Ok. This is a prime example of how hard it is to teach word parts.
1. AD- is indeed a prefix meaning "to/toward"
2. In the example of ADVIL, no word part (prefix) is being used. Maybe Advil is short for some kind of pain relieving drug? Or a blend of some kind?
3. In the example of ADRIFT, it is unclear to me if there is a prefix being used, but the definition means "to move/float freely". This could be considered an example oftoward, but the dictionary does not acknowledge a word part being used.
4. A strong example of AD- being used as a prefix would be the word ADOPT. AD- (to) OPTARE (choose) = ADOPT- to choose.
5. Conclusion- In the examples your students provided, I would still claim no definitive word part was being used. However AD- is a prefix meaning to/toward. It all depends on how you frame your argument.
6. This is where I am getting crossed up with teaching prefix, suffix, roots. Sometimes there is a clear example of word part being used and other times it is hard to tell. I still feel this is a great tool to have when working out definitions of words.