Take care here, as we now have a mixture of quarter notes and eighth notes. Although there is nothing on beat 1 + or 4 +, it helps to still count them, being sure to not to rush into the following beats.
The following two-bar exercise contorts the backbeat, displacing it by an eighth note and then bringing it back. We call this deviation from expected rhythms syncopation - things are not falling where you’d expect them to. The result is an unusual and engaging groove, but played well it can be every bit as funky as a groove with the usual backbeat on 2 and 4.
Play this groove with a bit of a twist by giving the last two beats (3, 4) a different sound. For example, play the snares as rim-shots (where your stick strikes the rim of the snare at the same time as the skin). As you hit the edge of the drum more closely with the tip of the stick, it gives a crisp, ringing sound, with stronger contrast.
Alternatively, try digging into the hi-hat more on those beats, taking the pressure off with your left foot slightly to increase the length of the sound. Hip-Hop drumming is as much about the sound you extract from the drums as what you play.
To finish this section on eighth notes, here is an eight bar groove with a two beat pick-up and fills in bars four and eight. Take it slowly and learn it perfectly, then try playing it along with a metronome or drum machine. Try experimenting with all the patterns you have learned and turn them into longer grooves. Many songs have four or eight bar repeating sections.
Sometimes a different cymbal sound is required for a song and drummers use modified cymbals to achieve this. An interesting effect can be achieved by draping a small chain across the ride cymbal from the stand. This emulates the sound of rivets (often used on older Jazz recordings) without needing to drill holes in your cymbals.