The other day, I came into class and had about five things to do at once before class could start: (1) set up the laptop and equipment (screen) so students could give presentations; (2) give out handouts; (3) get books and other materials out of my bag; (4) answer the questions of the nervous, hovering student who was about to do a presentation; (5) put information on the board. As I was doing all this, going from one to the other (writing on the board while the projector warmed up), another student, from his seat, started asking, "When are you going to collect our assignments that are due today?" "I have a plan," I said, and kept on writing, etc., to which another student stage-whispered to the first one, "and you're messing it up." They laughed.
Having that much go on in the minutes before class is a little unusual, but unless you're like a professor I once had who'd walk quietly into a room with his book, no notes, and launch immediately into a discussion of the day's reading without even a "Hello," there's some preliminary set up--staging?--before class can start: you have to get out the book, marker or chalk, notes, papers you intend to give back, and so on, and this takes a little time. Packing up takes a little time, too, because you want to clean the board and get out of there before the next class comes in.
The multitasking I like is the kind that occurs when students want to linger and talk about what we've just been saying in class or walk back to the building to keep the conversation going. The multitasking I'm lousy at, though, goes something like this: I'm frantically stuffing books, papers, computer, and the rest into a bag to get out of the classroom, and a student comes up and says, "I have to be absent on [a day a month away]; what will we be doing?" or "Can I meet with you on X day at X time?" or anything that involves something I have to remember. The same thing happens some times when I'm ready to start class and a student wants to come up and discuss some projected absence or an appointment.
Note to students: The pencil is my memory stick. If you don't see a pencil in my hand so that I can write down what you're telling me, the chances are good that I won't remember it.