Android software to write on anything? I currently do not own a smartphone or a tablet, but am interested in getting one or both that could help me with the following:

I am a teacher. I regularly have notes displayed on an overhead projector AND simultaneously write on a chalkboard. I would like to be able to write (using a stylus) directly onto the screen on top of what I am displaying.

I usually display notes in PDF or Powerpoint. If it would be possible to then save the written notes on the file would be a major plus, though not necessary.

Is this possible with Android devices – and if so, how could it be done?
This is definitly possible. There are even multiple approaches I could think of:


Screen mirroring
Some devices already ship with this functionality. My sister e.g. just got her new Samsung Galaxy S4 mini which I helped her to set up, and I noted a related "toggle" in the notification bar to switch "mirroring" on/off. Also, newer builds of the custom ROM cyanogenmod IMHO offer this feature. Especially via HDMI, this also should be supported (maybe requiring an additional app).
Remote Tools
iDev already mentioned Team Viewer in his comment. While the specific component to remote access the Android device itself only exists for few devices (the list might grow, some time given), there are several similar/comparable solutions, as VNC.
Other means
There might also exist specific "whiteboard apps", designed for exactly this purpose. I don't know such one (but I didn't explicitly check for), but searching the Playstore cannot hurt (to ease this, as the "official Google Play website is quite restricted in its search capabilities since its relaunch, I recommend using AppBrain for searching; it's an alternative "web frontend" to Google Play).