Had given is the verb phrase
For your second paragraph you should do some pros and cons of public and homeschooling, keep them even so it doesn’t look like all of them are just opinions of yours. Also you could add how kids of different ages feel about public and homeschooling. Put in more facts so you don’t keep saying the same sentence over and over in different words because that usually makes the reader get bored. To restate your thesis write it again in the last paragraph but with different words and change it up a little to mean the same thing but with a different structure. Also you should use evidence.
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Here’s what I think
