I'm redesigning a page for my team's Sharepoint site. However, I am not able to check out the page for some reason. I have Full Control permissions for the site and thought that would be enough, but that does not seem to be true. What permissions should I request so that I can check out the page and check it back in when I am done with my changes?
From the URL, you can find the page library to which this page belongs.
If the page url is http://sp/sites/team/SitePages/test.aspx, the page is exits in the site pages library.
if the page url is http://sp/sites/team/Pages/test.aspx, the page is exists in the pages library.
Remove test.aspx from the url, it will navigate to the library to which this page belongs.
Then you can go to library settings->versioning settings->choose yes for "Require documents to be checked out before they can be edited":
Are you sure that versioning is enabled on that pages library? As far as I recall the Contribute permissions level should be sufficient