The truth is that minor "chord shape" improvisation basically boils down to minor pentatonic scale improvisation, but don't be discouraged; this new method of looking at pentatonics may help you to better visualize the scale, and will surely be of tremendous value when you get to major chord improvisation.
The key is to always keep in mind the tonic, or root note of the chord. Then you can begin to identify the b3rd, 5th, and b7th scale degrees, and eventually recognize effective passing tones and interesting non-scale tones as well. (NOTE: "b" indicates a "flatted" note, as compared with the major scale.) Keep in mind that since the "chord shapes" are movable, we want to identify scale degrees as opposed to actual note names, as it is the purpose of the note that matters, not its alphabetical name. This way, if you transition to a shape and want to play the 3rd scale degree of the chord, you can do so, even though you may not know what the actual note name is.
This is how the minor pentatonic scale falls over the "E Shape" at the fifth position. If you don't understand the terms you're encountering, or can't identify the locations of the root note of the chord, then you're not quite ready to continue.
The sequence below demonstrates the sound of each note of the scale over the root chord, then gets a little more interesting. None of the notes sound "bad", nor are they all that compelling. It's like having steak and potatoes for dinner every night, some variety is needed, although the staples cannot be forgotten.