Trace the course of the Korean War as the first hot conflict of containment, and evaluate the domestic Second Red Scare even-handedly against real evidence of Soviet espionage.
Korea, freed from Japanese rule in 1945, had been divided at the 38th parallel into a Soviet-occupied north and an American-occupied south, each backing a rival government. On June 25, 1950, communist North Korea invaded the South; Truman committed American forces under a United Nations mandate (the Soviets, boycotting the UN at the time, could not veto it) without asking Congress for a formal declaration of war -- an important precedent for future presidential military action. General Douglas MacArthur's bold amphibious landing at Inchon in September 1950 reversed North Korea's advance dramatically, but when UN forces pushed north toward the Chinese border, China intervened with massive force that November, driving the front back to roughly where it had started. MacArthur publicly pressed for expanding the war into China, even suggesting nuclear weapons; Truman, insisting on civilian control of the military and a limited war, fired him in April 1951. Fighting stalemated near the original 38th parallel, and an armistice -- not a peace treaty -- ended the fighting in July 1953; Korea remains formally divided, and technically still at war, to this day.
At home, fear of communist subversion intensified alongside the war. The House Un-American Activities Committee investigated supposed communist influence in Hollywood starting in 1947; the "Hollywood Ten" refused to testify, citing the First Amendment, and were jailed for contempt and then blacklisted from the industry for years. Senator Joseph McCarthy's February 1950 speech claiming to hold a list of communists inside the State Department launched a years-long campaign of accusations often built on thin or nonexistent evidence, ruining careers through guilt by association; the televised 1954 Army-McCarthy hearings finally exposed his bullying tactics to a national audience, and the Senate formally censured him that December. Julius and Ethel Rosenberg were executed in 1953 for conspiracy to commit atomic espionage; declassified Soviet cable intercepts released decades later, in 1995, confirmed Julius had indeed spied for the Soviets, while historians still debate the extent of Ethel's own role -- both things are true at once: real Soviet espionage occurred, and the broader anti-communist crusade also violated many innocent people's civil liberties through unsubstantiated accusation and blacklisting.
Mastery looks like: They can sequence the Korean War's major turns (invasion, Inchon, Chinese intervention, stalemate), explain MacArthur's firing, and hold both truths about McCarthyism -- real espionage and real civil-liberties violations -- at once.
Common stumbles: Assuming Korea ended in a clear victory or a signed peace treaty, rather than an armistice that left the peninsula divided to this day; or resolving McCarthyism into a single simple verdict instead of holding both realities together.