Create your own Playlist on MentorMob!
Wednesday, March 27, 2013
Tuesday, March 26, 2013
Monday, March 25, 2013
Thursday, March 21, 2013
Concept 4 Problems Solving Trig Functions
Level 1
In this level, we simply take the trig function we have and find out how we get the given value through the unit circle. since we know that tan is x/y, we know that we can get the ratio rad3/3 with 1/2/rad3/3. the given points are found in the 60 degree, and also in 240 degree, since it is a positive function.
Level 2
The second level, we deal with simple problem solving. we must get the sin (x) by itself. In this case, we are getting no solution since sin must be -1<x<1.
Level 3
In this level, we deal with more complicated solving. we must get a common trig function, and since we know from the ratio identity, csc=1/sin, and cot=cos/sin. there is a common denominator, so we combine the equation. next, we must multiply sin to both sides. since we are now stuck, we must square both sides. we know that sin^2(x) is 1-cos^2. finally, we take what is given, and combine like terms, having a zero on the right side. we take out the common factor which is 2cos. then, we solve for both terms.
Don't forget that there may be extraneous solutions!
Level 4
In this level of problem, we are looking for half/double angles. We need to replace the function with "m", then solve for m. when we do, we take what is solve, 360 and 180, and equal it to x/4. put it as "x" and get the final angles.
Level 2
Level 3In this level, we deal with more complicated solving. we must get a common trig function, and since we know from the ratio identity, csc=1/sin, and cot=cos/sin. there is a common denominator, so we combine the equation. next, we must multiply sin to both sides. since we are now stuck, we must square both sides. we know that sin^2(x) is 1-cos^2. finally, we take what is given, and combine like terms, having a zero on the right side. we take out the common factor which is 2cos. then, we solve for both terms.
Don't forget that there may be extraneous solutions!
Level 4
Solving Trigonometric problems using Identites and Right Trianlges
When you are solving to find all trigonometric functions, there are two possible way to do so. One way is using right triangles to find all the function with given one we know. Using SOH CAH TOA , we are able to to find the trig functions of any other angle. O=opposite, H=hypotenuse, A=adjacent.
Since we are given sin=1/2 and cos=rad3/2, we all the required information we need. **problem worked out here------------->
The next way to find all possible trig function is using the identities. we must first know where the the functions will be located on the unit circle. since cos and sin are both in in the 1st quadrant, we now know that all possible answers will be positive. Now, here are the identities that we use:
tan=sin/cos
cot=cos/sin The work is shown here----->
csc=1/sin
sec=1/cos
Wednesday, March 20, 2013
Deriving the Pythagorean Identities
We are given the main identity of cos^2+sin^2=1. This identity is derived from the ratios of cos and sine in a right triangle. Cos is equal to x/1, that will be the first part of the equation. Sin is equal to y/1, that will be the second part of the equation. R=1. So our equation of the pythagoreon is x^2+y^2=r^2. By substituting the ratios we get cos^2+sin^2=1.
When we divide cos^2 to the entire eqution, we get the dervation of the next Pythagoreon identity: 1+tan^2=sec^2. *This occurs because cos/cos=1. We know that sin/cos=tan through the ratio identities. And finally, 1/cos=sec.
Our next derivation is derived when we dived sin to the entire equation: cot^2+1=csc^2. *Dividing sin will do this: cos/sin=cot, which is what we know from the ratio identity. sin/sin=1. And finally, 1/sin=csc.
Sunday, March 17, 2013
Reflective Unit O & P
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: Overall, i did well on the unit O and P Tests. Submitted all my WSQs, watching all the videos and practicing along at home. I took my time to finish the Practice Quizzes, and checking if the the answers are correct. For the most part, i managed to take my quizzes on time, except for the last ones, I had to rush through them. Also, i did not retake any of my quizzes, which might suggest why i did not the better grade i wanted. What is interesting is that I had gotten a better on my Unit P test then i did on my Unit O Test, and i has a disadvantage by not having internet at my home to study. I did my best to not fall completely behind by finishing my PQs and doing all my assessments. The Practice Test did give me the extra push to understand the material.
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:
a. At my time at home, i gave my full attention to the the online videos and the SSS packets. i took all the necessary notes and usually went ahead to do any other ones that were not required. The online summary i thought was important to help me explain what i had learn. I did not take advantage of any other online research or look up the concepts in the textbooks because i felt i was already understanding the material. The only resources i would use on Mrs. Kirch's Blog is the she would post herself. During class, I personally worked batter on my own, due to distractions and time. Although, when i did get stuck on some concepts, the discussions were helpful for me to get clarification. i would also do my best to ask questions to others who new the concept i has trouble with. The PQs i took the most time in. I felt that practicing these problems on my own will really help me understand. Sometimes, when the concept is already simply, yet there is so many of them, i tend to not finish them. Also, i felt the quizzes were important, but i did not manage my time to finish as good i i should have. i usually don't take my time to retake the quizzes. The Practice Tests are sometimes tedious, but are indeed important. The are intended to be done consecutively during the unit, be i do not do that. I usually do them in in large portions at a time, and when i do, i am even more confident on the day of the test. The actual assessment is greatly beneficial to my learning. In every test day, i make sure i have all the necessary things to use and remember everything from what i practice. In every test i have taken, not gotten lower than a 72%. (not counting Unit A-D).
b. One important thing i must need to improve on is to complete the assignment on time and not at the last minute. By doing so, i believe i would be able to learn at my full potential. For the most part, i do well when managing my work with the online videos and WSQ, along with the notes for the SSS. when i do get stuck on problems at home, i will do some search online to help me understand my mistakes and learn. During lass, i shall improve with my work ethic and remain focus the entire class period. I will separate myself from people if i have to, but also really take class time serious by getting help from Mrs. Kirch and my peers. With the PQs, i will make sure i finish the required ones during class. The biggest step i will do for the Quizzes is to finish them on time and to retakes when i need to. As for the PTs, i will need to finish them by concepts in order to stay on top of my work and make sure i look for the correction to see if any mistakes were made. All this i feel is perfect preparation for the assessment. More importantly, i will take necessary preparation on test day by doing PMI for my quiz packet.
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: a.I generally feel confident on my test day. I have my work finished, and have understood the concepts of the Unit. the times i did not feel confident is when there was incomplete work with my practice test or the notes of the SSS.
b.Compared with previous years in math class, i felt as though it has been a little tougher to learn, but much more effective. for example, In Collage Algebra, i would learn know all the concepts during the test, but will in class, it was difficult for me to fully practice.
c. Deeply, i felt like i have learn a lot of the math material this year compared to last year. The concepts are much more in depth, and the process of learning is even greater depth. While i was getting "As" on tests in my Algebra 2 class, i basically had to look up some information on the text book and learn the concepts on my own. in this class, i still manged to get high grades, and i am still responsible for my own learning.
d. Normally, i do understand the "why" behind the math. there are time when i have no clue as to why some certain concepts are derived from, for example, the Law of Cosines. I do not know why it is the formula a^2=b^2+c^2-2(a)(c)cosA, i do remember the formula. But as soon as i do, i remember them always. The procedure, in my perspective, are only the process of understanding the "why" behind the math.
e. The value of taking your time to do your work and to do it honestly is fairly important. doing a lousy job at things can lead to a bigger mess in the end. My success and performance always relates to the time i have committed on the subject or work. When i sow a little, i will only reap a little. when i sow alot, the reaping will be immense.
RESPOND HERE: Overall, i did well on the unit O and P Tests. Submitted all my WSQs, watching all the videos and practicing along at home. I took my time to finish the Practice Quizzes, and checking if the the answers are correct. For the most part, i managed to take my quizzes on time, except for the last ones, I had to rush through them. Also, i did not retake any of my quizzes, which might suggest why i did not the better grade i wanted. What is interesting is that I had gotten a better on my Unit P test then i did on my Unit O Test, and i has a disadvantage by not having internet at my home to study. I did my best to not fall completely behind by finishing my PQs and doing all my assessments. The Practice Test did give me the extra push to understand the material.
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:
a. At my time at home, i gave my full attention to the the online videos and the SSS packets. i took all the necessary notes and usually went ahead to do any other ones that were not required. The online summary i thought was important to help me explain what i had learn. I did not take advantage of any other online research or look up the concepts in the textbooks because i felt i was already understanding the material. The only resources i would use on Mrs. Kirch's Blog is the she would post herself. During class, I personally worked batter on my own, due to distractions and time. Although, when i did get stuck on some concepts, the discussions were helpful for me to get clarification. i would also do my best to ask questions to others who new the concept i has trouble with. The PQs i took the most time in. I felt that practicing these problems on my own will really help me understand. Sometimes, when the concept is already simply, yet there is so many of them, i tend to not finish them. Also, i felt the quizzes were important, but i did not manage my time to finish as good i i should have. i usually don't take my time to retake the quizzes. The Practice Tests are sometimes tedious, but are indeed important. The are intended to be done consecutively during the unit, be i do not do that. I usually do them in in large portions at a time, and when i do, i am even more confident on the day of the test. The actual assessment is greatly beneficial to my learning. In every test day, i make sure i have all the necessary things to use and remember everything from what i practice. In every test i have taken, not gotten lower than a 72%. (not counting Unit A-D).
b. One important thing i must need to improve on is to complete the assignment on time and not at the last minute. By doing so, i believe i would be able to learn at my full potential. For the most part, i do well when managing my work with the online videos and WSQ, along with the notes for the SSS. when i do get stuck on problems at home, i will do some search online to help me understand my mistakes and learn. During lass, i shall improve with my work ethic and remain focus the entire class period. I will separate myself from people if i have to, but also really take class time serious by getting help from Mrs. Kirch and my peers. With the PQs, i will make sure i finish the required ones during class. The biggest step i will do for the Quizzes is to finish them on time and to retakes when i need to. As for the PTs, i will need to finish them by concepts in order to stay on top of my work and make sure i look for the correction to see if any mistakes were made. All this i feel is perfect preparation for the assessment. More importantly, i will take necessary preparation on test day by doing PMI for my quiz packet.
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: a.I generally feel confident on my test day. I have my work finished, and have understood the concepts of the Unit. the times i did not feel confident is when there was incomplete work with my practice test or the notes of the SSS.
b.Compared with previous years in math class, i felt as though it has been a little tougher to learn, but much more effective. for example, In Collage Algebra, i would learn know all the concepts during the test, but will in class, it was difficult for me to fully practice.
c. Deeply, i felt like i have learn a lot of the math material this year compared to last year. The concepts are much more in depth, and the process of learning is even greater depth. While i was getting "As" on tests in my Algebra 2 class, i basically had to look up some information on the text book and learn the concepts on my own. in this class, i still manged to get high grades, and i am still responsible for my own learning.
d. Normally, i do understand the "why" behind the math. there are time when i have no clue as to why some certain concepts are derived from, for example, the Law of Cosines. I do not know why it is the formula a^2=b^2+c^2-2(a)(c)cosA, i do remember the formula. But as soon as i do, i remember them always. The procedure, in my perspective, are only the process of understanding the "why" behind the math.
e. The value of taking your time to do your work and to do it honestly is fairly important. doing a lousy job at things can lead to a bigger mess in the end. My success and performance always relates to the time i have committed on the subject or work. When i sow a little, i will only reap a little. when i sow alot, the reaping will be immense.
Thursday, March 7, 2013
Wednesday, March 6, 2013
Subscribe to:
Posts (Atom)