The Piano is a fantastic instrument to learn about musical concepts.
It is great to visualize and to experience musical concepts. It's very direct and understandable at once.
Once, a student (7) came over for an extra lesson which he didn't ask for and we ended up playing and learning a lot about:
Chromatic Scale, Half Tone and Whole Tone distances
Major Scale from various beginning by knowing the distances and by singing 'doremi, fasolatido'
Pentatonic Scale from C and from F# by singing 'doremi sola'
Rather high tones and their character (birds, soft tickings of the rain, a child/ a soprano singing)
Rather low tones and their character (dinosaurus, cello, bass)
We can do a lot just with those things! Improvising with the Pentatonic Scale is a very rewarding musical exercise. Knowing the scales, we can practice them regularly and it's so good for our piano fingers. The chromatic scale makes us aware of the half tone distance and the whole tone distance in the major and eventually minor scales. Different character of the various registers on the piano helps our fantasy in playing music.
On the same day, an adult students played her pieces/songs played with blocked chords and on the piano it's so easy to explain:
Different chords and how they are built
V- I relation
And I thought, that's it. That's all what I need to be able to learn my first piano pieces/songs for quite a long time! There's a lot to do with all this basic information. And on the piano it's so easy to see and to demonstrate.