Getting Started 
Misconception/Error The student does not understand what it means to write an equivalent expression. 
Examples of Student Work at this Level The student:
 Substitutes a value for x and attempts to evaluate the expression.
 Imposes an equal sign somewhere in the expression and attempts to â€śsolveâ€ť it.
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 Multiplies terms together and attempts to evaluate the expression.

Questions Eliciting Thinking What is the difference between an expression and an equation? What is the difference between rewriting and solving?
Do you know what â€ślike termsâ€ť are? Are the terms 4x and 8 like terms?
What does it mean to factor an expression? 
Instructional Implications Explain the distinction between an expression and an equation. Provide examples of each in both realworld and mathematical contexts. (E.g., Pose scenarios that provide the opportunity to write expressions and equations such as, â€śGena is twice as old as Mattie. Adam is three years older than Mattie. If the sum of their ages is 51, how old is each?â€ť). Review the terms variable, constant, and coefficient. Then guide the student to write expressions that represent each personâ€™s age in the problem. Ask the student to identify examples of variables, constants, and coefficients in the expressions. Then guide the student to use the information that the ages sum to 51 to write an equation. Ask the student to identify expressions within the equation making clear the distinction between an expression and an equation. Provide additional opportunities for the student to write expressions and equations.
Explain what it means for expressions to be equivalent and provide instruction on using the Commutative and Associative Properties to rewrite the terms of an expression in a more â€śconvenientâ€ť order. Review the Distributive Property and explain how it can be used to combine variable terms such as 5x and 2xÂ [e.g., 5x + 2xÂ = (5 + 2)x = 3x]. Eventually introduce the concept of â€ślike termsâ€ť and transition the student to simplifying expressions by distributing (when necessary) and combining like terms. Next use the Distributive Property to introduce the concept of factoring. Emphasize that the Distributive Property can be used to both expand (e.g., multiply) and factor expressions. Provide additional opportunities for the student to rewrite linear expressions with rational coefficients in factored form using the fewest number of terms. Guide the student to check factorizations by expanding and comparing to the original expression. 
Moving Forward 
Misconception/Error The student does not correctly apply the Distributive Property either to expand, factor, or combine like terms. 
Examples of Student Work at this Level The student combines like terms (either correctly or incorrectly) but does not factor the expression:
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Questions Eliciting Thinking How did you know which terms to combine?
What does it mean to factor?
What is the Distributive Property? How is it related to factoring? 
Instructional Implications Review the Distributive Property and explain how it can be used to combine variable terms such as 5x and 2xÂ [e.g., 5x + 2xÂ = (5 + 2)x = 3x]. Eventually introduce the concept of â€ślike termsâ€ť and transition the student to simplifying expressions by distributing (when necessary) and combining like terms. Next use the Distributive Property to introduce the concept of factoring. Emphasize that the Distributive Property can be used to both expand (e.g., multiply) and factor expressions. Provide additional opportunities for the student to rewrite linear expressions with rational coefficients in factored form using the fewest number of terms. Guide the student to check factorizations by expanding and comparing to the original expression. 
Almost There 
Misconception/Error The student makes computational errors when calculating with coefficients and constants. 
Examples of Student Work at this Level The student:
 Makes a sign error, rewriting 3x â€“ 12 + 6x + 9 as 3x â€“ 6x + 12 + 9.
 Says the sum of 12 and 9 is positive three.
 Factors 9x â€“ 3 as 3(x â€“ 1).

Questions Eliciting Thinking Which terms in the original expression are negative or contain a negative coefficient?
I think you made a mistake combining like terms. Can you check your work?
How can you check your final answer to determine if it is equivalent to the original expression? 
Instructional Implications Provide direct feedback to the student regarding his or her error and allow the student to correct it. Provide additional opportunities for the student to rewrite linear expressions with rational coefficients in factored form using the fewest number of terms. Guide the student to check factorizations by expanding and comparing to the original expression. 
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 uses the fewest number of terms and correctly factors each expression. The student writes:
 4x + 8 + 2 = 4x + 10 = 2(2x + 5)Â
 3x â€“ 12 + 6x + 9 = 9x â€“ 3 = 3(3x â€“ 1)

Questions Eliciting Thinking In the second problem, how did you know that you could combine 12 and 9? They are not next to each other in the expression.
In the second problem, how did you know that you could combine 3x and 6x? What property justifies this?
How is factoring related to the Distributive Property?
Are there any other ways to rewrite either expression in an equivalent factored form? 
Instructional Implications Challenge the student to factor each expression in a variety of other ways. (E.g., Ask the student to rewrite 4x + 10 as the product of Â and a linear expression so that their product is equivalent to 4x + 10.). 