Getting Started 
Misconception/Error The student does not recognize and as consecutive angles or understand its implications. 
Examples of Student Work at this Level The student:
 Sketches parallelogram ACBD (rather than parallelogram ABCD) and concludes that and are opposite. The student may or may not be able to continue.
 Correctly sketches parallelogram ABCD but writes an equation in which the expressions for the measures of and are set equal.

Questions Eliciting Thinking When sketching parallelogram ABCD, is the order of the vertices important?
What kind of angle pair is 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 angle measures. 
Examples of Student Work at this Level The student writes the equation (6x + 5) + (14x + 35) = 180. However, the student:
 Solves the equation incorrectly.
 Solves the equation correctly but makes an error in determining the measure of an angle, for example, subtracts the measure of from 180 to find the measure of .
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 measure?
What theorem did you apply when you wrote your equation?
What theorem can you apply to find the measure of ? 
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 Angles of a Parallelogram (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) + (14x + 35) = 180 and determines that x = 7. However, the student:
 Describes only one or none of the supporting theorems.
 Describes theorems incorrectly or incompletely.
 Describes a theorem using incorrect terminology.
 Describes a theorem that was not used in addition to describing the correct theorems.

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 measure of ?
Did you use all of the theorems you described?
What kind of angle pair is 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 Angles of a Parallelogram (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) + (14x + 35) = 180 and determines that x = 7, . The student describes appropriate theorems (e.g., consecutive pairs of angles of a parallelogram are supplementary and opposite angles of a parallelogram are congruent) to support his or her work.

Questions Eliciting Thinking When did you apply each of the theorems that you described?
Could you have found the measure of if you were given the measure of and the measure of ? If so, how? 
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. 