letter to a Math Analysis Honors student in my class next year

Dear next years students,

I wants to inform you that if you are in Algebra 2 Honors, there will be two types of teachers that you are susceptible of getting for Math Analysis; Kirch or Tamaoki, that is a 50% chance of getting either of them. If you get Tamaoki, I will assure you that your math career for next year will be extremely easy yet monotonous, but if you have Kirch, you will have a rather difficult beginning (everyone does) and in the worst case scenario, the whole semester but you will tend to enjoy her class socially. I am trying to scare you because it is true, there are people there that could not adapt quick enough, with their grades in jeopardy, but that can be prevented. If you watch the videos and stay consistent you will do well. If you don't do that, well conflicts happen. If you do however get Tamaoki, I'd advice you to watch Kirch's videos as reference because her videos do help as Tamaoki's ways of teaching can be quite confusing otherwise that class is an easy A. Of all this boring dialog that you have comprehended, what I'm trying to say is consistency-not the bad one the good one- is key to doing well in Kirch's class and well... all your classes for junior year.

It's easy to adjust to the flip classroom honestly most of you guys talk in class and don't pay attention to the teachers in traditional classes anyhow and refer to the internet at home to understand how to do that "one assignment". It's the same with Kirch's way of teaching; go home and learn through videos, go to class and talk about it-with a couple of side conversations here and there- and if you're confident take the quiz in class. All you need is the computer. Now lets get to the facts, we live in Santa Ana. It's all middle class and well to do here in South Santa Ana, but most people in Segerstrom live up North and not everyone is rich and owns internet, much less a computer, but that's solved, Mrs. Kirch has computers available everyday and if you don't have internet she can provide you with actual tangible DVDs that she created just for you guys, just another heads up for those who aren't technologically updated and wealthy.

Aside from that, like I said from the second paragraph, the Flip Classroom is much different from traditional classes as you do the learning at home and you do the homework which is classwork in class, and you take the quiz at your own time. Mrs. Kirch may say that you can go on your own pace in the flip classroom, but that only works for those who are impatient with slow learners and wants to move ahead. For example, you can't take a Unit A test in December just because that is your pace, you have to go by schedule, if you slack off you will get a support (homework) card. In other words you can go ahead but you can't fall behind. What you can expect in your daily life in her class are walking to the door, saying hello to Mrs. Kirch, sitting at your table, talking with your table, taking a quiz, going on the computer, and talking some more, that's about it, or course it's a different atmosphere during test days. 

Your year with Kirch and Tamaoki may be somewhat different as there is that common core that Obama recently established for all public grade school classes in the US, but the changes shouldn't be too drastic. 

 You can learn some KIRCH terminology and some tips in this video

Unit V Big Questions

Explain in detail where the formula for the difference quotient comes from now that you know!  Include all appropriate terminology (secant line, tangent line, h/delta x, etc).  Your post must include text and some form of media (picture/video) to support.

The difference quotient has something to do with the slope formula.

The difference quotient formula comes from a point in x and then the height in the point that shows the functions. We can find the secant line with the 2 points with point x then the second with x+ a number in this case h because variables are easier when numbers are ambiguous and because we can note that the distance from x to x+# is h. 

To find the tangent line we need to use the difference quotient formula and get h to the limit 0 because tangent lines are derivatives.