to rewrite expressions in equivalent forms.Â Provide instruction on solving equations using the Addition, Subtraction, Multiplication and Division Properties of Equality. Begin with onestep equations before introducing more complex equations. Model for the student the order the properties should be used to solve multistep equations.Â
Model 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 and justify each step. 
Moving Forward 
Misconception/Error The student applies some algebraic properties correctly but makes errors working with algebraic expressions. 
Examples of Student Work at this Level The student shows evidence of some understanding of how to apply the Distributive Property, properties of equality, and combining like terms but:
 Fails to distribute the negative appropriately through the parenthesis.
 Adds or subtracts a quantity twice from the same side of the equation.
 Makes sign errors when combining like terms.

Questions Eliciting Thinking What value is being distributed here?
What like terms do you see on the right side of the equation? How will you combine them?
When you added 4x to 4x on one side of the equation, what else should you have done to compensate for this? 
Instructional Implications Provide instruction and practice on using the Distributive Property with expressions that include negative integers. Have the student rewrite expressions such as 4xÂ  5(xÂ  2) as 4x + (â€“5)[x + ( â€“2)] until he or she is comfortable omitting this step. If necessary, review the order of operations conventions.
Review the reasoning that is used in solving equations. Ask the student to justify each step in the solution process by citing a specific algebraic property [e.g. transforming the equation x â€“ 5 = 8 to (x â€“ 5) + 5 = 8 + 5 is justified by the Addition Property of Equality]. Begin with simple, onestep equations requiring justification to ensure the student is proficient before moving on to more complicated equations.
Remind the student to show work neatly and completely to avoid sign errors. Sign errors are typical and can be reduced by focusing on precision and attention to detail. 
Almost There 
Misconception/Error The student uses algebraic properties to solve the equation correctly but makes a minor error. 
Examples of Student Work at this Level The student makes a minor error (e.g., failing to add two like terms), but all other work is complete and correct.
The student fails to distribute the negative but solves everything else correctly.

Questions Eliciting Thinking What value are you distributing here? When you multiply 5 by 2, what do you get?
You have a slight error in your solution. Can you find it? 
Instructional Implications Encourage the student to combine like terms on each side of the equation before applying properties of equality. This will minimize the number of terms in the equation and reduce opportunities to make errors.
Review the studentâ€™s error with him or her and provide feedback. Provide additional equations to solve and pair the student with another Almost There student to compare solution methods and reconcile any differences.
Provide the student with a completed problem that contains errors. Have the student identify and correct the errors.
Create a small group activity by putting students in groups of two or three and providing a different color pen for each student. Give the groups the same number of equations as group members. Have the students write each equation on a separate piece of paper. Have each student start the solving process with just one step of work and a justification in his or her pen color. Then have the students pass papers to complete the next step of the solution providing a justification. As the activity progresses, each student should be looking back at the prior steps of the solution process for each equation received to ensure they are correct and justified. 
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 work shows all steps in solving the equations accurately and correctly.

Questions Eliciting Thinking How did you find the value of x? Explain the steps you used.
How could you check to see if your answer is correct? 
Instructional Implications Challenge the student with more difficult equations and inequalities to solve.
Consider implementing MFAS tasks Solving a Literal Linear Equation (AREI.2.3), Solving a Multistep Inequality (AREI.2.3), and Solve for N (AREI.2.3). 