Scales and Arpeggios in Different Keys: Start by practicing scales and arpeggios in various keys. This will familiarize you with the piano layout and improve your ability to navigate the keyboard. Try to play these scales and arpeggios with different rhythms and dynamics to make them more interesting.
Call and Response: Play a short melody or rhythm, then try to 'respond' to it with a different melody or rhythm that complements or contrasts it. This can be done alone or with a partner. The idea is to listen and react, which is a crucial skill in improvisation.
Chord Progression Exploration: Learn and practice common chord progressions, such as the 12-bar blues or II-V-I progression in jazz. Experiment with playing these progressions in different keys, tempos, and styles. Try improvising melodies over these progressions using the notes from the corresponding scales.
Motif Development: Create a short, simple motif (a musical idea or phrase) and then explore various ways to develop it. This could include changing the rhythm, altering the pitches, playing it in a different key, or inverting it. This exercise helps in developing thematic material during improvisation and can lead to more structured and coherent improvisations.