The weekends do count, out of the 10 days they'd be out, up to 4 would be weekend days. So, really they'd have missed around 6 or 7 days of actual school. But it could also happen to fall in a public holiday, which will reduce the number of days even more. And there are school breaks throughout the year.
I find it hard to believe that many people are living such in the edge that, if their kid has to miss a week or so of school in a year their finance and jobs fully crumble.
There's 104 non school days regardless of any other days without school. It only takes 76 other days off (June 15-august 15 + 3 additional weeks off) is youe 180 days off.