Thomas’ 5 Ways Simplified

I’m teaching high school theology and we’re covering Thomas’ 5 ways to approach God philosophically. I’m trying to simplify the material down for their level. Below is my attempt. If any of my theologian friends would like to check my theology to make sure that I am properly representing Thomas (as well as possible for 9th-11th grade theology), please do so.
Argument From Motion:
    • Given: Nothing makes itself move, but things are in motion.
    • Therefore: Something must have given motion to things.
    • Therefore: Some “First Mover” must exist that gives motion, but never needed to be moved.
    • Finish: We call this First Mover “God.”
Argument From Cause
    • Given: Things don’t cause themselves.
    • Therefore: Something must have begun the causing of things.
    • Therefore: Some “First Cause” must exist that caused things, but was not caused.
    • Finish: We call this First Cause “God.”
Argument From Possibility and Necessity
    • Given: Things are generated and decay.
    • Therefore: It is possible for things to not exist.
    • Therefore: At some point in the past, there must have been a time when nothing existed.
    • Given: Nothing can come from nothing.
    • Therefore: There must have been some Necessary Being who always existed and gave existence to other things.
    • Finish: We call this Necessary Being “God.”
Argument From Gradation
    • Given: Things can be “more” or “less” of various perfections
    • Therefore: There must be a “most” to every perfection.
    • Therefore: There must be some Maximum Being which is the most perfect.
    • Therefore: Since this Maximum Being must be the most perfect, He is the most of all other perfections as well (goodness, truth, beauty, etc.).
    • Finish: We call this Maximum Being “God.”
Argument From the Governance of the World (Intelligence)
    • Given: Things in the universe naturally move toward a goal and work in an orderly way.
    • Therefore: Because the order is so intricate, we must assume that these things accomplish their goal by design, not by chance.
    • Therefore: There must be something that has designed the whole universe to act so orderly and acts to direct all things to their natural goals.
    • Finish: We call that designer “God.”