I honestly think closing most schools, and only keeping some open for key workers (NHS staff, police etc), would be the best option.
Too confusing and unfair--it means some kids are getting better education than others. A better idea would be cancel school for everyone, and have all-day childcare centers (holiday clubs type places basically) open for those children whose parents MUST work, CANNOT work from home, and have absolutely no other alternative.
As long as you ensured that only the absolute necessary minimum of kids were attending, and made sure that the childcare clubs were fairly small in scale, this would massively reduce vectors compared to having all kids in school.
That's more or less what they seem to have done here (Japan).
If society was better prepared for pandemics, we would have a clear set of criteria established for quickly triaging families into "Must have childcare when school is canceled" versus "Can do without childcare, at a pinch, for a month or so when school is canceled," and would have plans in place for quickly getting the holiday clubs set up and ready at short notice.