One well-known activity to teach elements music is the Suzuki method. It involves immersing the student into simple songs, usually childhood songs like "Twinkle Twinkle Little Star," to begin with. Songs that follow a major scale up or down to establish a familiarity with the scale. After a period of time, the student is then introduced to popular music, usually also with simple musical progressions, until she has built a mental picture or base to draw from. At this point an instrument is introduced and the student, using the base gained from prolonged listening to the music, has a musical aptitude already in place.
Playing by ear is an activity that most students can benefit from. Some scholars frown on it, but to a majority of students from inner-city, rural or less privileged demographics, playing by ear brings music into reality. Some prodigies actually excel at playing by ear and produce superior music through feeling. This activity benefits certain styles better than others. Blues, jazz and rock are probably the genres that most utilize playing by ear.
Imitation is exactly what it sounds like. To pick out individual notes or chord progressions note by note to imitate music. The activity of imitation is practiced painstakingly to reproduce music, usually done on piano or guitar, but works equally well on any instrument. Most rock guitarists of today have learned from simple imitation, then branched out from there. Imitation is a respectable activity to learn music because it enables the student to learn on his own. The motivation factor alone--to know that you can imitate a popular musician--is very beneficial.
Scales are the first and foremost element of music activity to benefit any musician, of any demographic, style or predisposition. Scales are the building blocks of all music. The activity of practicing scales builds hand strength, mental strength and confidence. A day of practicing nothing but the activity of ascending and descending scales can seem foreboding, but the disciplined gained from practicing scales is the single most beneficial thing any student can hope to gain.