Here’s an idea I loved from a classroom in Utah:
The teacher had a sign posted in the front of the room that had the following words on it – “Neighbors: Front door, Back door, Side door, Diagonal.” This sign reminded her to use her established “random” partnering system (when factors like academic level are not needed to pair students). Neighbors was her way of partnering students (they sat in groups of 4 desks). The kids knew who was their front door neighbor, side neighbor, and so on, so all she had to do was call out a neighbor and the kids would instantly pair up. This saved her lots of time paring up, and she changed seats enough that the kids never got too bored with one partner. When she called “meet a new neighbor”, the kids were free to work with any class member. Sometimes, she’d call “block party,” and the entire table would work together. I thought this was a great way to partner students and build community.