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asked them later whey they couldn't be friends anymore
Did she get meaningful responses from them? Anything which the two of you may discuss to a potentially lead to a better approach to friendship?

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she wrote numerous books titled "How to be Popular"
Are there good tips in her books? For example, anything which might lead to a discussion on how to implement the ideas on a day to day basis?

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sounding rather "know it all"
Afterward, at home, are you able to discuss what you observed and suggest alternate ways she might choose to say something?

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convinced that her older sister is better, smarter, etc than her and so ends up mad
Have you shared that perceiving (or misperceiving) that someone may have more (or be more) does not need to lead to negative emotions like anger or jealousy; For many people this type of perception may lead to admiration and emulating the person. It is a choice we make.

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How do people find friends or help their kid find friends?
From your post, discussing friendship may be key so that a kiddo is best able to utilize the opportunities presented by school, extracurriculars, etc to connect positively with others she meets.

Here is a link to an article on the Davidson Database, Tips For Parents: Gifted Children's Friendships

If a book may make a good discussion opener, there are many focused on social/emotional life available from Prufrock Press, Great Potential Press, and others. Some are written especially for children. Parents often pre-read books in order to prepare for discussion with their child when their child reads them.

Good luck to you and your DD with this. smile