Astronomy midterm question: seeing the third quarter moon in the dark sky?

Astronomy 210 Midterm 1, spring semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board was asked and answered[*]:
Pdg: Is it possible to see the third quarter moon when the sky is dark at night?
CON: Yes, it is very possible, you just have to be awake and up after midnight and the sky has to be clear, or reasonably clear. Don't wait until dawn.
Discuss why this answer is correct for an observer in San Luis Obispo, CA. Support your answer using a diagram showing the positions of the sun, moon, Earth, and an observer on Earth.

[*] answers.yahoo.com/question/index?qid=20170107045840AA6CMVF.

Solution and grading rubric:
  • p:
    Correct. Complete diagram and reasoning includes the following explanations:
    1. the third quarter moon, which is highest overhead at 6 AM, rises six hours earlier at 12 AM, and sets six hours after being highest overhead at 12 PM;
    2. the sun is up from 6 AM to 6 PM;
    3. so the third quarter moon can be visible in a dark sky from 12 AM to (just before) 6 AM.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Diagram and/or explanation has minor errors.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. May have not discussed why it is important to not "wait until dawn."
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to draw a moon phase diagram and apply rise/overhead/set times.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on a moon phase diagram.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Section 30674
Exam code: midterm01nghT
p: 15 students
r: 1 student
t: 2 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

Section 30676
Exam code: midterm01sP4m
p: 31 students
r: 1 students
t: 7 students
v: 4 student
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1337):

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