Projecting Lecture Notes

I apologize if this question has been answered thoroughly, but I didn't have much luck with a search.

I am a math professor and project handwritten examples in addition to lectures. I am looking for a tablet that will allow me to easily write notes that project live. Ipad seems to have a lot of great features, but I've seen mixed reviews for its capability to annotate while projecting.

Essentially, I just need an app that would allow me to write with a stylus and project as I write.

Is there something that does this and does it well?

Thanks for any input or reference to another thread.