Yes. My advice is a few things. You can start from a template, save as .docx, open that .docx to see if Pages can import and export it (then close the .docx). However (see below) you should ask a friend to open the document on a Microsoft computer before sending it to the teacher. Another way: Export to PDF, send PDF to teacher (looks perfect on Microsoft but cannot be edited by Word). You might need a computer that runs the same Microsoft. I'll try to justify those remarks as so:
Yes, well your teachers also cannot export .pages documents to you correctly. Infact I believe there is some federal policy concerning protecting students and teachers in these situations (which i do not list).
The best choice for BOTH is to save to PDF (Adobe) and give your teacher the homework.pdf, because it's always page perfect (and perfectly printed) viewed on any device, and seldom if ever a problem going in between ms/mac, modernly.
If the teacher refuses to accept PDF format, you can say the teacher is "forcing you to to purchase a particular product (a specific version of microsoft word infact) without having said this in the "course description" for the class. (they can't do that, if purchases are required they must be agreed before the student begins the class)
PDF and X of OS X came from Xerox Star (ie 6085) Workstation (internet transparent desktop and Xerox printing) from Palo Alto California labs in the 1970's. PDF has always been page perfect, and though there has been version changes, the changes are much less an issue than with Word and Pages. Only Adobe editors can use .pdf as a "native" edited format (others ca export to it but don't know how to import it and can't import their own export).
PDF is by far the most widely used format for publishing books, engineering documents, and more.
-------------------
#1 You can use Pages templates. They export/import to Word pretty good. There are reason why they do (they formatting style chosen). Likely you do not want to be a style/format doc editor wiz (ie, to take a class for doing so). Your choices there are PDF or to be forced to buy a Microsoft product**
#2 Your best move is to be quiet and pleasant as possible with the instructor. Say you've been working on it and you wish to send a PDF in addition to a .docx, incase there is still a problem. Instructors are infamous for downgrading students they have a prejudice against (ie, politics) and computer software does fall in the area of political for some instructors (or just "annoying students that make them think"). My advice is be careful none of all of it may be "fair".
** There are a few choices as to how to run Word: to buy Word for iMac and hope it's the same version of Word, to emulate MS OS, to have dual boot and boot into Windows (you bought), or to buy a cheap MS laptop which has Word pre-loaded free. The fact is any one of these might work or end up being a headache, the cheap ms laptop aside.