Insulating concrete basement floor

I have a basement floor in an old house - circa 1950's. I have to cut open the floor to move some plumbing around for a new bathroom and I'm researching different methods / techniques to use when pouring the new floor (I'll be laying down ceramic tile eventually). My current plan is as follows:
1) Lay down a layer of gravel over the existing tampered excavated area. 2) Lay down a polystrene foam insulation. 3) Pour concrete with a rebar mesh to re-inforce (I'll also need to paint a bonding agent down on the old concrete floor edges to ensure the new floor bonds to the old).
Is some of this overkill ? Although the rest of the concrete slab is still the original - is there any side-effect of using the foam insulation on only a portion of the floor ? Or is it useless unless it spans the entire area of the houses concrete slab ?
thanks in advance for any answers.
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So, you're cutting new "trenches" thru the concrete floor, doing the new plbg, then replacing the crete
I.ve done this and seen it done and I'll go along with #1 above, forget #2& 3 unless theres foam or a vapor barrier (plastic sheet) under there already. If not, there isnt much point in dropping in narrow trench strips of foam IMO. Just wet down the cut or broken edges for a bond, this stuff isnt going anywhere since you're tamping the fill before pouring.
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