Wednesday, March 27, 2013
Unit R: Student Problem 1 (Concept 1)
This problem is about using sum and difference formulas in concept 1 of unit R. In this concept all we must do is plug in our exact values of an angle, and we will get our exact answer.
We can always check our answers by just plugging them into our calculator.
Wednesday, March 20, 2013
Unit Q Blog Post 1: Pythagorean Identities
Deriving Pythagorean Identities
In this chapter we have 3 Pythagorean Identities:
1. sin²x + cos²x=1
2. 1 + tan²x=sec²x
3. 1 + cot²x=csc²x
Pythagorean Identity #1
For our first Pythagorean Identity, we can derive it from a unit circle. As you can see on the right, we have a right triangle labeled x, y, and 1 (hypotenuse is always 1).
From here, we can substitute or x and y value. 'x' will be substituted to become cosx, and 'y' will be substituted to become sinx.
We label 'x' value as cosx and 'y' as sinx because of the ratio identity, tanx. As a ratio identity, tanx=sinx/cosx. As a trigonometric ratio, tanx=y/x therefore, sinx will be in place of 'y' and cosx will be in place of 'x'.
Now that we have labeled our triangle, we can integrate the Pythagorean theorem, x²+y²=1.
Pythagorean Identity #2
For our second identity, we start with our first identity cos²x+sin²x=1. From here we can derive it and retrieve our second one.First things first, we have cos²x+sin²x=1. Now what we must do is divide the WHOLE equation by cos²x.
Once we do so, we can cancel out the two cos²x and it will become 1, sin²x/cos²x will become tan²x as a ratio identity, and 1/cos²x is equivalent to sec²x. So now we have our equation 1 + tan²x=sec²x.
Pythagorean Identity #3
For our second identity, we start with our first identity cos²x+sin²x=1. From here we can derive it and retrieve our second one.First things first, we have cos²x+sin²x=1. Now what we must do is divide the WHOLE equation by sin²x.
Once we do so, we can cancel out the two sin²x and it will become 1, cos²x/sin²x will become cot²x as a ratio identity, and 1/sin²x is equivalent to csc²x. So now we have our equation 1 + cot²x=csc²x.
All Pictures taken from here. I do not take credit for making any of these pictures.
Monday, March 18, 2013
Math Analysis Reflection
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.
On the Unit O Test, I feel like I did extremely well until I got the test results back. I made extremely minor mistakes. As I prepared for the retake, I didn't feel like any of the work I did was necessary. I retook the test and got a way higher score from learning from my mistakes. Overall, I felt like my test grade was very good for the Unit. For Unit P, my test grade was actually better than I expected. For this test I really gambled my luck. I got an 85 expecting to get something way lower. My quiz scores demonstrated that I made minor mistakes as well and fixed them on the assessment.
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.
The first step I take very seriously. I try to focus as much as I can to learn the material that I need to. I don't know how to improve my focus but I already try my best. For the second step, I do not take seriously at all. I feel like that is not necessary, I only use the videos and the packet. Same with step three and four. I try to do my PQs as much as I can until I feel very confident. The quizzes are pretty much a simulation of the test so try to take them seriously as well, If I feel like I am not confident, I would know what to study before the test day. For the test, I take my time and go over each problem slowly and this sometimes leads to conflict because the bell rings and I run out of time.
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?
On the day of the test, I feel somewhat confident. Realistically, the test is always intimidating, however I have learned to conquer my enemies, and step on the field as I if I am always going to conquer. Starting off with the first test in semester 2, I always circle the A+ on the corner of my test, believing that I would get that. Realistically I never earn the perfect score but I always earn a score that is fairly close to that. One time I did not circle the letter grade I predicted to get at all and I got a C, which was very coincidental, but now on every test it is like a ritual for me to circle A+. I feel like this year of math I have learned WAY more than last year. I feel like this class is more organized than any of my other classes from previous years. In my opinion, the practice quizzes help a lot. If I get something wrong, I can learn from my mistakes and never make that same mistake again on the test. I feel like the PQ, and PT Fall under the same category, and are just there for practice. Math this year has help me to understand why something happens in math. It is not just the procedure anymore, but the reasoning behind it. By deriving formulas from triangle, it has helped me understand that all these formulas do not simply pop up from the shadows. My work ethic is very inconsistent. There are weeks were I try very hard, and then there are weeks where I am so tired from how hard I've been trying. However, after the many months of junior year, I've started to prioritize math over my other classes. Work ethic is very important in real life. One slip off the track and it could be possible to never get back on. It is important to stay consistent through the whole year no matter how hard it is, it will eventually pay off. As of right now, I am currently trying my best to practice what I preach. I am still young and learning and math analysis this year has taught me a lot.
On the Unit O Test, I feel like I did extremely well until I got the test results back. I made extremely minor mistakes. As I prepared for the retake, I didn't feel like any of the work I did was necessary. I retook the test and got a way higher score from learning from my mistakes. Overall, I felt like my test grade was very good for the Unit. For Unit P, my test grade was actually better than I expected. For this test I really gambled my luck. I got an 85 expecting to get something way lower. My quiz scores demonstrated that I made minor mistakes as well and fixed them on the assessment.
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.
The first step I take very seriously. I try to focus as much as I can to learn the material that I need to. I don't know how to improve my focus but I already try my best. For the second step, I do not take seriously at all. I feel like that is not necessary, I only use the videos and the packet. Same with step three and four. I try to do my PQs as much as I can until I feel very confident. The quizzes are pretty much a simulation of the test so try to take them seriously as well, If I feel like I am not confident, I would know what to study before the test day. For the test, I take my time and go over each problem slowly and this sometimes leads to conflict because the bell rings and I run out of time.
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?
On the day of the test, I feel somewhat confident. Realistically, the test is always intimidating, however I have learned to conquer my enemies, and step on the field as I if I am always going to conquer. Starting off with the first test in semester 2, I always circle the A+ on the corner of my test, believing that I would get that. Realistically I never earn the perfect score but I always earn a score that is fairly close to that. One time I did not circle the letter grade I predicted to get at all and I got a C, which was very coincidental, but now on every test it is like a ritual for me to circle A+. I feel like this year of math I have learned WAY more than last year. I feel like this class is more organized than any of my other classes from previous years. In my opinion, the practice quizzes help a lot. If I get something wrong, I can learn from my mistakes and never make that same mistake again on the test. I feel like the PQ, and PT Fall under the same category, and are just there for practice. Math this year has help me to understand why something happens in math. It is not just the procedure anymore, but the reasoning behind it. By deriving formulas from triangle, it has helped me understand that all these formulas do not simply pop up from the shadows. My work ethic is very inconsistent. There are weeks were I try very hard, and then there are weeks where I am so tired from how hard I've been trying. However, after the many months of junior year, I've started to prioritize math over my other classes. Work ethic is very important in real life. One slip off the track and it could be possible to never get back on. It is important to stay consistent through the whole year no matter how hard it is, it will eventually pay off. As of right now, I am currently trying my best to practice what I preach. I am still young and learning and math analysis this year has taught me a lot.
Thursday, March 7, 2013
WPP #14 Unit P Concept 7
- This concept incorporates law of cosines in word problems
- Listen carefully as I demonstrate how to find sides and angles using the law of cosines
WPP #13 Unit P Concept 6
- This is about incorporating law of sines in word problems
- Watch carefully as I find the missing angles and sides of the triangle.
Subscribe to:
Posts (Atom)