Coloured Sticks
To split the class in half, use "warm colours" and "cool colours". For smaller groups, just hand out the number of the size you want. Can be popsicle sticks, coloured strips of paper, clothes pins, etc. Assign one person from each group to return them to you before they start with their tasks.
What's your Number?
Use student ‘numbers’ according to the class list e.g. 1-30. To divide the class in two groups, use "odds" and "events". To divide the groups in other ways, make use of number properties (e.g., multiples of 3, etc.). Be mindful of historical uses of numbering students and use your professional judgment.
Partner Map
Give students a sheet with a clock on it, for example, or a randomized set of distinct object drawings (e.g., a leaf, a shell, a button, etc.; alternatively, these could be related to a theme). Students write down the names of peers they enjoy working with for each hand of the clock or for each object. Teachers call out "Find your 2 o'clock partner.", "Find your leaf partner.", "Find your human body partner."
Magic Hat
Student names are placed in a hat, and you pick names out of the hat to form groups.
Musical Groups
In a large circle, play music while students pass objects (e.g., coloured sticks, pipecleaners, etc.) around the circle. When the music stops, each similar object will be in a group together (e.g., the pipecleaners).
Random Group Generator
Put student initials or other identifier into a random group generator. There are many available, but be mindful of putting student information into free tools.
Back to Basics
Create a durable card/foam cutout with one visible attribute that differs (e.g., shape, number, colour). Students who are handed a red card, for example, looks for other students with a red card.
Teachers could use cards with multiple differing attributes to discourage students from trading (e.g., shape and colours are distinct - red squares, triangles, and stars with various numbers of them, blue squares, triangles, and stars with various numbers of them) so that the teacher can select a different attribute for randomizing groups each time.