Parshas BaMidbar - counting shevatim and yichus of shevatim

Post-day off tiredness has hit.... trying to recover and get back into the swing of things. My son came home this week with a dvar torah to explain why the expression 'bnei Naftoli...' is used, as opposed to the term 'livnei...' (lamed at the beginning) used by the count of all other shevatim. His Rebbe explained that Moshe knew the sum total of klal yisrael, but needed to determine how many people were in each sheivet. To do so, all Moshe should have had to do is count 11 of the shevatim and then subtract that from the total. Nonetheless, Moshe counted this last sheivet, which was Naftoli, as well. II am stumped: how do we know Moshe knew the sum total, and where would he have known that figure from? The fact that this count matches the total of the earlier count is a chiddush, not a simple assumption!? I tracked the makor of this vort back to the Chasam Sofer, who offers no other elucidation. He does say a different pshat which works much easier - Moshe was trying to determine the yichus (as opposed to their exact number) of each member of klal yisrael, which was clear once 11 of 12 shevatim were counted. Any ideas???
One other parsha note. In our parshas Emor discussion of the issue of yichus, we developed the theme that yichus based on patrelineal descent is a din even for bnei noach; the chiddush of am yisrael is matrelineal descent, starting either from mattan torah or from Avraham (see machlokes Ramban/Chachamei Tzorfas end of Emor). The Kedushas Levi interestingly writes exactly the opposite: with respect to the umos ha'olam, yichus follows the mother (he says this is the sod of the name umah - the shoresh is eim, mother), but Am Yisrael after mattan Torah followed the yichus of the father. This is the meaning of 'vayisyaldu al mishpechosam l'bais avosam' - it was a new birth because a new order of lineage was introduced with mattan Torah. Make of it what you will.