(I also gave her a preview of the Modern deponent verb amar / yagid - "he said / will say" - but only so that she'd be prepared for it in the, well, future. I told her about doing the future tense with prefixes, but didn't get into the details of the grammar, because then you've gotta talk about Hiph'il with a Peh Nun, and, well, there'll be plenty of time for that.)
This is why I believe there can be, and should be, a shift in emphasis in Hebrew instruction toward teaching Biblical and Modern Hebrew concurrently. They're not two different languages - it's not like, say, Modern English and Anglo-Saxon. There are a few differences in the details (like saying "yagid" in Modern instead of the Biblical "yomer" for "he will say"), occasional oddities (like the vav consecutive in Biblical) and a few things the Modern grammar handles differently (like possessives with "shel-") but the large majority of the basic language is the same.
Traditionally people learned Biblical Hebrew because they wanted to study the Bible or the traditional Jewish texts, and Modern Hebrew because they wanted to visit, or emigrate to, Israel. But an integrated classical/conversational approach would give the learner access to the Jewish world as a continuum, from ancient to modern.
I've been reading Hebrew for most of my life, from when I first started wrestling with the grammar with Rabbi K. over Weingreen's book at age 15. I started tackling the modern Israeli form a few years ago, and while I wouldn't say I'm fluent, I do think I can claim a basic competency. I have tutored Hebrew informally a few times, but not on an ongoing basis.
Anyway, hopefully I'll get a chance to find out what works and what doesn't, because I am planning to spend a couple of weeks teaching Hebrew in Uganda this October.