If you have different calendars shared with you, iOS doesn't always show all of them in the built-in Calendar app. These steps will let you sync any and all of your Google calendars.
Go to https://www.google.com/calendar/syncselect and log in with your District login. You should see this page: 
Check any boxes for calendars that you would like to sync to your phone and click Save. Now any calendars that you've selected will show up in the iPhone Calendar app.
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