1. Feminist Criticism
In her essay "Representing Ophelia: Woman, Madness and the Responsibilities of Feminist Criticism," Elaine Showalter asks if Ophelia is "indeed representative of Woman," and if her madness stands "for the oppression of women in society as well as tragedy." This question is certainly not the only one that feminists would be interested in exploring, but it is one of the central concerns of critical scholarship over the years. Consequently, scenes in which Ophelia plays a significant role, although limited, provide some of the best opportunities to apply the feminist lens. Three scenes in particular would be appropriate:
a. Act 3, Scene 1 - From Ophelia's entrance after Hamlet's soliloquy to Ophelia's exit
b. Act 3, Scene 2 - From Hamlet's initial exchanges with Ophelia before the play begins to Hamlet's line "As woman's love."
c. Act 3, Scene 5 - Ophelia's first and second set of lines (she leaves stage and returns again at the end of the scene)
Feminist criticism also has carefully examined Gertrude's role in the play. The scene that would be most appropriate for exploration is Act 3, Scene 4 (when Hamlet confronts Gertrude in her private chamber).

2. Psychoanalytic Criticism
In her essay "Man and Wife is One Flesh," critic Janet Aldeman asserts that at the center of the tragedy of Hamlet lies the problem of Hamlet having to take on the qualities of the father's name by "killing off a false father." This problem is exacerbated because the two fathers (Old hamlet and Claudius) keep "threatening to collapse into one another, annihilating in their collapse the son's easy assumption of the father's identity." Aldeman's assertion suggests that the scenes in which Hamlet reveals his attitudes towards Claudius and Old Hamlet would be rich areas of exploration for this lens. The following scenes contain references to this conflict:
a. Act 1, Scene 2 - Hamlet discusses his sullied flesh and Claudius' actions).
b. Act 3, Scene 2 - The entire play-within-a-play, during which Hamlet acts as something of a chorus
c. Act 3, Scene 3 - Hamlet explains why he must wait to kill Claudius
d. Act 3, Scene 4 - Hamlet confronts Gertrude over her relationship with Claudius
e. Act 4, Scene 3 - Hamlet insults Claudius
All of these scenes will invite exploration through the psychoanalytic lens. There will no doubt be some groups who attempt to analyze the Oedipal implications of Hamlet's struggle.

3. Marxist Criticism
Marxist critics assert that texts often contain two discourses: one that reflects the ideology of the "official" or ruling culture, and one that reflects popular or traditional culture. In his essay "Funeral Bak'd Meats," Michael Bristol looks at how the "second world" of commoners, were mainly concerned with "the body, with eating, with sex, and with death." He contrast the discourse of the royals with that of the commoners (such as the gravediggers) to see how these two worlds reflect their station. Scenes that could be explored through the Marxist lens, with this idea in mind, include:
a. Act 2, Scene 2 - Hamlet confronts Rosencrantz and Guildenstern
b. Act 2, Scene 2 - Hamlet confuses Polonius and then welcomes the Players
c. Act 4, Scene 5 - Laertes confronts Claudius
d. Act 4, Scene 7 - Claudius discusses the rules of the official culture with Laertes
e. Act 5, Scene 1 - The gravediggers discuss law and the afterlife

4. Archetypal Criticism
Analyzing Hamlet through the archetypal lens yields a number of interesting possibilities. The scenes that you have students analyze depends on the specific archetype you wish them to explore. The following is a partial list of possible archetypes you could assign:
a. Gertrude could be viewed as The Femme Fatale
b. Ophelia could be viewed as The Innocent
c. Hamlet could be viewed as The Avenger
d. Claudius could be viewed as The Villain or Usurper (unlawful ruler)
e. The Ghost could be viewed in comparison with other western ghosts