A simple expansion on the interval identification challenge, this exercise has you identify multiple chord tones in relation to the tonic (root). The root is played first, and the tones are all in ascending order. This exercise is great for bridging the gap between intervals and chords. Once you get comfortable, try increasing the number of tones and expanding beyond an octave of range.
Now we're getting serious about music theory. Rather than the "generate random pitches and name them later" approach, this exercise takes a more scalar approach to chord tone identification. You pick which chord tones you want to hear (3rd, 5th, 7th, 9th, etc.) and those chord tones will sound with different qualities (major, minor, diminished, augmented, etc.). Your job is to identify the qualities of the chord tones. Start in diatonic mode for an easy introduction to familiar chord shapes, then switch to jazz mode and start adding some 9ths, 11ths, and 13ths if you really want a challenge.