Define your vlans on the managed switch.
Vlan1 - Dept 1 and so on
Extend a cable from the Managed switch to the unmanaged switches in the department.
Place this port on the managed switch depending on the department (say port gets conencted to dept2 then put port 2 in vlan2)
The only problem with your setup is the limited mobility the user will have.
HTH, rate if it does
Narayan