I think the number was even bigger at one time, but nowadays it's typically western with 1-2 kids. Семья and семь is a funny coincidence which is fairly exploited, like writing as "7я".
I think I read somewhere that it represents the standard family: three children, two parents and two grandparents.
Would that be the maternal or the paternal grandparents, or how does it work?
се́-ять ‧ to sow ‧ ‧ Cognates: sative, sation, season
sation ‧ ‧ A sowing or planting ‧ ‧ From Latin satio, from serere, satum (“to sow”). Doublet of season.
Cognates: disseminate ‧ inseminate ‧ seminar ‧ seminary ‧ seminarian ‧ seminate ‧ IE cognate dictionary
sem·i·nal ‧ of a work, event, moment, or figure) strongly influencing later developments
disseminate ‧ propagate
This is a mare coincidence. The Slavic word for family comes from the same root that gave the English home. Back in the pre-historic times it was pronounced with a palatal ḱ in the beginning, which in the Germanic, Italic, Celtic, and Greek languages equalized with the ordinary k, while in the Balto-Slavic and in the Indo-Iranian it has evolved to a sibilant sound - in Russian, in particular, it has become just s.
PS семья is unrelated with семя (seed), either. The later comes from the word for "sowing".
Note: Since “big” is here used as a predicate adjective, one would ordinarily use the predicate (short) form in Russian. But «большой|большое|большая|большие» is exceptional in not having its own predicate form «*бóлеш|*бóльшo|*большá|*больши́». So instead, one either uses the attributive (long) form, as in the given translation, or substitutes that of «великий|великое|великая|великие»=“great”: «вели́к|велико́|велика́|велики́».