Getting Started 
Misconception/Error The student is unable to draw an exterior angle of a triangle. 
Examples of Student Work at this Level The student:
 Creates a new angle at vertex B.
 Labels the interior angle at vertex B as the exterior angle.
 Provides no answer or indicates he or she does not understand.

Questions Eliciting Thinking What is meant by an interior angle of a triangle? Can you show me an example of an interior angle?
What is an exterior angle of a triangle? Can you draw an example?
If I extend (demonstrate for the student), which angle is the exterior angle? 
Instructional Implications Review the following terms: interior angle of a triangle, exterior angle of a triangle, nonadjacent (or remote) interior angles. Assist the student in extending and identifying an exterior angle at vertex B. Show the student that there are two exterior angles at each vertex formed by extending all sides of the triangle at each vertex. Guide the student to observe that each pair of exterior angles at the same vertex is vertical and, therefore, congruent and that the interior and exterior angle at each vertex form a linear pair. Provide additional examples of triangles and ask the student to draw an exterior angle at each vertex.
Guide the student in translating the statement of the Exterior Angle Theorem into a specific statement (e.g., equation) about the given diagram. Provide a few more examples of triangles with exterior angles drawn and ask the student to write equations that show the relationship between the measure of each exterior angle and its two nonadjacent interior angles.
Assist the student in developing an informal justification of the Exterior Angle Theorem using tracing paper. Then review previously established theorems about angle relationships, such as: (1) a linear pair of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then guide the student to logically reason about the relationship among the measures of , , and . 
Moving Forward 
Misconception/Error The student is unable to apply the Exterior Angle Theorem to write an equation. 
Examples of Student Work at this Level The student is able to extend and identify the exterior angle formed as . However, the student is unable to apply the Exterior Angle Theorem to write an equation that describes the measure of . The student:
 Writes an equation in which sides are set equal to angles.
 References an angle or a side but does not write an equation.
 Writes an incorrect equation.

Questions Eliciting Thinking Can you show me the location of each angle in your equation? Is it true that the sum of the measures of the three interior angles is equal to ?
What does the Exterior Angle Theorem state? Does your equation model this?
Show me how you would write the sum of the measures of and . According to the theorem, what does the sum of those two nonadjacent angles equal? 
Instructional Implications Review the following terms: interior angle of a triangle, exterior angle of a triangle, nonadjacent (or remote) interior angles and assist the student in understanding the Exterior Angle Theorem. Guide the student in translating the statement of the theorem into a specific statement (e.g., equation) about the given diagram. Provide a few more examples of triangles with exterior angles drawn and ask the student to write equations that show the relationship between the measure of each exterior angle and its two nonadjacent interior angles.
Assist the student in developing an informal justification of the Exterior Angle Theorem using tracing paper. Then review previously established theorems about angle relationships, such as: (1) a linear pair of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then guide the student to logically reason about the relationship among the measures of , , and .
Review how to name angles and sides and how to refer to their measures and lengths. Provide feedback to the student regarding any misuses of notation and ask the student to revise his or her responses. 
Almost There 
Misconception/Error The student is unable to provide a clear justification for the theorem. 
Examples of Student Work at this Level The student:
 Provides an example rather than a justification.
 Provides a statement, whether true or not, that does not justify the theorem. (e.g., “The angles of a triangle put together equal 180°.”)
 Provides insufficient justification.

Questions Eliciting Thinking What do you know about the relationship between an exterior angle and its adjacent interior angle?
What do you know about the sum of the measures of the interior angles of a triangle? 
Instructional Implications Assist the student in developing an informal justification of the Exterior Angle Theorem using tracing paper. Then review previously established theorems about angle relationships, such as: (1) a linear pair of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then guide the student to logically reason about the relationship among the measures of , , and .
Review how to name angles and sides, and how to refer to their measures and lengths. Provide feedback to the student regarding any misuses of notation and ask the student to revise his or her responses.
Provide additional opportunities to justify the relationship between the measures of angles. Assist the student in transitioning from using tracing paper to developing a logical argument. 
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 extends and identifies the exterior angle formed as . The student writes the equation and provides an informal justification. For example, the student:
 Traces and , then redraws them so they share a vertex and a side. Then the student uses tracing paper to compare the combined angles to , demonstrating that they are congruent.
 Explains that and are supplementary (or = 180°) since they form a linear pair. The student also observes that = 180° (because the three measures of the interior angles of any triangle sum to 180°). The student then reasons that so that .

Questions Eliciting Thinking What other angle relationships could you identify if you draw a line parallel to through point C and consider and as transversals? 
Instructional Implications If the student used a demonstration using tracing paper to justify the Exterior Angle Theorem, review previously established theorems about angle relationships, such as: (1) a linear pair of angles is supplementary and (2) the measures of the interior angles of a triangle sum to 180°. Then ask the student to logically reason about the relationship among the measures of , , and .
Ask the student to draw a line through point C parallel to and reason about the angle relationships formed by the intersection of a transversal ( or ).
Consider implementing other 8.G.1.5 tasks to further assess the student. 