Getting Started 
Misconception/Error The student lacks the algebraic skills necessary to identify the equivalent expressions. 
Examples of Student Work at this Level The student:
 Randomly circles expressions with little or no work shown.
 Cannot correctly multiply two binomials.
 Cannot correctly square a binomial.
 Shows minimal work and then circles expressions that are not equivalent.

Questions Eliciting Thinking What does equivalent mean? What makes expressions equivalent? Are you able to determine that these expressions are equivalent as they are written?
What type of expressions are these? What can you do to determine which ones are equivalent? What can you do to make it easier to compare these expressions?
Can you explain to me what you did to determine which expressions are equivalent? 
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. Explain and model use of 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 Explain that binomials can be squared by rewriting them as the product of two factors and then multiplying: = (a + b)(a + b). Provide additional opportunities to multiply and square binomials in the context of a variety of problems.
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 MFAS task Finding Missing Values (ASSE.1.2) or the NCTM activity Equivalent Expressions http://www.illustrativemathematics.org/illustrations/87. 
Moving Forward 
Misconception/Error The student chooses an expression that is not equivalent. 
Examples of Student Work at this Level The student determines that is equivalent to â€“ 10x + 21. 
Questions Eliciting Thinking Why did you factor out a two (or divide all terms by two) in expression number three? Is the two still part of the expression after you factored? 
Instructional Implications Review the difference between factoring a common factor from the terms of an expression and dividing both sides of an equation by a constant. Remind the student that any term factored from an expression is still a factor of that expression. Explain that if two expressions are equivalent, they will be identical when written in the same form, consequently â€“ 20x + 42 is not equivalent to â€“ 10x + 21. 
Almost There 
Misconception/Error The student identifies the equivalent expressions but cannot correctly name all three. 
Examples of Student Work at this Level The student states the three equivalent expressions are 2, 5, and 6 [i.e.,Â â€“ 4, (x â€“ 3)(x â€“ 7), and â€“ 10x + 21] but cannot describe correctly the form in which each is written. 
Questions Eliciting Thinking What is standard form for a quadratic expression? What is factored form? What is vertex form? 
Instructional Implications Review terminology that describes the various forms of quadratic expressions: vertex form, factored form, and standard or expanded form. Describe the value of each form and what it readily conveys about the graph of the corresponding quadratic function. Provide opportunities for the student to identify the form of a quadratic function, given a function such as y = + 8, as well as any feature of the graph that particular form conveys [e.g., the graph is an upward opening parabola with a vertex at (3, 8)]. 
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 states the three equivalent expressions are 2, 5, and 6 [i.e.,Â â€“ 4, (x â€“ 3)(x â€“ 7), and â€“ 10x + 21]. The student then states that expression 2 is written in vertex form, expression 5 is written in factored form and expression 6 is written in standard or expanded form.

Questions Eliciting Thinking Other than rewriting the expressions, is there any way you can determine which expressions are equivalent?
Why is it important to be able to write quadratic expressions in different forms?
What does factored form tell you about the graph of the quadratic?
What does vertex form tell you about the graph of the quadratic?
What does standard form tell you about the graph of the quadratic? 
Instructional Implications Ask the student to consider what each form (e.g., vertex form, factored form, and standard or expanded form) conveys about the corresponding quadratic function. Give the student an expression in one form and have the student rewrite the expression in the other two forms.
Challenge the student with the NCTM activity Animal Populations http://www.illustrativemathematics.org/illustrations/436 which requires students to determine which of two algebraic expressions is greater. 