For a complete lesson on the properties of addition, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the following addition properties: the commutative property of addition, which states that a + b = b + a, the associative property of addition, which states that (a + b) + c = a + (b + c), and the identity property of addition, which states that a + 0 = a.