How Do You Differentiate Archea and Bacteria in the First Week of High School Biology???

I have a long standing interest in biology education -- I seriously considered it as at least a career to explore -- but now I really have skin in the game.  TNG just executed a schedule move that will defer his biology this year to the second half of the term, but I also have a niece who is taking AP Biology at her STEM high school.  Even in his short time in biology class, TNG has succeeded in asking for homework help that has me scratching my head.
As soon as TNG brought his textbook home, I gave it a bit of a lookover.  One immediate check was how it discussed classifying organisms; a few years ago the end-of-year biology unit was using a textbook teaching the 7 kingdom system, which has been obsolete for easily 30 years.  Admittedly, I was taught it too back in the late '80s, which reflects both the appalling slowness of education to catch up to major discoveries in biology and the challenge of dealing with a field that keeps having major discoveries.  

Consider other subjects. My college 2-semester physics class effectively ended at the end of the 1800s with Maxwell's Equations.  Intro chemistry is all pre-WW2, and only a few topics in my organic chemistry sequence were any later than that; host-guest complexes were touched on and we learned some basic NMR analysis.  In contrast, my son's book covers PCR (1980s) and probably should at least touch on RNAi (1990s) and CRISPR (2010s).  

Or consider all the wrong things I've learned in biology lessons over the years.  In kindergarten I was taught we have 4 basic tastes and the tongue mapped them.  As an undergrad we were told that alternative splicing was a rare event, and in graduate school mammalian cloning still looked like an impossibility.  Rewriting textbooks is the rule, not the exception in biology.

Making textbook writers life even more difficult is that virtually every "rule" in biology has an exception.  Even some of the most fundamental rules aren't quite universally true.  Biological systems work to maintain homeostasis -- but does this really apply to specialized structures such as spores?  Even defining life challenges us, as edge cases such as prions, viruses and plasmids frustrate clean category drawing.

But going back to my title, one of the homework assignments was to differentiate the three domains of life.  Eukaryotes are easy; they have a nucleus but the other two don't.  But without knowing a lot of deep technical detail, how do you distinguish bacteria from archea in a satisfying manner?  The book gave out the fuzzy "many archea are extremeophiles", but I was under the impression there is no shortage of known non-extremophile archea, plus there are plenty of bacteria that live in insane conditions. 

If I were teaching the course, what would I do?  One idea might be to say "only later in the course will we see why".  An adventurous route might be to introduce the idea of molecular phylogenies very early.  While this might at first blush seem very technical, it is after all the dominant mode of taxonomy these days, especially for microorganisms. Also, I believe one can explain the idea very easily, and it certainly lends itself to a computer-aided laboratory exercise.  That would be a good way to get ideas about DNA and evolution out front as well.

But perhaps I'm missing something.  Perhaps there is a simple explanation of the difference between bacteria and archea that any school-age child can understand that I'm just clueless about.  If so, please share it in the comments!