1. I'm worried about my new school.

Why don't you join a club?
Why don't you make new friends?
Why don't you talk with your homeroom teacher?
Why don't you talk with the school counselor?
Why don't you talk with the counseling teacher?
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Are they all right? At the bottom, are both expressions OK?
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2. I'm worried about my math.
3. I'm worried about math.

4. I'm worried about my height.
5. I'm worried about height.
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Do we have to add 'my'? If we don't use 'my,' does it have any difference?

1. All of the suggestions you have mentioned are valid ways to address your worry about your new school. Joining a club can help you meet new people who share similar interests and create a sense of belonging. Making new friends is another great way to ease your worries, as they can provide support and companionship throughout your time at the school. Talking with your homeroom teacher can help you address any concerns or issues you may have, as they are there to provide guidance and support. Additionally, speaking with the school counselor or counseling teacher can be beneficial, as they are trained professionals who can provide you with coping strategies or offer counseling services to help alleviate your worries. Both expressions at the bottom are okay to use, as they convey the same message.

2. "I'm worried about my math" and 3. "I'm worried about math" are both acceptable expressions, but they slightly differ in meaning. "I'm worried about my math" suggests that you are specifically concerned about your performance or understanding of the subject, while "I'm worried about math" suggests a general worry or concern about the subject as a whole.

4. "I'm worried about my height" and 5. "I'm worried about height" are similar to the previous example. "I'm worried about my height" implies that you are personally concerned about your own height, while "I'm worried about height" implies a general concern or worry about the concept of height in general. By using "my," you are indicating that the worry is directed at yourself, whereas omitting it implies a broader concern.

1 - all are good.

2 & 3 - You might better say, "I'm worried about my math skills." #3 is fine as is. Both do mean the same thing, really.
4 & 5 - If you are worried about how tall you are, #4 is good. If you are worried about climbing too high, #5 is good. They do not mean the same thing.