Final answer:
Children learn to manipulate ideas, use abstract thinking, and solve problems with hypothetical situations during Piaget's formal operational stage, which begins around age 11.
Step-by-step explanation:
During Piaget's formal operational stage, a child learns to manipulate ideas, concrete objects, or events and use abstract ideas and hypothetical situations in solving problems. This stage typically begins around age 11 and continues into adulthood. At this stage, children develop the capacity for abstract thinking and can consider multiple possibilities, engage in hypothetical reasoning, and solve problems by systematically testing hypotheses. In contrast, the concrete operational stage allows children to think logically about concrete events, but not abstract concepts.