Distinguish enumerated, reserved, and concurrent powers, and trace how the balance of federal-state power has shifted over American history.
Federalism divides political power between a national government and state governments, each sovereign in its own sphere rather than one simply controlling the other. The Constitution sorts power into three categories. Enumerated (or delegated) powers belong only to the national government -- coining money, declaring war, regulating interstate and foreign commerce, and running a postal system, mostly listed in Article I, Section 8. Reserved powers belong to the states under the Tenth Amendment -- running elections, regulating marriage and family law, overseeing most education, and policing most crime. Concurrent powers are shared by both levels at once, such as the power to tax, to build roads, and to operate courts. Where state and national law directly conflict within an area the Constitution assigns to the national government, the Supremacy Clause (Article VI) settles the matter: national law wins.
The balance between national and state power has never been fixed -- it has shifted, sometimes dramatically, across American history. Early on, states' rights carried enormous weight; the Civil War and Reconstruction shifted real power toward the national government, especially through the Fourteenth Amendment. The Great Depression pushed the balance further still: the New Deal of the 1930s relied on a broad reading of the Commerce Clause to justify sweeping new national programs, a reading the Supreme Court eventually accepted. The Civil Rights Movement of the 1950s-60s again used national power, courts and Congress, to override discriminatory state laws. More recently, some Supreme Court decisions, including United States v. Lopez (1995), have found limits to Congress's commerce power, part of a trend some call "New Federalism." This balance is genuinely, actively contested today: some argue a strong national government is necessary for consistent rights and standards across all fifty states, while others argue that keeping more power at the state level lets states function as "laboratories of democracy," testing different policies and better reflecting local preferences. Both positions have serious, long-standing support in American political thought, and the right balance remains a live question in courts, Congress, and elections.
Mastery looks like: They can correctly sort a given power as enumerated, reserved, or concurrent, explain the Supremacy Clause, and state the strongest argument on both sides of the ongoing national-versus-state power debate.
Common stumbles: Assuming federalism debates have one obviously correct answer, or forgetting that concurrent powers exist and trying to force every example into a strict national/state split.