For any girl that grew up playing any kind of organized basketball prior to 1970, you may have played under rules different than today's game. It was called six-on-six, or girls basketball, or sometimes referred to as "granny-style basketball".
The most archaic aspect of the game was that a player could play only half-court defense or offense. Never both. There were no centers and only forwards could shoot the ball. If the old girls rules applied today, we'd never experience seeing the visual wizardry of outstanding college guards like Jennifer Azzi, Diana Taurasi, Sue Bird or Dawn Staley.
A variant of the girls rule (played in New Jersey until 1975) allowed 2 players to play full-court, 2 players half-court on defense and 2 players half-court on offense.
Although these rules began their phase out in 1958, it took 37 years for the rules to be phased out completely. The last 2 states to play six-on-six basketball were Iowa in 1993 and Oklahoma in 1995.
The below YouTube video is taken from an Iowa girls state championship game played in 1976. The quality is rather poor, but from the fan turnout and pace of the game, it's understandable why Iowa was one of the last states to phase out a popular and very successful school sport.