I don't think this module achieves its learning objective. The stated goal is to help students distinguish between objective and subjective tones of writing—and the implicit goal is to demonstrate why it matters. I don't feel much closer to either goal after reading this.
The stress the lesson continually makes is between "formal" and "informal," not objective and subjective. More importantly, it gives no examples of "here's a paragraph that comes across as very subjective" and "here's the same thing stated in an objective tone." Wouldn't that be more helpful to show the student the stakes? Instead, the only thing I feel like I can hang my hat on after reading this is four examples of different styles of sentence beginnings and some paragraphs that tell me about tone and diction and syntax without showing me anything so I actually understand these terms. I know we'll go into more detail in later lessons—why not save the detail for later, then, once we understand why we need to know it? Set a clearer focus here on showing the importance of wording, and giving only the basics to suggest where we're headed with the next lessons.
Also, the definition of syntax given below used the linguistics-oriented sense of the word, instead of the writing-oriented sense. We don't need to talk about the set of rules that govern English grammar and SVO order, but instead about why you should change up your sentences to avoid putting the reader to sleep.
I deleted the elements on credibility, because they seemed distracting.