Working with manipulatives becomes social if everyone is doing it at the same time. Students can work on their own individual work sheets, but sit together at the same table, perhaps sharing manipulatives. They can watch each other, talk with each other, share opinions or ideas as they like, but you do not ask them to come up with a joint solution, or to decide whose solution is "correct"; both of those scenarios require group skills of compromise, clarification, ability to disagree, cooperation and so on.
Another example of group work that does not require high levels of group skills is a think-pair-share activity. Here you present a problem to the whole group, ask them to think about it and come up with a solution individually, then pair up with another student to share their solutions and how they arrived at them. If the problem is one that has a numerical solution, students will be more likely to be interested in each others’ solutions if they have arrived at the same answer, so you might ask them to pair up with someone who got the same answer as they did. Students simply tell each other about their process, and are not required to come to a common solution, or to present a joint analysis. Again, you are interested in the fact that they share solutions, and that they talk together about a math process. Some will be more skilled than others; for many students, their ability to talk about math will be much lower than their skills in computation or problem solving. Give them lots of practice in talking, and accept any kind of talking about math as a step in the right direction. Watch their ability grow with practice.
Any activity that gives people a chance to move around has many benefits: it provides an opportunity for laughter and socializing, which helps make the group safe for people to take risks in their learning; it reduces boredom; it gives a chance for students to help each other unobtrusively; it gives a chance to talk about math, and it is useful for many students, including some trauma survivors, to be able to show the "right" answer without having to speak or assert their opinion, where they can move in a group and so be more hidden. Particularly for students who are kinesthetic learners, movement promotes learning and retention.
Following are a few activities which take only a few minutes to do. Enough examples are given that the activity can be repeated over many days, each time with one or two examples.