My children come home with many examples of their homework or tests that have pasukim or other types of writings on them. They also have old "nach" workbooks that contain significant printing of nach verses along with the worksheets in the books filled out. I recently built a big fire and burned all these paper items, along with my old arba minim from a few years back. (the arbe minim were just an afterthought) Was this the wrong way to do this? Do these photocopies and workbooks need to go to a genizah? I never feel good about throwing them out with the trash if I put them in a clean grocery bag first, so I thought burning is a more respectful way. They burned fully and are just ash with no recognizable lettering on them anymore. Thanks!
If there is no name of G-d either in Hebrew or English, and no complete verse is written, genizah is not necessary and any respectful disgarding (such as burning) is proper. If there are full verses there may be stricter opinions, but the basic halacha is that genizah is not necessary. This is especially true if the print used is not "Ktav Ashurit" - that is a type of print that would be acceptable for a Torah scroll (if hand wriiten). See Minchat Yitzchak 1;17(par. 14)