Hi Kim!
You are correct that the magic your way tickets only go up to 10 days. If you want to visit parks for 11 days, you can buy a one day ticket or an annual pass. If you think that you will be visiting Disney World again in the next year, I highly recommend that you consider buying an annual pass. You can read a question and answer about annual passes
HERE.
If you don't want to go to the expense of buying another ticket or an annual pass, there are lots of things you can do that don't require you to use a day on your tickets. You could spend the day relaxing at your resort pool and have dinner at one of the resorts. You could visit Downtown Disney where you can spend some time at DisneyQuest ( which does require you to purchase admission). There are also two waterparks and miniature golf nearby. Disney also offers watercraft rentals, programs for kids like pirate cruises and tea parties - the list goes on and on! It can be a lot of fun to find things to do outside of the theme parks.
Unfortunately, if you wish to visit more than one park in the same day, you will have to have the park hopper option on your tickets. When you enter a park, your ticket is electronically marked, and will not be accepted at another turnstile that same day. You can re-enter the same park, but not a different one.
I hope this helps! Have a wonderful vacation!