Final answer:
The task developed by Piaget that is most likely to show performance differences between the two age groups (ages 5-6 and 8-9 years) in Study 1 is deciding whether a given quantity of a liquid changes if it is poured from a narrow container to a wide container.
Step-by-step explanation:
The task developed by Piaget that is most likely to show performance differences between the two age groups (ages 5-6 and 8-9 years) in Study 1 is Deciding whether a given quantity of a liquid changes if it is poured from a narrow container to a wide container (Option C).
Piaget's theory of cognitive development suggests that children in the preoperational stage (ages 2-7) have difficulty understanding conservation, which is the idea that some properties of objects or substances remain the same even when their appearance changes. In the given task, the children would be required to understand that the quantity of liquid remains the same when it is poured into a different container with different dimensions. This ability is typically acquired during the concrete operational stage (ages 7-11). Therefore, the older age group (8-9 years) is more likely to perform better in this task compared to the younger age group (5-6 years).