The router sends nothing between
subnets. The package has destination IP. For this IP address within the network segment sends a broadcast ARP request.
Anything with a large network will not happen. For this and there are the cached MAC addresses, switches instead of hubs, routers. Show the teacher at least an article in Wiki https://ru.wikipedia.org/wiki/ARP
If the teacher is very high, you can take a book of Tanenbaum or Cisco ICND.