So here is how I group my students using the elements on the periodic table. I have 26 poker chips, each with a symbol of an element from the periodic table. On lab days or whenever I want to randomly put students into groups, I have each student blindly grab one of the poker chips from a container.
I have chosen elements in groups of four from the periodic table because I have four students per lab station. Since I have 26 students, I needed two extra elements, H & He. Each lab station is labeled Alkali Metals, Alkaline-Earth Metals, Nitrogen Family, Oxygen Family, Halogens, Noble Gases & Hydrogen/Helium. Students move to a lab station based on the element poker chip they chose. At this point, the students have some choice. They may choose with whom they work with based on the students at the station. The two students with hydrogen and helium do not go to a lab station based on the group/family. Instead, because H and He are unique they have a lab station to themselves.
I like this method because it reinforces the idea that elements are in groups/families on the periodic table and it refreshes students' memories of the names of the groups/families on the periodic table. It saves time in class because students are not milling around looking for a partner. They grab a poker chip and find a partner.
Sometimes, I have those stray students because some kids are absent or one of my classes has less than 26 students. After all of the students are in groups, I just go around and quickly condense them into one or two groups or if there is time I have one or two kids pick again.
Thanks
Dan