Sorry, but you're only calculating what's explicitly stated in most teacher contracts...not what's implied.
I'll admit I'm only at my school from 7:30 to 4 on most days, and I do have 2 "free" periods...(although they are only non-teaching periods. I still have other duties I might have to perform like proctoring a test for some students who missed a day, or, depending on if it is the fall or spring semester, head up some student extra-cirricular group). What I don't have is "free" time.
These hours might seem in line with most other 8 hour a day jobs, but there is a load of work involved with planning out my lessons, making sure my book is straight, keeping parents informed, dealing with administrators, and staying on top of grading my assigned work.
I'd say, conservatively, I probably work 10-12 hours a day both at the school, and at home. More in the spring when I coach baseball. What they pay me for coaching isn't worth the time I put into it. I do it because I enjoy it.
I also don't think you realize many teachers are forced into extra-curriculars. Sure, they get paid for it, but I know many of my colleagues would rather be at home than coaching the district mandated debate team, or playing host to an FFA event.
Do you know how many dances I have to chaperone a year? Do you know how many Saturdays I've lost because my school wanted to have a dance that night? I wasn't paid for that, and legally I could weasel my way out of them, but I need my job. It doesn't look good if you constantly say no.
When summer comes around I have some extra free time, but not 3 whole months straight like everyone seems to think. I go to workshops, and seminars to improve my skills. I pay for these out of pocket. I meet with administrators during summer months. I am planning lessons for the next semester while I'm off on vacation. Lord help me if they force me from one subject to another because they can't find someone to teach algebra.
This happens, especially to newer teachers who have no clout. That teacher with 2 years under his belt who just got a comfortable rhythmn teaching a subject he went to school for is now teaching something completely different. For the first year of him swicthing subjects he'll be just days ahead of his students relearning, and teaching himself the material.
BUT...you're right about the parents. Some can be a headache. Everyone thinks their child is a special snowflake and should have great grades. Everyone believes their child is the bestest human in the world. I HAVE NO PROBLEM WITH THESE PARENTS. They care. It is the ones who never show up to PT meetings. The ones who could care less if their child is falling behind.
Oh...I almost forgot about IEP plans. Yeah. It would take too long to explain why, but yeah...they're a lot of fun for teachers.
tl;dr- I work hard, all throughout the year. I put in as many hiurs as an investment banker sometimes. I'm asked to donate time and money to school functions, and groups. I can't really say no. I buy my own supplies, which generally means I'm buy 5 or 6 students their supplies for the year. I make 42k a year, have no job security because I'm in a right to work state. I'm 40 and still paying off college loans.