How do you know when he;s finished?
When they stop eating
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Sometimes there is some body language like turning the head away and looking elsewhere, it's not always obvious.
Mine rarely drops any food by accident but when he is finished eating he begins to purposely drop it over the side of his high chair. I've spent a couple of months explaining to him that this is unnecessary and he is just starting to get the idea so now he pushes his plate away ever so slightly (oh yes, we progressed onto plate and bowl eating rather than directly off the tray) and if I am quick I catch it, otherwise the lot would go over the side lol
It is still hard to tell though, he sometimes looks finished and then just as I'm about to clear up he launches into round two and polishes off another entire meal-worth. I do not know where he puts it!
You can teach a sign for finished, either an official sign language one or your own home sign. If you do it each feed LO will likely pick it up.