I'm still hammering this out, but it works as-is:

@echo off
rem Simple script to map a drive using the new IP provided.
echo Enter final octet:
set /p OCTET=

net use z: \\10.0.100.%OCTET%\c$ /user:inside\<username> <password>

I'd like the octet entry and the echo to be on the same line, but aside from that, working as advertised.