Getting Started 
Misconception/Error The student’s proof shows no evidence of an overall strategy or logical flow. 
Examples of Student Work at this Level The student:
 States the given information, but is unable to go any further.
 Writes a proof with no logical structure although it may contain some true statements or statements that would appear in the proof.

Questions Eliciting Thinking What are you trying to prove?
Did you think through a plan for your proof before you started? Did you consider what you already know that might help you to prove AC + CB > AB? 
Instructional Implications Review theorems that will be used in the proof (e.g., the Converse of the Isosceles Triangle Theorem and the Inequalities Within a Single Triangle Theorem). With the student, develop a general strategy for the proof. For example:
 Locate point D on such that CD = AC.
 Show > so that DB > AB can be concluded.
 Use the fact that DB > AB to show that AC + CB > AB.
Then assist the student in providing the details. Correct any misuse of notation. If necessary, review notation for naming angles (e.g., ) and describing angle measures (e.g., ) and guide the student to write equations and congruence statements using the appropriate notation.
Next, provide the student with the statements of the proof and ask the student to supply the justifications. Then have the student analyze and explain the proof.
Encourage the student to begin the proof process by developing an overall strategy. Provide an additional statement to be proven and have the student compare strategies with another student and collaborate on completing the proof.
Provide additional opportunities to prove theorems about triangles. 
Moving Forward 
Misconception/Error The student’s proof shows evidence of an overall strategy but the student fails to establish major conditions leading to the prove statement. 
Examples of Student Work at this Level The student appears to understand the need to show > D in order to conclude that DB > AB. However, the proof contains significant omissions or logical inconsistencies.

Questions Eliciting Thinking Can you explain your strategy for this proof?
How will showing that DB > AB help you show AC + CB > AB? 
Instructional Implications Review a general strategy for the proof, for example:
 Locate point D on BC such that CD = AC.
 Show so that DB > AB can be concluded.
 Use the fact that DB > AB to show that AC + CB > AB.
Then assist the student in providing the details. Correct any misuse of notation. If necessary, review notation for naming angles (e.g., ) and describing angle measures (e.g., ) and guide the student to write equations and congruence statements using the appropriate notation.
Provide additional opportunities to prove theorems about triangles. 
Almost There 
Misconception/Error The student’s proof shows evidence of an overall strategy, but the student fails to establish a condition that is necessary for a later statement in the proof. 
Examples of Student Work at this Level The student writes a logically coherent proof but omits some statements that support a major conclusion. For example, the student states but does not establish . The remainder of the proof is correct with the possible exception of the misuse of notation.

Questions Eliciting Thinking How do you know that ? Shouldn’t this statement be proven first? 
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 notation for naming angles (e.g., ) and describing angle measures (e.g., ) and guide the student to write equations and congruence statements using the appropriate notation.
Provide additional opportunities to prove theorems about triangles. 
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 a complete and correct proof of the Triangle Inequality Theorem such as the following:
Choose a point D on such that CD = AC.
Since CD = AC, then in triangle ACD, (by the converse of the Isosceles Triangle Theorem). Since (by the Angle Addition Postulate), then so that (by Substitution), . Consequently, DB > AB (by the Inequalities Within a Single Triangle Theorem). Since DB = DC + CB (by the Segment Addition Postulate), then CD + CB > AB (by Substitution). Since CD = AC, then AC + CB > AB (by Substitution). 
Questions Eliciting Thinking Why was it necessary to locate point D so that CD = AC?
How is the Isosceles Triangle Theorem different from the converse of the Isosceles Triangle Theorem? 
Instructional Implications Provide additional opportunities to prove theorems about triangles.
Consider implementing other MFAS tasks aligned to MAFS.GCO.3.10 that require the student to prove statements about triangles. 