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gwern comments on Expecting Short Inferential Distances - Less Wrong
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A plastic bottle out of the trash. It's transparent but flexible and almost weightless. See how well the lid has been made? It makes a water-tight seal.
It might be the most valuable object in Greece.
And then when you've got his attention, show him decimal notation.
And stirrups for his horse. And lances.
Once he's hooked, show him why things float. And how a ball rolling down an inclined plane moves 1, 4, 9, 16 as it accelerates.
Show him Cartesian geometry. And how to play go with lines scratched in the ground and coloured stones. Make a recorder and play him some songs.
He'll teach you Greek.
Show him how to send messages using flashing mirrors. Show him Playfair's cipher. Perspective drawing. How to make a magnifying glass. Newton's cradle. Make a model boat out of bronze.
I suspect in a day in Ancient Greece, you'd see so many easily solved problems that my list would look naive. You don't need modern technology. You need the things that were discovered just after the mediaevals recovered what the Greeks already knew.
This is one of the more interesting approaches to the Connecticut Yankee in King Arthur's Court (as I dub this species of thought problem) - that you don't need any special preparation because your basic background means that you'll spend the rest of your life in the past rushing around yelling 'don't do that, you idiot, do it this way!'
Diplomacy might actually be the best preparation.