Getting Started 
Misconception/Error The student is unable to apply relevant theorems to find the missing angle measures. 
Examples of Student Work at this Level The student is unable to find some or all of the missing angle measures. For example, the student knows that some of the angles in the diagram measure 104° (in addition to ) but is unable to correctly determine which other angles measure 104°. Additionally, the student is unable to determine that other angles in the diagram measure 76°.

Questions Eliciting Thinking Do you know what this pair of angles (pointing to a pair of vertical angles) is called? How do you know these angles have the same measure?
Can you identify a linear pair of angles in this diagram? What is true of linear pairs of angles? How do you know this? 
Instructional Implications Review the definition of vertical angles and the Vertical Angles Theorem. Introduce a proof of the Vertical Angles Theorem and then give the student opportunities to apply this theorem in a variety of problem contexts.
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.
Review the definition of corresponding angles and the Corresponding Angles Theorem. Emphasize the condition under which this theorem can be applied (i.e., two parallel lines are intersected by a transversal) and give the student opportunities to apply this theorem 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 all missing angle measures. However, the student either provides no justification or:
 Writes a single statement that does not make mathematical sense.
 Describes two sets of congruent angles without providing a justification.

Questions Eliciting Thinking Do you know the mathematical term used to describe and ? How do you know these angles are congruent?
What theorem supports this statement?
Do you know the mathematical term used to describe and ? How do you know these angles are supplementary? 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., vertical angles, linear pair of angles, supplementary angles, and corresponding angles). Review postulates and theorems that will be needed in the justifications (e.g., the Vertical Angles Theorem, Linear Pairs Postulate, and Corresponding Angles Theorem). Explain that when justifying mathematical work, the student should cite relevant definitions, postulates, and theorems to support computational work. For example, model explaining that and the adjacent 104° angle form a linear pair so must be supplementary by the Linear Pairs Postulate. Consequently, their measures sum to 180° by definition of supplementary angles. Guide the student to write and solve an equation such as to determine that the . Assist the student in reasoning that since and are vertical, is also 76° by the Vertical Angles Theorem. Ask the student to find and justify the measure of . Guide the student to apply the Corresponding Angles Theorem to find all other angle measures in the diagram.
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:
 States that and are vertical so must be congruent. However, when asked how he or she knows that vertical angles are congruent, the student is unable to cite the relevant theorem.
 States that because and sum to 180° but does not cite the Linear Pairs Postulate to justify this conclusion.
 Justifies the measures of angles by identifying types of angle pairs but does not reference relevant postulates or theorems.

Questions Eliciting Thinking How do you know vertical angles are congruent?
What do you know about a linear pair of angles? How do you know that a linear pair of angles is supplementary? What does supplementary mean?
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 to support conclusions drawn about angles 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 and are vertical so that and justifies this conclusion by citing the Vertical Angles Theorem. The student then observes that and form a linear pair of 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 writes an equation such as and solves it to determine that the . The student reasons that since and are vertical, is also 76°. The student identifies the following as pairs of corresponding angles: and , and , and , and and cites the Corresponding Angles Theorem to conclude that , , , and . 
Questions Eliciting Thinking Are vertical angles always congruent? Are corresponding angles always congruent? What must be true of this diagram in order to use the Corresponding Angles Theorem?
What must be true of the diagram in order for all of the angles to be congruent? What would the measure of each angle be under these circumstances?
Can you think of a realworld application of the Corresponding Angles Theorem? 
Instructional Implications Consider implementing MFAS task Proving the Alternate Interior Angles Theorem (GCO.3.9). Then ask the student to prove the Corresponding Angles Theorem. Consider implementing MFAS task Proving the Corresponding Angles Theorem (GCO.3.9). 