Appreciating each step of the unfolding process in its own context.

Having stumbled upon the concept of ביאה במקצת, the Gemara decides to make this the locus classicus of that topic.

The Gemara compares the derivative Mishnah with the Toras Kohanim which serves as its source.

The first "mission cycle" drifts further and further away from our Mishnah and our topics of discussion, and deals with a wide-ranging list of issues.

What appears to be the sequel to the opening Mishnah of the 2nd perek somehow finds its way into the middle of the discussion of מחשבה הפוסלת

The Chafetz Chaim restructures yet another sugya in his Likutei Halachos, this time just to allow the exegetical process to unfold in sequence.

Another example of the Gemara's methodical treatment of issues as they arise, not necessarily in order of their centrality.

The Gemara unexpectedly stumbles upon a fundamental distinction between the respective natures of the inner and outer Mizbeiachs.

Understanding our sugya based on the background from the 3rd Perek

Background from the 3rd perek which is necessary for understanding our Sugya