Monday, June 3, 2013

Letter to Math Analysis Honors Students (2013-2014)

Dear Future Math Analysis Honors Students,

          For many much of my classmates this year has been filled with struggles, lots of due dates, but most importantly, PROGRESS. While some may feel that math is easy and others might find it on the challenging side, this math class is like unlike any other math class you will ever have -- and I mean that in a good way. Your year in math will be functioning in a way that will make you responsible for your own learning. You will be tested on how well you manage your time, how seriously you take every piece of work (including the WSQs), and how determined you are to learn the math. Will certain units may be easy, you will be thrown harder units as the year progresses and you can not simply rely on your prior basic algebra skills to solve. In this classroom, you must carry yourself with integrity. Yes, cheating on your PQs and PTs will get the job done, but when test day come, you will not have mastered the Unit as well as you thought. Some may think that they can cram and do quick review and some may even get away with it, HOWEVER, on the final you will not have it this easy. You will suffer from your lack of comprehension of the unit and that will definitely hurt your grade. There will be times when you feel extremely overwhelmed and frustrated with the work load, but its best to throw those feelings aside and just get through the work rather than waste X amount of time complaining. Sometimes you may feel like that one WPP is a waste of time and is meaningless, but it really will help you better understand that concept. As I said before, this all depends on how motivated and focused you are. Moreover, do not expect something you do not deserve. For example, if you cheated on your PQs or PTs or did not try hard on the other work that was assigned to you, don't expect to get an A on the test-- be reasonable. This is one of those classes where hard work counts. Its not just memorizing, it is UNDERSTANDING. The flipped classroom may take some time to get used to, but with time, it will become very easy. Mrs. Kirch has given you all of the tools (videos, SSS Packets, WSQ Charts, WSQs, etc.) it is up to you to use them, and use them wisely. With the flipped classroom you can learn at home and bring your questions and do your work at school. Of course, as I have mentioned before, you MUST use your time wisely. If you spend half the class period pretending to do your work, than for that night not only do you have to watch the videos for the new concept, but you also have to do the PQs for the previous concept. DON'T GIVE YOURSELF MORE WORK. In class you actually get to have one on one time with the teacher and ask your classmates for help. You can also get ahead when you know that you have a huge project coming up or an essay due soon. Personally, because I came into this class with an open mind I easily adjusted to the flipped classroom and my work ethic drastically increased. Lastly, in a regular classroom you probably did a few math problems for homework, the teacher lectured in class, then assigned homework on the lesson. With the flipped class room, you move past the normal homework practice problems and you literally interact with math. You make your own problems, your own videos on how to work your own problems. You get to make tests and you experience math in new ways. You finally move past knowing a concept, you actually realize its importance, its derivation, and how that comes into play with the real world. In the end, it is all up to you. Mrs. Kirch can not force you to do the work-- it is up to you to decide to do it. It is your responsibility. That does not mean you are alone. You still have support at school. That is nice to know, isn't it? Good luck, everyone!

- Yours Truly, Arlene S. (Period 6 - Princess table D with Tien N.,  
 Tiffany T., Grecia G., Miriam L., & Jessica R.)

Sunday, June 2, 2013

Unit V. BIG Question



  • What is this video about?   This video goes over how to derive the difference quotient. It also describes the resemblances of small secant lines to tangent lines.


  • What does the viewer need to pay special attention to in order to understand the concept? Understand that a secant line hits a graph at TWO points whereas a tangent line hits the graph at only ONE point. Moreover, the smaller the h (delta x, dx) the more the secant and tangent lines resemble one another. Lastly, solving the difference quotient is like evaluating the derivative except for the derivative we take it a few steps further by using the "Limit Definition of the Derivative." In the video I refer to this in mathematical terms: the limit as 'h' approaches 0.

Monday, May 27, 2013

Unit U. BIG Questions

Unit U. BIG Question #1


 

Unit U. BIG Question #2


 

Unit U. BIG Question #3


Wednesday, April 24, 2013

Unit T. BIG Question #4




  • What is this video about?   In this video I explicitly focus on why sine and cosine do NOT have asymptotes and why the other four trig graphs do.  I also go over the basics of the trig functions when referencing the Unit Circle.


  • What does the viewer need to pay special attention to in order to understand the concept? Although I don't quite center the attention on the visuals of the graphs, they are a big part on why I made this video. Asymptotes are what are drawn on the graphs and I simply made this video as a rationale to demonstrate the purpose of why not all of the trig graphs have them (redundant, I know! But that is how important this is if I am emphasizing it twice!!!)

Tuesday, April 23, 2013

Unit T. BIG Question #3




  • What is this video about?   This video  goes over why a "normal" tangent graph is uphill where as a "normal" cotangent graph proceeds downhill. Besides their differences, I also detail some of the similarities between tangent and cotangent. 


  • What does the viewer need to pay special attention to in order to understand the concept? Pay attention to the use of the unit circle ratios of sin(x)/cos(x) for tangent and cos(x)/sin(x) for cotangent. By understanding this, you will see why we have asymptotes where we do. Also understand how asymptotes play into the why "normal" tangent graphs are uphill and "normal" cotangent graphs are downhill.

Unit T. BIG Question #2




  • What is this video about?    In this video I give an in-depth clarification on the relationship between sine and cosine parent graphs with tangent, cotangent, secant, and cosecant. I also highlight asymptotes and their role in the parent graphs of these trig function. 


  • What does the viewer need to pay special attention to in order to understand the concept? For best results, be sure to pause and rewind as needed throughout the video. Don't be afraid to give your brain time to process all of the information I am throwing at you!!! 

Sunday, April 21, 2013

Unit T. BIG Question #1

Unit T: BIG Question Part 1a.

 


  • What is this video about? 
    This video gives a thorough explanation for the reason that sine and cosine have a period of 2pi, whereas tangent has a period of simply pi. With this information and knowledge, one will be able to understand why the graphs (whether they are parent graphs or shifted graphs) of sine, cosine, and tangent look as they do.
  • What does the viewer need to pay special attention to in order to understand the concept?
     Pay attention to the importance of the Unit Circle and how that relates to why the pattern of the periods are the way they are. 




Unit T: BIG Question Part 1b.







  • What is this video about? 
    This video goes over how sine and cosine have amplitudes of 1 and why the other trig function do not have amplitudes. I do cover asymptotes as well so that is basic review from previous units. The Unit Circle will be very prominent as far as amplitudes and asymptotes go.

  • What does the viewer need to pay special attention to in order to understand the concept?
      When I say "You'd think their graphs would look the same..." I am comparing the cotangent parent graph to the tangent parent graph. [7:38 of the video]. Moreover, when describing cotangent I say "amplitudes" but I really meant to say "asymptotes."  Lastly, please do pay special attention to how the Unit Circle relates to the parent graphs of each trig function - I did show it many times and mentioned it countless times for a reason!!!