Your teacher meant acts, not scenes. Othello has five acts, but each act has many scenes, some of them very short without notable quotes. Here are quotes from each act.
1. Iago: "But I will wear my heart upon my sleeve
For daws to peck at: I am not what I am." Act 1, Scene 1
This is a great quote from one of literature's greatest villains: Iago. When someone wears his heart on his sleeve, he shows his emotions outwardly, so all know why he is acting the way he is. But Iago is wearing false emotions, so dead that crows could eat them as they eat dead flesh. He wants others to see him one way, but not the way he really is.
2. Iago: "for whiles this honest fool
Plies Desdemona to repair his fortunes
And she for him pleads strongly to the Moor,
. . . .
And by how much she strives to do him good,
She shall undo her credit with the Moor.
So will I turn her virtue into pitch,
And out of her own goodness make the net
That shall enmesh them all." Act 2, Scene 3
Iago here reveals his plan to destroy Othello. Iago has already gotten “this honest fool” Cassio drunk and demoted. He has convinced Cassio to fix his demotion by pleading his cause through Desdemona, Othello’s young, beautiful wife. He has also gotten Desdemona to argue Cassio’s case to Othello. Iago will try to make Othello believe that Cassio and his wife are lovers. Iago knows that Desdemona is empathetic to Cassio’s misfortune and that her motives are beneficent, but he hopes to make Othello believe otherwise.
3. Desdemona: “my noble Moor
Is true of mind, and made of no such baseness
As jealous creatures are, it were enough
To put him to ill thinking.” Act 3, Scene 4
Iago has talked his wife into stealing Desdemona’s handkerchief given her by Othello. Desdemona has been looking for it and is in a dialogue with Emilia. Innocent Desdemona tells Emilia that Othello is not a jealous person and it’s a good thing because if Othello were jealous, her losing the handkerchief might get him thinking negatively.
4. Iago: “As he shall smile, Othello shall go mad;
And his unbookish jealousy must conster
Poor Cassio’s smiles, gesters, and light behaviors
Quite in the wrong.” Act 4, Scene 1
The evil Iago is trying to pull off one of his tricks. He has convinced Othello to stand out of earshot while Iago talks to Cassio about Desdemona. If Cassio acts familiar, that will prove that he and Desdemona have something going. However, Iago is really asking Cassio about Bianca, a prostitute who is found of Cassio. His trick works and Othello becomes jealous.
5. Othello: “Then must you speak
Of one that loved not wisely, but too well;
Of one not easily jealous, but, being wrought,
Perplexed in the extreme; of one whose hand,
Like the base Judean, threw a pearl away
Richer than all his tribe;” Act 5, Scene 2
This speech occurs after Othello has killed Desdemona in a fit of jealousy and after Iago’s treachery has been revealed. He is talking to Lodovico who is there to arrest him. Othello claims that he is not a jealous person, but once made jealous, his rage was uncontrollable. He realizes that Desdemona was indeed innocent, a pearl that he threw away.
I hope these quotes help you. My reading of Othello was from Literature and Society: An Introduction to Fiction, Poetry, Drama, Nonfiction by Pamela J. Annas and Robert C. Rosen, Pearson Education, Inc. 2007. I used this text in LIT2480, which I taught last semester.