To answer the question regarding Piaget's stages of cognitive development, it is essential to understand the characteristics of each stage that Piaget defined. Jean Piaget, a renowned Swiss psychologist, outlined four key stages of cognitive development:

1. Sensorimotor Stage (0-2 years): In this stage, infants learn about the world through their senses and interactions. They lack the ability to perform "mental operations." This stage does not involve hypothesis testing or generalization.
2. Pre-operational Stage (2-7 years): At this stage, children begin to use language and think symbolically, yet their thinking is still intuitive and egocentric. They are not yet capable of performing operations or thinking in a systematic, logical manner.
3. Concrete Operational Stage (7-11 years): During this stage, children start to think logically about concrete events. They gain a better understanding of the concept of conservation and can perform operations on concrete objects. However, abstract thinking is still limited.
4. Formal Operational Stage (11 years and up): This is the stage where individuals develop the ability to think about abstract concepts. They can perform mental operations on theoretical problems, engage in systematic planning, and conduct mental experiments (hypothetico-deductive reasoning).

With the above descriptions, we can analyze the question:

Question: According to Piaget, when children reach the point of being able to generalize and engage in mental trial and error by thinking up hypotheses and testing them in their heads, they are in which stage?

The scenario described is characteristic of the Formal Operational Stage because it involves abstract thinking and the ability to hypothesize and test ideas mentally.

Correct Answer: Formal operational stage

Other options, such as the Sensorimotor, Pre-operational, and Concrete Operational stages, are not correct because they do not involve the ability for abstract and theoretical thinking. Thus, this confirms the appropriateness of the answer.