I've used this activity on the first day of my Geometry class. It allows students to get to know multiple peers' names, and it reviews basic algebra skills, operational skills, and vocabulary that they will need throughout Geometry. I think it would also be appropriate for use in an Algebra 1 class, or for a quick recap in Algebra 2.
The document contains a chart with 15 boxes. The boxes ask students to find someone who can recall the ways to solve a system of equations, find someone who can graph x = 2, etc. I first have my students go around and gather names only, not answers. I do not let them repeat any names, and I ask them to write the names themselves instead of just handing their paper over. (I think that's more effective in getting them to learn their classmates' names.) I then have everyone return to their seats, and I display the chart on the board. I ask a random student to state whose name they had in the first box. (Let's say it's Joe.) I then call on Joe to EXPLAIN his answer for the first box; I record it on the board, and the students record it on their papers. I then ask Joe who he had in the next box, and the process continues. If it happens to come back to Joe again later in the process, I usually would skip him and jump to someone new. However, only students who volunteered their name for a particular box are called on for that box, so it doesn't put anyone uncomfortably on the spot.
I've included the chart and the answers in this file. There is an editable Word document if you want to revise any of the boxes, as well as a PDF.