When you say "cans", I assume you're talking about aluminum cans, and not old iron/tin cans, right?
Because if you mean aluminum cans, then welcome to the harsh cruel reality of metal detecting: certain items share conductivity TIDs. An entire aluminum can, can sound like a quarter or half or whatever. Of course you might be able to discern that it is a larger signal (size wise) than a coin-sized target.
But if you mean iron/tin cans, then you are doing something wrong. You should easily be able to pass rotting iron cans no problem, with your discriminator.
As far as "pop tops" (I assume you mean pulltabs) then ... again ..... welcome to the harsh cruel reality of detecting. Pulltabs and related aluminum sized objects read all over the mid-scale of the detector's TID. Like in the range of nickels, gold jewelry, certain tokens, etc... You can pass them, and go strictly for high conductive copper and silver coins, if you want. But this would start to falter if you're talking very deep targets, since deeper silver and copper coins waffle around on the TID's.
Based on the pix you give (a jungly forest bottom terrain), it appears you're going to have stuff be really deep in the underbrush crud. And based on the description of cans and poptops all over (sounds like kids go there to party), I'd say you need to find a better place to hunt. One-room school house sites are often a "bust" anyhow. Prior to the 1920s, kids just didn't carry change. So unless the school house was used for other adult purposes (grange hall, church, stage stop, etc...) my experience is that most 1 room school houses aren't that productive. And if I started to hunt one full of junk like you describe, I'd just cross that off my list of places to reconn.