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 Do you know what the properties of equality are and how to use them?
When you solve an equation, what are you trying to find?
How do you begin the process of solving an equation?
It looks like you were trying to use the Distributive Property in the first step. Can you start over and show me this step again? 
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.
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 = qÂ and equations of the form px + q = r and p(x + q) = rÂ 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 SubtractionÂ or Applying Rational Number PropertiesÂ to provide additional review for students struggling with rational number operations. 
Moving Forward 
Misconception/Error The student makes errors applying the Distributive Property. 
Examples of Student Work at this Level The student:
 Fails to distribute completely.
 Fails to distribute a negative sign.

Questions Eliciting Thinking Can you show me how you applied the Distributive Property? What is the sign of the product of two negative numbers? 
Instructional Implications Review the Distributive Property. Explain how this property can be used to expand expressions. Provide examples of expressions of the form a(b + c) and ask the student to carefully show the factors that will be multiplied before completing the multiplication [e.g., initially rewrite an expression such as 5.2(3x â€“ ) as 5.2(3x) â€“ (5.2)()]. Caution the student to be careful when distributing a negative number especially over subtraction [e.g., 3(x  5)]. Consider suggesting rewriting subtraction in terms of addition, {e.g., 3[x + (5)]}, before distributing.
Explain that an equation of the form a(b + c) = d can also be solved by first dividing each side of the equation by a. Ask the student to solve the equation using this approach and to consider the advantages or disadvantages of dividing first rather than distributing.
Remind the student to use substitution to check solutions in the original equation. Provide additional opportunities to solve linear equations with rational coefficients that require the use of the Distributive Property. 
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 requiring distribution of rational numbers 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 task Linear Equations  3. 