Getting Started 
Misconception/Error The student does not recognize and as a pair of opposite angles or understand its implications. 
Examples of Student Work at this Level The student:

Questions Eliciting Thinking When sketching parallelogram ABCD, is the order of the vertices important?
What kind of angle pair are and ? What do you know about this kind of angle pair? 
Instructional Implications Review conventions in naming parallelograms and guide the student to sketch parallelogram ABCD correctly. Ask the student to revise his or her solution. If the student does not recognize the need to rewrite the equation, then review theorems related to the angles of a parallelogram (i.e., opposite angles of a parallelogram are congruent, consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a quadrilateral is 360°). Guide the student in applying the appropriate theorem to write an equation. Ask the student to solve the equation and find the measures of all four angles. Ask the student to describe any additional theorems used.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures. 
Moving Forward 
Misconception/Error The student errs in solving the equation or finding an angle measure. 
Examples of Student Work at this Level The student writes the equation 6x + 5 = 9x – 16. However, the student:
 Solves the equation incorrectly.
 Solves the equation correctly but makes an error in determining the measure of an angle.
The student also may not be explicit in describing any theorems used. 
Questions Eliciting Thinking Can you explain how you solved your equation?
Can you explain how you used the solution of your equation to find the angle measures?
What theorem did you apply when you wrote your equation? Shouldn’t the measures you found for and be the same?
What theorem can you apply to find the measures of and ? 
Instructional Implications Provide feedback on any errors made and allow the student to revise his or her work. Review theorems related to the angles of a parallelogram (i.e., opposite angles of a parallelogram are congruent, consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a quadrilateral is 360°). Guide the student to apply and cite these theorems when finding the measures of the angles of a parallelogram.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures.
Consider implementing MFAS task Finding Angle C (GCO.3.11). 
Almost There 
Misconception/Error The student is unable to correctly or completely describe the theorems used. 
Examples of Student Work at this Level The student writes the equation 6x + 5 = 9x – 16 and determines that x = 7, = = 47°, and = = 133°. However, the student:
 Describes only one or neither theorem.
 Describes theorems incorrectly or incompletely.
 Describes a theorem that was not used in addition to describing the correct theorems.
 Describes a theorem using incorrect terminology.

Questions Eliciting Thinking How did you know how to write your equation? What theorem did you apply when you wrote your equation?
What theorem did you apply to find the measures of and ?
Did you use all of the theorems you described?
What kind of angle pair are and ? and ? 
Instructional Implications Review theorems related to the angles of a parallelogram (i.e., opposite angles of a parallelogram are congruent, consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a quadrilateral is 360°). Ask the student to describe the theorems used to both write the equation and to find the measures of the angles. Explain that it is not necessary to describe other theorems related to parallelograms that were not explicitly used. Correct any misuse of terminology.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures.
Consider implementing MFAS task Finding Angle C (GCO.3.11). 
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 writes the equation 6x + 5 = 9x – 16 and determines that x = 7, = = 47°, and = = 133°. The student describes appropriate theorems (e.g., opposite angles of a parallelogram are congruent, consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a quadrilateral is 360°) to support his or her work.

Questions Eliciting Thinking When did you apply each of the theorems that you described?
Was it necessary to calculate the measures of both and ?
Suppose you calculated different measures for and . What would you have done next? 
Instructional Implications Provide the student with similar problems in which solutions of equations are noninteger rational numbers.
Provide the student with problems in which expressions for three angle measures are given using two variables so that the student must write and solve a system of equations.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures. 