Getting Started 
Misconception/Error The student does not recognize that the product of two binomials is a trinomial. 
Examples of Student Work at this Level The student:
 Attempts to identify f, g, and h without multiplying the binomials.
 Attempts to rewrite the expression in a nonequivalent form.Â

Questions Eliciting Thinking What type of expression is (2xÂ  3)(3x + 1)?
What type of expression is + gx + h?
What can you do to the binomial expression to rewrite it as a trinomial?
What can you do to the trinomial to rewrite it as a product of two binomials? 
Instructional Implications Provide instruction on using the structure of an expression to identify ways to rewrite it. Review key vocabulary (e.g., quadratic, trinomial, binomial, factored form, expanded form, terms, coefficient, constant). Guide the student to recognize that a polynomial of the form + bx + c is in expanded form and an expression of the form (x + d)(x + e) is in factored form. Be sure the student understands the relationship between the expanded and factored forms of trinomials.
Review multiplying binomials.Â It may be helpful to begin by multiplying two twodigit numbers in expanded form.Â Explain and model using the Distributive Property to multiply two binomials. When the student is ready, allow the student to use more efficient methods such as â€śFOIL.â€ť Provide additional opportunities to multiply binomials in the context of a variety of problems.Â
Review factoring trinomials of the form + bx + c in which a =1. Encourage the student to be systematic and thorough in listing factors of c that might serve as constants in the linear factors. Remind the student to find the product of the factors as a check and to be particularly mindful of potential sign errors. Provide additional opportunities to factor trinomials in the context of a variety of problems.
Consider using the NCTM activity Equivalent Expressions http://www.illustrativemathematics.org/illustrations/87. 
Moving Forward 
Misconception/Error The student recognizes that the product of two binomials is a trinomial but is unable to write the new form correctly. 
Examples of Student Work at this Level The student:
 Attempts to multiply (2xÂ  3)(3x + 1) but makes errors.
 Attempts to factor + 2xÂ  24 but makes errors [e.g., factors the expression as (x + 8)(x â€“ 4) or (x + 12)(x â€“ 2)].Â

Questions Eliciting Thinking What is the process for multiplying binomials? Explain to me what you did. What did you distribute?
How do you factor a trinomial? Explain to me what you did. Did you check your factoring by multiplying the binomials? 
Instructional Implications Provide instruction on multiplying binomials. Explain and model using the Distributive Property to multiply two binomials. When the student is ready, allow the student to use more efficient methods such as â€śFOIL.â€ť Provide additional opportunities to multiply binomials in the context of a variety of problems.
Provide instruction on factoring trinomials of the form + bx + c in which a =1. Encourage the student to be systematic and thorough in listing factors of c that might serve as constants in the linear factors. Remind the student to find the product of the factors as a check and to be particularly mindful of potential sign errors. Provide additional opportunities to factor trinomials in the context of a variety of problems.
Consider using the NCTM activity Equivalent Expressions http://www.illustrativemathematics.org/illustrations/87. 
Almost There 
Misconception/Error The student correctly rewrites each expression but cannot correctly identify the values of all the requested variables. 
Examples of Student Work at this Level The student:
 Rewrites the expressions but does not identify the values of the variables.
 Does not understand that the variables f, g, and h represent only the coefficients and includes and/or x when describing their values.
 Makes a sign error when identifying the value of a variable (e.g., describes the value of m or n as 4 instead of 4).Â

Questions Eliciting Thinking In the expression +gx + h, what word describes f, g, and h? What is the coefficient of in â€“ 7x â€“ 3?
What are the terms in each binomial factor of (x + m) (x â€“ n)? What are the terms in (x + 6) (x â€“ 4)?
If you substitute your values for m and n into (x + m) (x + n), will you get the factorization of ? 
Instructional Implications Review the terms coefficient and constant. Ask the student to identify the coefficients and constants in (2x â€“ 3)(3x + 1) and + 2x â€“ 24. Explain that the variables f, g, and h represent coefficients and constants in the expression + gx + h and that m and n represent constants in the expression (x + m)(x + n). Assist the student in understanding that these variables might represent negative, as well as positive, values. Revisit this issue when introducing the quadratic formula. 
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 expands (2x  3)(3x + 1) as â€“ 7x â€“ 3 and states that f = 6, g = 7 and h = 3.
The student factors + 2x  24 as (x + 6) (x â€“ 4) and states that m = 6 and n = 4. 
Questions Eliciting Thinking What are the coefficients and constants in the expressions + gx + h and (x + m)(x + n)? 
Instructional Implications Provide more challenging expressions to factor (e.g., expressions that are quadratic in form such as â€“ â€“ 36).
Consider using MFAS tasks Quadratic Expressions (ASSE.1.2), Determine the Width (ASSE.1.2), and Rewriting Numerical Expressions (ASSE.1.2) if not previously used. 