Final Blog post

The post is a letter to a Math Analysis Honors student in my class next year.  

1.              What do you want to say to them to help them have the most successful year possible?  

2.              How can they best adjust to the flipped classroom and learn to work with all the technology I require of them?  (do you have any specific tips for them or experiences you could share?)

3.              What can they expect to be different from their previous math classes?

 

1.Well the key to getting an A in this class is to simply watch the videos. Once you watch the videos everything will be smooth. Don’t fall behind because it will back fire and you will be trying to catch up all year. I didn’t have the most successful year but you guys are new and I hope you don’t make the mistakes I did. Regardless of how much work it is, it will benefit you in the future.

2.Well at first it will seem scary but its simple and basic, just go home watch video take notes then come to school and ask questions, discuss, and do some practice. Be sure to practice and get used to it by the summer, it will be worth it in the future you will have a great start and will understand and be adjusted to the Flipped class room.

3.You will fell the difference but you have to accommodate to the way the teacher teaches. This will be stronger more effective way to learn your material. You can watch the lesson over and over again until you get it. There are lots of resources given by the teacher; a lot more help then pervious math classes. You will fell frightened at first but it will benefit you to better understanding of the math material.

Unit V blog post

The difference quotient is the ratio of the change in y-values over the change in x-values. It's simply a more complex variation of the formula for slope. Using Secant line and tangent line. 

A and B are points on the graph of f. A line passing trough the two points A ( x , f(x)) and B(x+h , f(x+h)) is called a secant line.

The slope of the parabola at the point (2,4). As you see in the picture the graph will be y=x^2 with a tangent line at (2,4)

Unit U blog post

1. A continuity function is a function where there are no jumps no holes no asymptotes.

A discontinuity is a function with a hole, an asymptote, a jump, or oscillating behavior. 

2. A limit is the intended height of a function. A limit exist when the intended height approaching from the right and left are the same. A limit doesn't exist when you get different intended heights approaching to the left and approaching to the right. The difference from a limit and a value is that even if you have a hole (which is the value) on the intended height it will still be a limit, but its value wont be  .

3. We evaluate limits numerically we will get x-values really close to the original "x" from both the right and the left. There we will see if the intended height will be the same , which will tell us if we have a limit or not.  

To evaluate limits graphically we look at the graph, we look at the point as x approaches whatever from the right and the left, from there we can conclude if its a limit or not. 

To evaluate limits algebraically we simply just substitute the x approaches to the function. However sometimes it might not work so we use factoring, if that also fails we multiple by the conjugate.  

CITATIONS: 

maretbccalculus2007-2008.pbworks.com

www.analyzemath.com

tutorial.math.lamar.edu

Unit T post #4

Why do sine and cosine NOT have asymptotes, but the four other trig graphs do? 
Well then sine and cosine do not have asymptotes because they will be 1 which will make them 0. There them having no asymptote.  And for the 4 rest trig functions they will have some because even if they are equal to 0 they will have an asymptote Tangent and cotangent at 0 and 180 , or pi. Secant will be 0. As well as cosecant. 

Unit T post #3

Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill?
This is because there ratios are both over 1. Cotangent is the reciprocal of tangent , there for it will be the exact graph but tangent going from down to up, and cotangent going from top to bottom.

www.analyzemath.com

Unit T post # 2

How do the graphs of sine and cosine relate to each of the others? 

Tangent?  tanx=sinx/cosx. if sine and cosine are positive, tangent is also positive. If one of them is negative, tangent is negative. If both are negative, obviously tangent is positive. Therefore there would be asymptotes where cosx=0, so where x is equal to zero. There would be asymptotes at pi/2 and also at 3pi/2 and it would go on forever. 

Cotangent? cotx=cosx/sinx. The ratio of cosx/sinx because of triangles would be x/y . Therefore, there would be asymptotes where y is equal to 0 which would be at 0 and pi.\

Secant?  Since secant is the reciprocal of cosine, you would have an asymptote where 1/x this will be undefined, so where its x=0 on the unit circle which would be 0 and pi. 

Cosecant? Cosecant is the reciprocal of sine,  1/y. There would be asymptotes where y=0 because i-1/0 is 0. y=0 so there would be asymptotes at pi/2 and 3pi/2 and will go on forever.

Unit T Post #1

How do the trig graphs relate to the Unit Circle? 
A. Period ? Why is the period for sine and cosine 2pi, where as the period for tangent and cotangent is pi? 
The period for sine and cosine is 2pi because the period infers to how long it takes to repeat the patterns of positive and negative values based on the different quadrants. Also, for sine how we know its 2pi because the pattern is positive to positive to negative to negative, which is one full rotation . and is similar to cosine.  On the other hand for tangent and cotangent it takes half of the unit circle to repeat the pattern of positives or negatives so there period is pi. 
B. Amplitude? How does the fact that sine and cosine have amplitudes of one ( and the trig functions don't have amplitudes) relate to what we know about the Unit Circle? 
This most importantly is related in how the radius of the circle is 1. The greatest values that are on the unit circle to the left and the right is 1 as well as up and down. picture: www.rasmus.is

Assessment #4

http://www.youtube.com/watch?v=jO3x00GzlKo&feature=youtu.be

Assessment #3

http://www.youtube.com/watch?v=fNUjHNVbvOg&feature=youtu.be

Assessment #2

Well the sum formula and the half angle formula , are one of the same. They are both correct ways to solve a problem. The answers dont seem to be the same but if we plug them into our calculator they will be the same. I made a mistake on the sum formula I ment to put + rad3 on the Tan. So it is the same    just a different way to do it.  Its the same because for one you use exact unit circle measures by splitting it into two , and for the half angle you are doubling it to get something alike but that is just one angle.

Unit R: Concept 3 student 3

This problem deals with trigs of an inverse trig function. We will find the value of the expression without using a calculator. In my problem you need to first of all label, the two parts U and V. Once you do that you can separate them and get both the sin and cos. Then we will plug them back into our formula. We will then get an answer. That will be all.

Unit R: Student Problem 2 concept 2

Well in this problem we are dealing with sum and difference formulas when given values of right triangles. Well first we begin by drawing the appropriate triangles in the correct quadrants. We will find the missing side of the triangle. We plug them in the sum and difference formula. We need to make sure we use all the formulas to get all the exact answers for all three sin, cos, and tan. We will have varies answers for all of them , but some will repeat.

Unit R: Concept 1

This problem deals with exact values of sums or differences. My problem deals with sums. We are given a radian therefore to be easier we convert it to degrees. For degrees we make sure we used a degree that is on the unit circle. Make sure you add both of the sines , cosines , and tangents together to get just one single sin, cos , and tan. This will allow us to get our answer correctly.

Unit Q concept 4 problems

Unit Q concept two blog post PQ problem 5

Deriving the Pythagorean Identities

Main Identity :                                       cos^2 (-) + sin^2 (-) = 1

Back to Unit Circle:

So in the Pythagorean theorem the square of the long side equals the square of the two other sides added together.
                             ex    x^2+y^2=1
On the other hand the unit circle, the longest side is the radius which always equals 1. X is our cosine while Y is our sine. so they added together they will equal 1.
                                     ex   cos^2 (-) + sin^2 (-) = 1

Deriving the Two Remaining Pythagorean Identities:
The pictures above will show you how. 

Math Reflective Blog Post

1. How have you performed on the Unit O and P tests? What evidence do you have from your work in the unit that supports your test grade (good or bad)? Be specific and include a minimum of three pieces of evidence.

 RESPOND HERE: I have performed very poorly do to the lack of preparation i had. I tried atleast 5 problems from each concept but it seemed to not benefit me at all. The evidence that my work reflected was bad it was not much practice at all. First of all i some how knew how to do the quizzes but i never learned how to do anything properly how taught to me, i went my own way and it back fired. I lacked there deserved the grade i got.

2. You are able to learn material in a variety of ways in Math Analysis. It generally follows this pattern: → Your initial source of information is generally the video lessons and SSS packets followed by a processing and reflection activity via the WSQ
 → individual supplemental research online or in the textbook before class
 → reviewing and accessing supplementary resources provided by Mrs. Kirch on the blog
 → discussion with classmates about key concepts
 → practice of math concepts through PQs → formatively assessing your progress through concept quizzes
 → cumulatively reviewing material through PTs
 → Final Assessment via Unit Test.

 Talk through each of the steps given in the following terms: a. How seriously do you take this step for your learning? What evidence do you have to support your claim? Make sure to make reference to all 8 steps. b. How could you improve your focus and attention on this step to improve your mastery of the material? What specific next steps would this entail? Make sure to make reference to all 8 steps. \ 

RESPOND HERE: I don't really take these steps seriously, i tend to go my own way and teach myself. I just go through the little notes on the sss packet and try to do something to get the answer in the back for the pqs from there if i get them right i go ahead. Then my final review is to do the practice test. Well I dont have much to talk about in regards to the 8 steps because i dont follow them.

 3. Reflect on your learning this year thus far by considering the following questions:
a. How confident do you generally feel on the day of a Unit Test? Give evidence and specifics to back up your answer.
b. How well do you feel you have learned the math material this year as compared to your previous years in math? Give evidence to support your claim.
c. How DEEPLY do you feel you have learned the math material this year as compared to your previous years in math? Give evidence to support your claim.
d. Do you normally feel like you understand the WHY behind the math and not just the WHAT/HOW? Meaning, do you understand why things work, how they are connected to each other, etc, and not just the procedures? Explain your answer in detail and cite specific evidence from this year.
e. How does your work ethic relate to your performance and success? What is the value of work ethic in real life?

RESPOND HERE: I dont feel confident at all. I dont prepare, i dont really watch the videos. I feel like i dont learn everything i am too pressured. I am used to the traditional way of teaching, and i will stop there...... I do understand how everything ends up working together. FOr example most of the trig functions go together like the unit circle. Well my work ethic for this class is horrible, i cant learn at home so yeah.

Wpp 13 : Unit P concepts 6-7a

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Wpp 14: Unit P concepts 6-7 b

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WPP 11: Unit O concept 9

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WPP 12: Unit O concept 10

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Parabola Conic Section

1. Parabola, a parabola is that any point from the focus to the parabola, perpendicular to the directix will be equal in length. It plays the role of a parabola is that we can then tell if the parabola works cause the distance from any point to perpendicular to the directix will be the same distance. The shape is symetrical.

2. Well the "P" in a parabola will make the parabola either skinny or wide. If the P is small for example, 1/4 it will be really skinny. On the other hand if it is large like for example 5 it will be really wide. 3. well for a parabola, there is a 3 dimensinal figure which is called a plate. This shape allows to send waves of information. Due to the structure it allows you to communicate better in sending waves for example a dish from cable.

citations: http://www.k12math.com/math-concepts/algebra/conics/parabola-directrix.png http://www.wyzant.com/Help/Math/Algebra/Conic_Sections.aspx http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/9/98/Radio_telescope_The_Dish.jpg&imgrefurl=http://en.wikipedia.org/wiki/File:Radio_telescope_The_Dish.jpg&usg=__3_S9mViS6MkXKw2FDpSgH5JYBAc=&h=2746&w=4291&sz=5411&hl=en&start=10&sig2=WXsCtunNumZm2qLpNyZInw&zoom=1&tbnid=8FgevpexBll-DM:&tbnh=96&tbnw=150&ei=4zEMUfrNA-HxiwLj9IDwCw&prev=/search%3Fq%3Ddish%26hl%3Den%26safe%3Dactive%26gbv%3D2%26tbm%3Disch&itbs=1