Getting Started 
Misconception/Error The student does not have an effective strategy for justifying the theorem. 
Examples of Student Work at this Level The student:
 Attempts to explain why rigid motion preserves angle measure.
 Claims that the two base angles are supplementary, and therefore, sum to 180°.
 Explains that if you measure each angle and sum the measures, the result will be 180°.

Questions Eliciting Thinking What does the Triangle Sum Theorem state? How can you use a protractor to demonstrate the theorem?
Can you think of anything else that equals 180°? What is the measure of a straight angle? Can you use the tracing paper to show that the three angles of the triangle can form a straight angle?
Can you trace the two base angles so they are adjacent? Do they sum to 180°? What does a 180° angle look like? 
Instructional Implications Explain what the Triangle Sum Theorem means and allow the student to verify the theorem by carefully measuring the interior angles of a variety of triangles (e.g., acute, obtuse, and right) and summing the measures. Then assist the student in developing an informal justification for the theorem using tracing paper. Guide the student to trace all three angles of the triangle and redraw them to form a straight angle. Help the student devise an appropriate explanation to support the drawing. Model the use of correct mathematical terminology and notation.
Provide the student with several triangles which vary in classification (e.g., acute, obtuse, and right), encourage the student to trace and redraw the three angles of each triangle so they form a straight angle, and guide the student to conclude that the measures of the interior angles of any triangle sum to 180°. Consider implementing the CPALMS Lesson Plan Triangles: Finding Interior Angle Measures (ID 38498), a handson lesson that allows students to investigate the Triangle Sum Theorem. 
Making Progress 
Misconception/Error The student provides an explanation without supporting evidence. 
Examples of Student Work at this Level The student:
 Describes a demonstration that will show that the measures of the angles sum to 180° but does not actually complete the demonstration.
 Suggests drawing a line through one vertex parallel to a side of the triangle and says that this demonstrates that the angle measures sum to 180°.

Questions Eliciting Thinking You described a nice demonstration that sounds convincing, but can you complete the demonstration?
How does this drawing show that the angle measures sum to 180°? Can you provide some of the details? 
Instructional Implications Assist the student in developing an appropriate justification based on the approach the student took. For example, if the student uses tracing paper to copy the angles and redraw them as adjacent angles, help the student draw a diagram that illustrates this and devise an appropriate explanation to support the drawing. Model the use of correct mathematical terminology and notation. If the student draws a line through one vertex parallel to a side of the triangle, assist the student in providing enough detail to make the explanation convincing.
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 provides an adequate yet informal justification of the theorem. For example, the student:
 Traces the three interior angles on tracing paper and redraws them so that all three angles share a vertex and each pair of angles shares a side. The student explains that since the three angles combine to form a straight angle, their measures sum to 180°.
 Draws a line through point C parallel to forming three angles that combine to form a straight angle and, therefore, have measures that sum to 180°. The student names the two outer angles (from left to right) and (the middle angle is the same as interior angle C of the triangle). The student uses the Alternate Interior Angle Theorem to deduce that is congruent to and is congruent to . The student explains that this means that .

Questions Eliciting Thinking If the student used a tracing paper demonstration ask, “Suppose you drew a line through point C parallel to . Are there any congruent pairs of angles formed?”
If the student reasoned using congruent angles formed by parallel lines and a transversal ask, “Could this explanation be applied to a right triangle? An obtuse triangle?” 
Instructional Implications If the student used a tracing paper demonstration to explain the relationship among the measures of the interior angles, ask the student to draw a line through point C parallel to and use this diagram to reason about the interior angle measures.
Ask the student to explore quadrilaterals to determine if the sum of the measures of the interior angles is the same in all quadrilaterals.
Consider implementing other MFAS tasks from standard 8.G.1.5 to further explore the student’s understanding of angle relationships in the context of parallel lines and a transversal. 