If you want some cultural/historical context for the direction/style of some of the episodes, I'd recommend checking out Mad Men Unbuttoned. It's a light touch in most cases (meaning it's not super in-depth history lessons), but kinda fascinating and just confirms the thought and care put into the show.
Find a used copy of Natasha Vargas-Cooper's "Mad Men Unbuttoned: A Romp Through 1960s America", which you can order for $1.55 on Amazon. It is formatted exactly like your assignment for your class: each section spotlights a particular historical or cultural event from the '60s and discusses how it was depicted on the show.
(ETA: the book only covers the series through the first three seasons, but it's still an amazing resource. And some of of Vargas-Cooper's blog entries which formed the basis of the book are still online.)