Following a big payout last year for not doing enough to comply with the Children’s Online Privacy Protection Act, YouTube made changes to the features available on content made for children.
That basically includes the majority of videos you might want to watch in your kindergarten class.
While there were a multitude of features that were effected, ranging from voting on videos, to allowing videos to autoplay or making comments, one key feature of video management for teachers was removed: the ability to save videos onto custom playlists.
There seems to be two work-arounds for this challenge. The first is to save your videos as bookmarks on your web browser or similar (for example, saving a link to the video in your teacher folder, where you have online access to such a folder).
The other solution seems to be to save the video to a playlist via the YouTube search results page (see above) by clicking the icon to the right of the video name. Existing videos that were “made for children” and are already on playlists don’t seem to be affected. Hopefully, the ability save such videos to playlists will be restored in the future.