The solution to that is having 12 months of 4 weeks each, and one week of solstice every 3 months. One quarter then is 13 weeks in total. That makes it so each quarter perfectly matches a season and keeps it all in sync with solar time. In the ideal case you also match the school holidays to the solstice, and the winter solstice includes new year’s day and leap day, making it just a bit longer for Christmas holidays.
The solution to that is having 12 months of 4 weeks each, and one week of solstice every 3 months. One quarter then is 13 weeks in total. That makes it so each quarter perfectly matches a season and keeps it all in sync with solar time. In the ideal case you also match the school holidays to the solstice, and the winter solstice includes new year’s day and leap day, making it just a bit longer for Christmas holidays.
Yes, I’ve given this a bit too much thought.