For school glue sticks, the magic words are 'acid-free' and 'washable
If it says acid-free and washable on the package, it’s fine for school. For smooth application without clumps, go with a gel-based glue stick from a known brand and don’t press so hard.
The acid-free part matters because you don’t want artwork or photos to yellow over time. Washable matters because otherwise you’ll be scrubbing glue off clothes, hands, and desks. Any “school glue stick” from a major brand will hit both — Elmer’s, UHU, and
