Final answer:
The two most important criteria for division of labor in bands are gender roles, with women gathering and caring for children and men hunting, and the group's mobility, which influences their territorial access and resource management.
Step-by-step explanation:
The two most important criteria for the division of labor in bands are based on gender roles and mobility. Within the bands' structure, there was a clear division based on gender, with women primarily gathering plant foods and small animals, while men focused on hunting larger animals. Women also predominantly took care of small children. Moreover, mobility played a crucial role in the division of labor, as bands moved across territories, following seasonal cycles and managing resources. These groups relied on a collective understanding within their members, also forging connections with other groups for resource access in times of scarcity.