Getting Started 
Misconception/Error The student is unable to correctly apply relevant theorems to find the missing angle measures. 
Examples of Student Work at this Level The student attempts to apply relevant theorems but does so incorrectly.

Questions Eliciting Thinking Can you identify a linear pair of angles in this diagram? What is true of linear pairs of angles? How do you know this?
Cover up one of the transversals and ask the student to identify a pair of corresponding angles and a pair of alternate interior angles.
What does the Corresponding Angles Theorem (or the Alternate Interior Angles Theorem) say? 
Instructional Implications Review the definition of a linear pair and the Linear Pair Postulate. Provide examples of linear pairs of angles. Give the student opportunities to find missing angle measures in diagrams involving linear pairs of angles.
If needed, review the definition of interior angles, corresponding angles, and alternate interior angles, and the Corresponding Angles Theorem and the Alternate Interior Angles Theorem. Emphasize the condition under which each theorem can be applied (i.e., two parallel lines are intersected by a transversal) and give the student opportunities to apply both theorems in a variety of problem contexts. 
Moving Forward 
Misconception/Error The student can find the missing angle measures but is unable to adequately justify his or her answers. 
Examples of Student Work at this Level The student correctly finds both missing angle measures. However, the student:
 Provides the correct angle measures with minimal or no justification.
 Provides an explanation that contains errors or is significantly incomplete.
 Describes the computations used without providing justification.

Questions Eliciting Thinking What is the mathematical term used to describe and its adjacent angle? How do you know these angles are supplementary? What theorem supports this statement?
Can you explain how you found the measure of ? How do you know these angles are congruent? What theorem supports this statement?
What does it mean to justify your work? What postulates or theorems have you used in finding these angle measures? 
Instructional Implications Review the terms that apply to the angles and the angle relationships in the diagram and their definitions (e.g., linear pair of angles, supplementary angles, and corresponding angles). Review postulates and theorems that will be needed in the justifications (e.g., Linear Pairs Postulate and Corresponding Angles Theorem). Explain that when justifying mathematical work, the student should cite the relevant definitions, postulates, and theorems that are used to support computational work. For example, model explaining the 119° angle and its adjacent angle form a linear pair and are supplementary by the Linear Pairs Postulate. Consequently, their measures sum to 180° by the definition of supplementary angles. Ask the student to provide a justification for concluding that the measure of is 61° and assist the student in citing the relevant theorem.
Provide additional opportunities for the student to find missing angle measures using similar diagrams and to justify his or her work. 
Almost There 
Misconception/Error The student is unable to cite relevant definitions, postulates, or theorems that support some aspect of his or her work. 
Examples of Student Work at this Level The student correctly calculates each angle measure and provides a justification for each calculation. However, the student is unable to cite a relevant definition, postulate, or theorem to support some aspect of his or her work. For example, the student:
 Is unable to explain why the angle adjacent to the 119° angle is 61° although he or she correctly applies the Alternate Interior Angles Theorem to conclude that .
 Provides justifications without explicitly stating the conclusion. For example, the student states the Corresponding Angles Theorem but does not explicitly state that this theorem allows one to conclude that the .
 States that corresponding angles are congruent without stating why (i.e., citing the Corresponding Angles Theorem).

Questions Eliciting Thinking How do you know these two angles are supplementary? What does supplementary mean?
What were you justifying with this theorem?
How do you know corresponding angles are congruent? Are they always congruent? 
Instructional Implications Provide feedback to the student concerning any error or omission in his or her justification. Explain that a complete justification includes any relevant definitions, postulates, or theorems that are used to support conclusions drawn about angle measures or equations written to model angle relationships. Provide additional opportunities for the student to find missing angle measures using similar diagrams and to justify his or her work. 
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 observes that the 119° angle forms a linear pair with each of its adjacent angles and states that if two angles form a linear pair, then they are supplementary by the Linear Pairs Postulate. Consequently, their measures sum to 180° by definition of supplementary angles. The student subtracts 119° from 180° to determine that each adjacent angle measures 61°. The student reasons that, for example, since and a 61° are corresponding, then the by the Corresponding Angles Theorem.
The student uses similar reasoning to conclude that .

Questions Eliciting Thinking Do adjacent angles always form a linear pair?
What must be true of this diagram in order to use the Corresponding Angles Theorem (or the Alternate Interior Angles Theorem)?
Why can’t the 76° angle be used to find the measure of ?
Can you think of a realworld application of the Alternate Interior Angles Theorem? 
Instructional Implications Assess the student on his or her understanding of the proofs of the Corresponding Angles Theorem and the Alternate Interior Angles Theorem. Consider implementing MFAS tasks Proving the Alternate Interior Angles Theorem (GCO.3.9) and Proving the Corresponding Angles Theorem (GCO.3.9). 