Hey there!
There are three types of cloud computing – Infrastructure as a Service (where the user controls everything about a service, often providing storage space, networking features, and computers), Platform as a Service (where the user controls less than an IaaS user would but is given the tools to edit their programs and applications with a built-in infrastructure), and Software as a Service (where the user uses pre-established infrastructures and applications and only controls the way they use them instead of maintaining them).
Because the program is completely third party and cloud-based, this is an example of a Software as a Service. The teachers will only be utilizing the application to record grades and such and everything else will be controlled and maintained by the third party.
Hope this helped you out! :-)