I did a super simple partner composition activity with my grade 2 and 3 students and by just spontaneously calling it a "secret handshake" rather than a body percussion composition, the kids were sooooooooo excited! It also led to some very interesting and creative compositions.
In pairs, students write an 8 beat rhythm pattern (two measures) using ta, ta-a, ti-ti, rest, and/or ti-ka-ti-ka.
Students decide on body percussion together that matches the rhythm pattern that they wrote. When demonstrating this, show different ways partners can connect. When students are composing their body percussion, watch for a group that clearly shows their rhythm and have them demonstrate for the class.
Have pairs perform their compositions for the class, having the rest of the students demonstrate their audience behaviour skills!
Have students write out their compositions with graphic notation.
Have pairs teach another group their handshake.
It sounds simple, and maybe you already do something like this, but the kids loved it! I will forever be using the term "secret handshake" for this activity!