1. She is good at dancing.
2. She is good at dance.
(Which one is correct? Are both correct?)
3. I am a student at Class 1-1.
4. I am a student in Class1-1.
5. I am in Class 1-1.
6. I am a first year student in Class
1-1.
7. I am a first grader of Class 1-1.
(Are all grammatical?)
1. and 2. would have slightly different meanings. 2. would apply to someone studying dance as a career, as in ballet. "dancing" usually refers to social dancing in pairs.
3. is not grammatical.
6. and 7. may be redundant, if "Class 1-1" is one of the first grade classes. Still, 6. is OK, but 7. is awkward. It sounds like you are studying the class itself.
1. Both sentences are grammatically correct, but the first sentence, "She is good at dancing," is more commonly used. When you want to express someone's proficiency in a particular activity, it is more natural to use a gerund form (ending in -ing) of the verb.
2. The second sentence, "She is good at dance," is less common, although it is acceptable grammatically. However, in this case, it might be interpreted as referring to a specific style or genre of dance, rather than dancing in general.
Regarding the second set of sentences:
3. "I am a student at Class 1-1." This sentence is grammatically correct and commonly used. It indicates that you are enrolled as a student in a specific class.
4. "I am a student in Class 1-1." This sentence is also grammatically correct and conveys the same meaning as the previous sentence. "In" is commonly used to indicate being part of a specific class or group.
5. "I am in Class 1-1." This sentence is grammatically correct and commonly used. It simply states that you are a member of Class 1-1.
6. "I am a first-year student in Class 1-1." This sentence is grammatically correct and provides additional information about the student's year level. It implies that you are in your first year of being a student in Class 1-1.
7. "I am a first grader of Class 1-1." This sentence is also grammatically correct, but it is more commonly used in American English, where "first grader" refers specifically to a student in the first grade of primary/elementary school. In other English-speaking countries, it may be more common to say "first-year student" or simply "student" without specifying the grade.