When I first started quilting, I kept the math aspect of it at arm's length, but over time realized that the math for quilting is nothing harder than what we learned in grade school--definitely nothing to fear. The more you work with it, the easier it gets.
To figure out the size of your quilt back, measure your quilt top: 55" x 62"
Add 3" to the right side and 3" to the left side: 55" + 6" = 61"
Add 3" to the top and 3" to the bottom: 62" + 6" = 68"
61" x 68" is the size you need your quilt back to be.
To know how many 11.5" squares you need horizontally, divide 61" by 11.5" to get 5.3. Round down to 5.
To know how many 11.5" squares you need horizontally, divide 68" by 11.5" to get 5.9. Round up to 6.
5 squares in one direction multiplied by 6 squares in the other direction equals 30 squares--done!