> Why do some places call their school for younger children “Cheder”
technically, it should only be if it fits in a room. Many old school did. I think in many places, a teacher would teach a class at his home, possibly with different ages going to different teacher. I am not sure how widespread this was, but I saw this described in several books, including R Kamenetsky’s biography by his son.
I wish we could re-adopt this system. It creates more competition – between independent teachers, rather than schools, and competition is envisioned by Gemora and later poskim as an appropriate approach to education (guilds and competition restrictions are generally allowed in business, except education and perfumes). So, you would then be able to mix & match a Chumash class from a litvishe yeshiva, a Tanya class from a Chabad Rebbe and a math class from a MO school. And reduced overhead.