Final answer:
The latent function of the 'leagues' mentality in the context of social conventions is to socialize children into behaviors like teamwork and following rules, preparing them for the adult world.
Step-by-step explanation:
The latent function of the 'leagues' mentality in the context of social conventions is the socialization of children into behaviors such as teamwork, following a schedule, and using textbooks. This hidden curriculum prepares children for the adult world and teaches them how to deal with bureaucracy, rules, expectations, waiting their turn, and sitting still for hours. By participating in competitive activities like relay races or math contests, children learn about winners and losers in society.