Some of the scales that fall outside the major and minor scales and modes are called synthetic. Of these, the whole-tone,the diminished and the pentatonic scales are the most commonly used in contemporary music.
The first approach is to use the A minor pentatonic scale over the entire progression for the classic blues sound.
The next approach would be to use the A major pentatonic scale over the entire progression to give it a southern rock type of feel.
The next approach is to use the A major pentatonic over the one chord and the A minor pentatonic over the four and five chords.
Another approach would be to use the A minor over the one chord, D minor pentatonic over the four and E minor pentatonic over the five chord.
A different method would be to use A major pentatonic over the one chord, D major pentatonic over the four chord and the E major pentatonic over the five chord.
The last approach i'll show you here is to use A mixolydian pentatonic over the one chord, D major pentatonic over the four chord and E minor pentatonic over the five chord.
Here is the five movable minor pentatonic scale patterns in A minor.
Here is the five movable A major pentatonic scale forms.