The document discusses three properties of addition: the commutative property, the associative property, and the identity property. The commutative property states that changing the order of the addends does not change the sum, so a + b = b + a. The associative property allows adding groups of numbers in any order without changing the result, so (a + b) + c = a + (b + c). The identity property indicates that adding zero does not change the number, so a + 0 = a.