No need to make it complicated: what about this...
Just scribble a rectangle on a piece of paper, and say "there are 100 billion stars in our galaxy"....
Then, color off (let's say) 1/3 of the rectangle, and say "only one third of those are the sort of star that could have life, so that's blah billion"
Then, color off (say) 9/10ths of that box, and say "we believe about 90% of those have planets - so that's blah billion"
Then, color off (say) 1/20th of that box, and say "of those with planets, it seems that about 1 in 20 have Earth-like planets. Now we're down to blah billion..."
and so on.
(Note: the Drake equation has a number of fairly silly terms relating to "nuclear war!", which were added as political sops in that era; suggest ignore these unless you want to sound 90 years old!)
So just scribble a box or draw a line on a piece of paper ... or maybe use "a bag of marbles" as the other answer suggests.
Just BTW there is in fact an entire documentary (I noticed it on "Netflix") called "The Drake Equation" which does exactly what you say...
.. it is not really very good as I remember. I think the guy simply draws a line in the ground, to do the "fractions" demo, you know? (ie, they just erase more and more of the line). It doesn't need to be more complicated than that.
It's worth noting that the Drake equation simply points out:
(i) if you multiply those three or four fractions together, you get the number of civilizations in the galaxy. Which is self-evident.
but, the whole point is
(ii) we have utterly no clue - not even vaguely - what most of the fractions are,
You could say it's a written formula, which, helps clarify our thinking on, something we are utterly clueless about. So rather than just vaguely saying "we're utterly clueless," we can speak more clearly about the nature of our cluelessness!
(iii) very admirably, the issue of "How many stars have planets?" ... one could say that issue has been somewhat settled these very years, as we speak - that's great.