The broad topic for this question is: The Relationship(s) of Second Temple Judaism and Early Christianity.
Part 1: Briefly explain the difference between "Second Temple Judaism" the "the Jesus Community" that arises as a result of the Jesus' life, ministry, and death. Briefly explain how "the Jesus Community" at its earliest stages (during the lifetime of Jesus and just afterwards) related to Second Temple Judaism. (Hints: Look at the Cambridge Companion for help here. Historically and theologically, what did Jesus and the first generation of his disciples have in common with Second Temple Judaism? Around what issues might they have diverged from Second Temple Judaism?)
Part 2: Briefly explain the development of early Christianity relative to Second Temple Judaism. That is, in the years following the death of Jesus (roughly the last 60 years of the first century), in what ways did the ongoing communities of followers of Jesus relate to Second Temple Judaism? What issues and events seem to sharpen the distinction between these generations of believers and Second Temple Judaism? (Hints: You may wish to consider portrayals of the relationship found in the Letters of Paul, the Gospels, and the Acts of the Apostles. You should also consider the ways in which these Christian texts use and reinterpret Hebrew Scriptures.)
Part 3: (Thinking question): Given your comments in the preceding
sections, how is early Christianity best understood -- as a sect
within Second Temple Judaism, as a separate religion, or as something
else (if the latter define it)? If it is best understood in different
ways at different times within the first century, explain why,
and when changes occur.
Final hint: If you choose to only write the longer essay, make
sure that Part 2 of this essay includes a significant discussion
of how the OT is used in the NT. You want to show me that you
are able to tie together these two parts of the course. This is
helpful for those that write this essay as part of the final,
but those students will also be able to demonstrate and understanding
of the OT from questions that are drawn directly from that part
of the course.