However, it is also public so make sure you tell students that they should only use first names.
Another alternative which I used yesterday in a classroom is an etherpad. (https://etherpad.mozilla.org/) Again this is an open document, but is not included in any search engines. The advantage of the etherpad is that each person who uses it is given a different color highlight so it is easy to see who has done what. (Video on opening an etherpad here)
With either option then the hard part is sharing the URL (the web address of the page) because they tend to end in a looooong string of random numbers and letters. (for example this is an etherpad https://etherpad.mozilla.org/SL2ewWbm2R and this is a google document https://docs.google.com/a/rbchs.com/document/d/1OhXsRzjkHP0iel46VaI3GazY4JfxZPNCOB5whitZf1Q/edit)
I like to use http://tinyurl.com/ to make the address easier to remember. To use tinyurl take the web address of the page one of the really long URL’s from above and paste it into the first box. Then I like to add a custom alias in the box in the bottom, such as murphypad1. This way it is easy to remember and type into the browser. Then click Make TinyURL!. (Video on how to do that here) Because every web address has to be different you cannot reuse the same custom tinyurl more than once.
You can use both an etherpad and google doc again and again. Here is an international company that reuses the same note pad for meetings on a monthly basis https://teach.etherpad.mozilla.org/mentors-thursday Yes they hold monthly meetings with an open notepad and not only can anyone watch live, but you could participate if you want.