Look into the capabilities of your switches. If they support 802.1q VLAN
trunking, then you can create a teacher's VLAN and a thin client VLAN.
(VLAN means Virtual LAN, and is like having a separate subnet. Packets
sent out over a VLAN trunk have a special tag in front indicating the
VLAN.)
With proper configuration of your router (assuming it also supports VLANs),
it can route between the subnets. By the way, you could even use a Linux
box as a router between the two VLANs. Linux has VLAN support, I believe,
or you could use two network cards and not even have to worry about VLANs.