Explain how Inca road-building, terrace farming, and record-keeping solved the challenges of governing a huge empire across mountainous terrain.
The Inca Empire, called Tawantinsuyu ("the four regions") by its own people, expanded rapidly under the ruler Pachacuti starting around 1438 CE, eventually stretching over 2,500 miles along the Andes Mountains from modern Ecuador to Chile -- one of the largest empires in the world at the time, built almost entirely on foot and llama-back, without wheeled vehicles.
Andean geography is extreme: steep mountains, thin air, and little flat land. The Inca solved this with engineering rather than avoiding the problem. They carved terraces -- flat farming steps -- into mountainsides, which controlled erosion and created enormous amounts of new farmland at different altitudes, letting them grow different crops depending on elevation. They built the Qhapaq Nan, a road system of more than 24,000 miles including rope suspension bridges across deep canyons, allowing runners to relay messages across the empire remarkably fast for foot travel. And with no alphabetic writing system, Inca officials tracked tribute, population, and resources using the quipu, a system of knotted and colored cords that could record numbers and categories precisely enough to administer millions of people.
Mastery looks like: They can explain how terraces, the road system, and the quipu each solved a specific challenge of governing a huge empire across mountainous terrain.
Common stumbles: Assuming a civilization without alphabetic writing had no real record-keeping, or underestimating the scale of the Inca road system.