Learn Turkish: Öğrenci kaseti bir kalem ile sarıyordu. - The student was winding the cassette with a pen.

The root verb is sarmak (to wind or wrap). First, we drop the -mak and add the present continuous suffix -ıyor to get sarıyor (is winding). Then, we add the past suffix -du to make it "was winding". So, sar + ıyor + du = sarıyordu.

Why is there an -i at the end of kaseti?

That is the definite accusative case. Because the student is winding a specific, known object ("the cassette"), we add the -i suffix to kaset to show it is the direct object of the action.

Could I write kalemle instead of kalem ile?

Yes, absolutely! ile means "with". You can write it as a separate word (bir kalem ile) or attach it directly as a suffix (bir kalemle). Both are grammatically correct and mean the same thing, but attaching it is much more common in everyday spoken Turkish.

Does sarmak always mean "to wind"?

It has a few closely related meanings! sarmak generally means to wrap, roll, or wind. You will often see it used for wrapping a gift, rolling food (like a dürüm), or, as in this classic 90s example, winding a cassette tape.