Getting Started 
Misconception/Error The student cannot correctly identify a pair of vertical angles. 
Examples of Student Work at this Level The student identifies a nonvertical pair of angles as vertical. 
Questions Eliciting Thinking Do you know what adjacent angles are?
Are vertical angles different from adjacent angles? 
Instructional Implications Review the meaning of the following: adjacent angles, vertical angles, supplementary angles, linear pair of angles. Ask the student to use the diagram on the worksheet to identify examples of each. Suggest a measure for one of the angles and ask the student to calculate the measures of all other angles in the diagram.
If necessary, review the distinction between notation for naming angles (e.g., < 4) and describing angle measures (e.g., m < 4) and guide the student to write equations and congruence statements using the appropriate notation.
Review the Substitution Property and the Subtraction Property of Equality. Then guide the student through a proof of the congruence of vertical angles such as the one suggested in the Got It level of the rubric. Prompt the student to supply the justifications of the statements. Then have the student analyze and describe the strategy used in the proof.
Provide the student with frequent opportunities to make deductions using a variety of previously encountered definitions and established theorems. For example, provide diagrams as appropriate and ask the student what can be concluded as a consequence of:
 point M is the midpoint of
 < A and < B form a linear pair
 m < A + m < B = 90
 is the bisector of
Provide the student with additional examples of proofs of statements about angles. Ask the student to prove simple statements and provide feedback.

Moving Forward 
Misconception/Error The student identifies a pair of vertical angles but is not able to prove that they are congruent. 
Examples of Student Work at this Level The student:
 Says, “Vertical angles are always congruent” and does not provide a proof.
 Says that vertical angles are congruent because both are 90 degrees.
 Provides a vague and unconvincing argument.
 Makes some relevant observations but does not write a complete proof.

Questions Eliciting Thinking You said that, “Vertical angles are always congruent.” Do you think you could prove this statement?
Do vertical angles always measure 90°?
Which angle pairs actually sum to 180° in this diagram? How can that lead to the conclusion that m < 1 = m < 4? 
Instructional Implications Review the Substitution Property and the Subtraction Property of Equality. Then guide the student through a proof of the congruence of vertical angles such as the one suggested in the Got It level of the rubric. Prompt the student to supply the justifications of the statements. Then have the student analyze and describe the overall strategy used in the proof.
Provide the student with additional examples of proofs of statements about angles. Ask the student to prove simple statements and provide feedback.
If necessary, review the distinction between notation for naming angles (e.g., < 4) and describing angle measures (e.g., m < 4) and guide the student to write equations and congruence statements using the appropriate notation. 
Almost There 
Misconception/Error The student has an effective strategy for the proof but fails to establish a necessary condition or provide justification for a statement in the proof. 
Examples of Student Work at this Level The student does not provide support for statements in the proof (and the student uses poor notation).

Questions Eliciting Thinking How do you know that and ?
How does this lead to the fact that ? 
Instructional Implications Provide the student with direct feedback on his or her proof. Prompt the student to supply justifications or statements that are missing. Correct any misuse of notation.
If necessary, review the distinction between notation for naming angles (e.g., < 4) and describing angle measures (e.g., m < 4) and guide the student to write equations and congruence statements using the appropriate notation.
Challenge the student to use the fact that vertical angles are congruent to prove other statements about lines and angles. 
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 correctly identifies < 1 and < 4 (or < 2 and < 3) as a pair of vertical angles. The student presents a convincing proof that vertical angles are congruent. For example, the student writes:
 and since each forms a linear pair and are, therefore, supplementary.
 By substitution,
 By the Subtraction Property of Equality,
 By definition of congruent angles, < 1 < 4.

Questions Eliciting Thinking What parts of your explanation refer to definitions, postulates, or theorems? 
Instructional Implications Challenge the student to use the fact that vertical angles are congruent to prove other statements about lines and angles. 