How to penalize students who copy each other but don't realize they have plagiarized? I gave my students an opportunity to rewrite one of their papers for extra points. As I was grading, I realized that two papers were almost identical. They had a similar structure, organization, and presented ideas in a similar manner. I asked the students about plagiarism but they denied it. Since it was a rewrite, I told them that I wouldn't add any points to their grades and they should never do this again. 

One of the students, however, emailed me stating that she is worried their final assignments might look similar as well. She was trying to convince me that her paper is her original work and the second student "worked really hard to make sure their papers don't look alike!". 

She included screen shots of their fb conversation as evidence. In FB conversation the one with the original work is telling her friend to use her paper as a basis but change the sentences and examples so it won't look like plagiarism. 

This is a clear case of plagiarism. Correct? I am not sure how to handle it. I know they are not realizing that's plagiarism, otherwise they wouldn't have shared those fb conversations. So I don't want to report to the school (yet!). But I am also not sure how to penalize them? Give a zero for the assignment? What do you recommend? Should I give zeros to both of them?
Learn about your school's policy. Learn about whether your school has an honor code, defines plagiarism in its catalog, or requires mandatory training such as an online orientation. Many schools have specific rules about what kind of punishments are allowed, and these rules may be based on their own interpretations of local laws or their past experiences with lawsuits. For example, my school's policy specifically tells us that we are not allowed to give a student a failing grade in the course for dishonesty, and it also spells out different levels of consequences for a first and second offense.

Look at your own syllabus to see what you said about plagiarism; usually administrators will support you on anything that's laid out clearly in your syllabus.

Don't assume that administrators will support you. Their priorities may be very, very different from yours.

Once you have done all your homework, talk to your dean and propose how you want to handle the issue. Make sure your dean is on board with what you plan to do. Consider "soft" penalties such as forcing the students to meet with the dean.