Describe how the Eastern Roman (Byzantine) Empire preserved and adapted Roman government, law, and Greek culture for nearly a thousand years after Rome fell.
While the west collapsed, the eastern half of the Roman Empire did not just survive -- it thrived for nearly a thousand years more. Historians call it the Byzantine Empire, named after Byzantium, the old Greek city that Emperor Constantine rebuilt as his new capital in 330 CE and renamed Constantinople (today it is Istanbul, Turkey). Constantinople sat on a narrow strait between Europe and Asia, so every ship trading between the two continents had to pass its harbor -- a location so valuable, and so well defended by massive walls, that the city survived siege after siege for centuries.
The Byzantines still called themselves Romans, but their world looked different: they spoke Greek instead of Latin, and their branch of Christianity became what is now called Eastern Orthodox. Emperor Justinian (ruled 527-565 CE) tried to reconquer lost western lands, but his longest-lasting achievement was legal, not military: he ordered scholars to collect and organize centuries of tangled Roman law into one clear code, the Corpus Juris Civilis. That code shaped the legal systems of many European countries for centuries afterward -- when a modern lawyer talks about "civil law," the idea traces back to Justinian's project. His wife, Empress Theodora, was a powerful advisor who reportedly convinced him to stand firm during a riot that nearly cost him his throne.
Mastery looks like: They can explain how Constantinople's location and Justinian's legal code helped the Eastern Empire outlast the west by nearly a thousand years.
Common stumbles: Assuming "Rome fell" means the whole Roman world ended in 476 CE, instead of realizing the eastern half remained a major power for another millennium.