Contrast Spartan society, government, and values with Athens, focusing on the agoge, the helot system, and Sparta's mixed government.
While Athens experimented with democracy, the polis of Sparta, in the region of Laconia, built one of history's most disciplined military societies instead. Spartan government mixed several parts: two kings ruling jointly, a Council of Elders (Gerousia) of older citizens, an Assembly of citizens, and five annually elected officials called ephors who could even overrule a king. Sparta's economy depended on helots, the conquered population of neighboring Messenia, forced into state-owned servitude and vastly outnumbering actual Spartan citizens -- a constant fear of helot revolt shaped nearly every Spartan institution.
To maintain a permanent, ready army against that threat, Spartan boys entered a harsh state-run training system called the agoge around age seven, emphasizing discipline, endurance, and obedience over individual comfort or expression. Unusually for the era, Spartan girls also received physical training, since Spartans believed strong mothers produced strong warriors. Spartans valued equality among citizen-warriors, simplicity, and suspicion of foreign luxury and ideas -- values so distinctive that the English word "spartan" still describes anything plain and without comfort. Sparta and Athens were often rivals, though they allied against a shared threat in the very next lesson.
Mastery looks like: They can accurately contrast Spartan and Athenian government, education, and values, citing the agoge and the helot system specifically.
Common stumbles: Assuming Sparta had no government structure beyond kings, or picturing Athens as free of enslaved labor by comparison.