Within Baptista's household, Lucentio (disguised as Cambio) and Hortensio (disguised as Litio) instruct Bianca. The two squabble for Bianca's attention, Hortensio wanting to teach her music while Lucentio wants to teach her philosophy. Bianca tells Hortensio to tune his lyre while she listens to Lucentio's lecture.
Lucentio and Hortensio's teaching is really just an excuse to spend time with Bianca and attempt to convince her to marry them—to "teach" her to love them.
While pretending to teach Bianca Latin, Lucentio reveals his true identity to Bianca and tells her that he is in love with her. Hortensio says his instrument is ready, but Bianca pretends it sounds out of tune so that she can finish talking to Lucentio. She whispers to Lucentio that she doesn't know him and thus doesn't trust him. She tells him not to be presumptuous with his love, but also not to despair.
Lucentio reveals his true identity to Bianca, but remains disguised for most of the play's other characters. But even though Bianca now knows who Lucentio is, she still does not truly know him (as she herself remarks) and is suspicious of how genuine the real Lucentio actually is.
Bianca declares that she is ready for her music lesson now, and Hortensio sends Lucentio away. Under the pretense of teaching Bianca musical scales, he encourages Bianca, "take [Hortensio] for thy lord," (iii.1.78). A servant interrupts and tells Bianca that she must help Katherine prepare for her wedding. Bianca, the servant, and Lucentio leave. Hortensio notes that Cambio (really Lucentio) is in love with Bianca and thinks to himself that if Bianca gives in to the affections of a lowly tutor (he doesn't realize that Cambio is really Lucentio), perhaps she is not for him.
Bianca cleverly uses the music lesson to bring her meeting with Lucentio to an end. There is perhaps more to her than a simple, obedient, pretty woman. Hortensio is upset by the prospect of Bianca loving someone of a lower social standing—never considering the fact that he himself is pretending to be of a lower social standing and perhaps someone else is as well—revealing how important social status and wealth are to his conception of marriage. He only wants a wife who wants a rich nobleman.