Monday, December 10, 2012

Prove it!

Chapter 3 test at the end of this week (Thursday or Friday depending on what section you are in).  

We are wrapping up proofs and you really need to practice them and complete as many as possible (even studying other worked out proofs).  I have posted many proofs worked out on my school website.  Take a look before coming to class.  You are expected to attempt all proofs.  Click on the Ch. 3 resources link on the website.


Also, you will be provided practice resources to get ready for this test.  Chapter 3 is a long chapter so be sure you go back and practice all sections of the chapter.  I have made a practice test but there are also the practice tests and review sections at the end of the chapter.  The more you practice the more confident you will be.


Sunday, December 2, 2012

Sines_Signs_Everywhere theres Signs

Good but not great results on the 3.4_3.5 Quiz.  Not 80% above 80 but close.  I believe if everyone routinely drew a coordinate plane simple diagram we would hit 80% above 80.

The most missed problem was number 6.  You will see it tomorrow or Tuesday, but it basically involved working backwards from a Sec of 5/4 to get the Sin Value.  Everyone got the ratio correct but a little less than half of the class adjusted the Sine to have a negative "sign". 

If a diagram was drawn and the angle drawn carefully (it stated the angle was in Quadrant IV) I bet nearly everyone would have gotten full credit.

There is also a direct link between those who take time on their HW to draw the diagram for these problems and students who write answers only. Develop good habits because Trigonometry is highly visual.

One final thought.  Think of the unit circle as a round paddle wheel (like on an old ship).  If the water surface is the x-axis (y = 0).  Every sign (and csc) value will end up being negative if it under water.

We should be wrapping up chapter 3 this week but it may go a little into next week (long chapter).  Expect at least one more quiz later this week for chapter 3.  Also, I am available for help in room 225 after school on Mondays and Friday and am always in the computer lab in rm 108 until 3:00 on Thursdays.

Sunday, November 18, 2012

Being Thankful_Rule of 3

Only 3 school days this week!

3 resources
Check out my website for some 3.3 sample resources
(D-period should check some HW before class tomorrow)

Check the website for Old Trig. problems to practice, meaning you can expect some more difficult SOH-CAH-TOA problems.  Practice the tough ones to night and check with your classmates

The internet - One thing I want everyone (C and D-period) to do by Tuesday and search for, and print out a good one page unit circle memory sheet.  You can also look ahead into Ch. 3 to see what is coming up as well.


REFLECTION FROM LAST WEEK
72% of C-period got an 80% or above on the first part of the "Quest".  The most missed question involved translating an angle to radians and leaving the result"in terms of pi" as a fraction in simplest term.    The second most missed concept involved converting angular velocity to revolutions per minute (see HW 3.3)

 
KEY GOAL OF THE WEEK STARTING 11/19/12
Know the exact and approximate values of the sine, cosine, and tangent of
 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles


Sunday, November 11, 2012

Newport RI 41 29

Question of the week: (due next class) 
The town of Newport, RI is located at approximately 41 degrees 29 minutes North.  This is the latitude of Newport, RI.
Use this information to determine
a) the decimal degrees of Newport
b) how many miles Newport is from the equator (nearest mile) and
c) the angle (in radians) a turn would it be to measure from the core of the Earth from the equator up to Newport’s latitude. 
You may need to do some digging to see if you can find conversions from “latitude” to actual miles.
EVERYBODY is expected to do this on paper and hand it in next time we meet. 
The first three students to post an answer in the comments section (just answer one part in the comments section of this blog) and explain in a short sentence how they got the number will receive their HW credit AND a homework pass or reduced HW assignment for the upcoming quarter.
  Quarter One Reflection
In our classroom management plan and on the quarter one pacing guide, I mentioned a goal of having over “80% above 80” above on each assessment.  This means for our 20 student class, 16 scored above an 80%.   
This happened for C-period on Friday 3.1/3.2 quiz and nearly happened for D-period (one student off).    Great job!  
Since this helped your scores, I put it in for the 1st quarter grades.  (HW grades are not in yet and nothing will be final until after Tuesday on icue, don't obsess about checking).
Looking forward
 We are just getting started in Chapter 3, which is the “real trig.”  We will be continuing on with section 3.3 but also following up with some of the things I found out in the pre-test (that Geometry one).  Most people understand similar triangle material (a foundation of trigonometry) but enough students did not understand straight forward “SOH CAH TOA” problems that I need to build that into our lessons this week.  If you do understand this (more than half of us) please help out those around you when this comes up again.
 Quarter 2 Changes
While watching the Patriot game and checking the Ch. 2 homeworks, it is clear to me we have some very strong leaders with HW, some in the middle who are doing it but not always getting it, and a few who don’t routinely do HW.  One change I am making for next quarter is to let my leaders lead more.  If all students (100%) check in with homework each day with those around you, your scores (and more importantly your understanding) will go up.  I wil be speaking with my “leaders” and I will be collecting daily Homework from those students who scored very low during quarter one for homework.  If it is still not getting done we will have mandatory “overtime”, coming in after school.
I plan on switching up the seats a little bit too, if you have a preference in the part of the room or know you want to be near someone you work well with, shoot me an email at gsteppen@mpsri.net before Tuesday. 
Now go determine that partial simple distance around part of the earth problem.  Be sure to cite any sources you have about conversions, radius of the Earth or anything.
Mr. Steppen

Monday, November 5, 2012

Unit Conversion_extra credit opportunity

This week we are really getting into the new stuff, actual Trig!

We have converted graphed angles in standard position and talked about what it means to be coterminal and convert from decimal degrees to degrees-minutes-seconds(3.1). 

Today (Monday) we learned how to convert degrees to radians and vice-versa.  It all boils down to a complete circle having 360-degrees and if we know the definition of a radian, a complete circle is 2pi radians.  And a more useful version is that every 180-degrees is equivalent to pi radians.

Extra credit opportunity:

For C-period, we did not define a radian clearly.  The first person from C-period to explain what a radian is in the comments section of this blog gets 10 credits of HW applied to Q1 or a free HW pass for next quarter.  I recommend going to www.khanacademy.org and searching "radian".  One of the videos should give a clear explanation.  Post a comment below with your definition and put your initials or name at the end of the comment.

For D-period, we did define radian.  So the first D-period student to state exactly how many radians comprise a full circle (to the nearest hundredth) you get the same extra credit deal.  Just state the number and put your initials or name in the comments section.

Quarter Ends Friday.  So we are pretty much done except what I am checking for HW and one short 3.1/3.2 quiz Thursday or Friday. 

If you are reading this and did not do the "function drawing" HW on the back of the jack o lantern sheet, that can be handed in by the end of the week as a HW credit to bring up you grade.

Monday, October 29, 2012

Don't need power

to do Homework!  Hopefully, everyone is enjoying and being safe with these couple of days off of school.

What a great time to be sure all of you homework problems are complete as we finish up chapter 2.

Sunday, October 21, 2012

Do you understand graphically...what tools are you using?

We will be wrapping up the Functions Graphing Chapter this week (Chapter 2)

There will be about three new objectives we have to learn by mid-week and the Chapter 2 Test will most likely be Thursday or Friday and cover all the chapter 2 material except 2.7/2.8 (which will not be covered or assessed).

Here is an overview of the new learning targets for this week:

Be able to …                               
            factor using multiple techniques (including completing the square  and by grouping)
            write a quadratic equation given a graph and vertex
(connect to transformations understanding)
            find all zeros (real and non-real) of polynomial functions and understand multiplicity

In addition, we will be practicing material (especially real-life applications) of the functions material we learned in section 2.1-2.6. 

Speaking of real-life applications.  Most real-life situations that can be modeled by functions are not "factorable".   If you are completing a take home quiz or have a quiz coming up you need to be very familiar with finding zeros of functions and using other graphing calculator tools like intersections, etc.

For the large number of you who have not purchased your own graphing calculator, you are putting yourself at a disadvantage.  I did not have mine at home this weekend and did find some online versions.  If you are using any online application be sure you can find zeros and intersections of functions.  A quick search (and updating my java) did allow me do find one decent online calculator.  You can try this one if you have not found something already.  http://www.calculator-grapher.com/

Again, we are not just drawing graphing graphs.  We are finding solutions. Many online version or "apps" draw nice graphs. But you need to do calculatoins with precision and are expected to be able to do that at home.

If anyone wants to share a good site and/or post some images from online calculator website.  Please do so in the comments section.







Sunday, October 14, 2012

Quadratics!

This week will be another week partially interupted by the NECAP exam.  The good news is that the next few sections we are covering are really review of Quadratics and Polynomials (and may help you prepare for the NECAP as well). 

Tomorrow, we will review different types of factoring and discuss a good common approach to factoring Quadratics and Polynomials and will practice with a fun puzzle activity.

I really need to get a good idea of how well you know the 2.3 - 2.5 material and if you completed this weekends handout, that will give me (and you) and great idea of where you are at.

In fact, as a bonus, if you are reading this tonight and go to my website:  http://www.mpsri.net/page.cfm?p=1567 you will find worked out solutions to 2.4 - 2.5 posted under Chapter 2 resources.

If you bring in any evidence that you review this site before class tomorrow, or just simply comment that you checked out this blog tonight, you will earn 5 points extra credit for this Homework.  I will try and post another handout on the website tonight too, that give you a better description of how to score yourself. 

Good luck on the NECAP and don't forget, you can access  many of the released problems from 2007 - 2011 and check your solutions if you do a little poking around on the internet. 

Monday, October 8, 2012

Function Graphing (Ch. 2 week 1)

General - This week we will be  our understanding of graphing different types of functions compared to their parent functions, describing those comparisons algebraically and using math vocabulary, and recognizing even and odd functions.   We will be using a graphing calculator lesson to understand those connections and you will get some feedback (in fact some sample student work with feedback will be posted on the website after Tuesday’s lesson.  The two main text sections this week are 2.2 and 2.1.
3 Key Graphing Process Goals
  • Numerically – Recognize and label key feature coordinates (usually 3-5) and show work using a table of values
  • Algebraically – Understanding from various forms of given function(s).                                     y = a (x – h)?+k       and where it will graph relative to parent function (translate, reflect, dilate, etc.) because of the given coefficients.
  • Verbally – Once you see the patterns, you need to build your math vocabulary to describe what is going on with each function

3 Key Products (All due the class after they are assigned)
·         Text HW  2.2 70/12-30  show given graphs with key features labeled, draw resulting diagrams using a different color pen.  See sample solutions to HW 2.2 on website for guidance about what level of detail is expected to earn a 4 for homework
  • Handout 2.2b – Backside of Transformations Handout (after receiving exit slip feedback)
·         HW 2.1   61/Practice 1-27,34
                                                                      Most likely will have a 2.1 – 2.2 quiz after Weds.
Other Comments
If you did poorly on the Ch. 1 Test, you are expected to make corrections to your exam , redo any missed or incomplete Ch. 1 homework and then see Mr. Steppen about a retake exam.

Monday, October 1, 2012

2009 Necap Practice Exam and starting 2.1

Happy Monday Night,

As I mentioned in class today, I am going to start posting a Sunday night post so everyone in my Trigonometry class is expected to check in at least once a week, usually Sunday night after 8 pm is the best time.  In fact, if you are reading this right now you should become a follower of the blog and  check out to see if there are settings to automatically update you when a new post has been submitted.

Mainly the blog will be a short summary of what we did the previous week and a preview of what is coming up for the week ahead.  I will informally monitoring to see who is participating.  Many of your upcoming college courses may have an online element, so participating with this is good practice in a different style  of communication.

This post is a bonus because I just got a list of who is missing class this week due to the NECAP writing test.  The majority of you are not missing Trig. class (lucky you).  So the plan is to continue on to Chapter 2 (Section 2.1 - 2.2 Graphing Functions this week. 

For my D-period students, you have already been given the task of completing the 2009 Math NECAP released items for homework by Wednesdays class as Homework [20 points].  You can access my website to get that document (see previous blog post for a direct link to website).  However, if you want a printed out copy I was able to print out 25 copies today and for the first five D-period students that stop by 225 in the a.m.  I can give you a copy.  In fact, you will earn extra credit for being the first to read this blog and follow up!  For my    C-period students, you will receive a copy in class tomorrow.

I will see everyone before the NECAP writing assessment, but in any case good luck!  And, by completing the 2009 released Math Items you will be already preparing for the Math NECAP in two weeks.  For my few non-11th graders, the questions are good practice and most relate to our class content anyways.

Life is just a circle.
  

Sunday, September 30, 2012

Thinking Left to Right

A key theme to wrap up Chapter 1 and transition into Chapter 2 (Function Graphing) will be
“Thinking Left to Right”
Just like in English class where we read sentences left to right, in mathematics, we read our graphs left to right and analyze the behavior of a function.  As I read a graph left to right: are my outputs increasing, decreasing, or staying constant?  

We also want to identify any key features on a graph.  Key features may include: any points where the rates of change...change.  Usually, we also want to identify important points like what is happening when the input is zero or basically any points that help us analze the graph.
This will make more sense after we review some of the 1.7 problems on Monday.  But before that, go to my website and take a look at how some of the class work and solutions look compared to yours.  This solutions are posted in the Chapter 1 resource folder. 
Don’t forget -  You should routinely be developing 3 good habits to help yourself learn:
(1)  Attempting and completing all assigned problems daily before the next class
(2) Checking solutions with your classmates and on my website at http://www.mpsri.net/page.cfm?p=1567 (or get there through the MHS website); and
(3) Revising any problems you did not previously understand (use pen if you original was in pencil) after you have seen more sample solutions and talked with your classmates.  Use your resources! 

When I collect and check homeworks, it would be great to see some misunderstanding initially but then evidence that you learned after your first attempt.  That is part of learning! 

Monday, June 4, 2012

"Final" Post

After school today, I reviewed some parabola graphing problems with a student and made a pretty detailed answer key.  It can be found at my website http://www.mpsri.net/page.cfm?p=1567&lastid=1568&do=logoffadmin under Ch. 11 Conic Sections. Anyone who was having trouble with that 11.4 section should take a look.    Also, while I was at my website, I went ahead and posted our topic list (green sheet) and a

new and improved list of practice problems (I am not going to print this out for class)

The first student(s) that complete a detailed step-by-step answer key for the problems that were not already in the Senior review practice problem set, may get some extra credit.  If the explanation of work is detailed but clear and concise.  Most of the problems are the same so it will not be re-assigned.


The final assignment sheet can be found at https://docs.google.com/document/d/1tvfq4BBxxEncYys4J_BF-0NH-Eh9W__D0qRm3Vsv3ow/edit


To be successful on the final, you really need to revisit older topics and make sure you have mastered them. 

Sunday, May 20, 2012

Conic Sections

Plan on wrapping up conic sections this week (we will just learn and be assessed through 11.4.  Tomorrow (Monday) will focus on Parabolas and the next time we meet will be a review day and then our Chapter 11 test will most likely be Thursday.

For our Seniors, we may begin a little cumulative review early which will benefit everyone.  Seniors will be taking their final exams

UPDATE:  Here is a link to our revised assignment sheet:  https://docs.google.com/document/d/15iD4bZXiOUJeephsJmGyvTlS73NXgyiZWUd7t-R0XW0/edit

Since the Junior Breakfast is not until 8:30 on Thursday, C-period will have the Ch.4 Test during 1st period on Thursday (not Friday).  A little pre-breakfast appetizer.

Tuesday, May 1, 2012

Khan Academy to Review Partial Fractions

A quick update to link you to our end of chapter homework assignments to prepare for the Chapter 7 test at the end of this week. 

Clink on this link https://docs.google.com/document/d/1WNKIqELmfW3jCc7zAD4-3YVPlSjtYpfYp2EpHph9pYc/edit to see our last couple of assignments if you want to start preparing for the test.

Basically, you need to wrap up 7.7 (Square Root Functions), practice a few more partial fractions 7.8b, and then do a mixed set of review problems I named 7R for Review.

One final note.  Viewing the second and third partial fraction videos on http://www.khanacademy.org/ is very helpful for section 7.8.  The third video corresponds to problems 379/#15-16 with the repeated factor in the denominator.  If you go to Khan Academy just search "Partial Fraction" and view the second and third videos.  It takes a while, but is worth it.  (I even earned a good listener badge). 

With all the color coding, it is much easier to follow than the book examples.

Lots of learning takes place outside of class.  Learn to find and use good resources.

Monday, April 9, 2012

Chapter 7 and Depressing Polynomials

Short post today and some accurate/creative responses may earn reduced homework.

Question 1 - What is a depressed polynomial? (in your own words)

Question 2 - Why did the polynomial choose to be become depressed?  (joke responses/ meaning based responses glady accepted)

Sunday, March 25, 2012

Wrapping up Chapter 6 - Test on Friday

This week we will be finishing the equation sections of Chapter 6 and preparing for the Chapter Test.  The results from last weeks quiz were pretty good.  The class averages were around 80%.  Some students are having trouble with the proofs on the back side and there are still some errors popping up when simplifying many of the tangent formulas.

Be prepped to hand in the last 3 homeworks (6.4-6.5) on Tuesday and be pretty thorough about checking your solutions in class as we are not having another quiz before the Test.   The Chapter Review assignment will be worth 20 credits and graded on accuracy.

Below are the assingments from the google document:  For the full assignment sheet click on https://docs.google.com/document/d/1vUohN90Jrh5DBIpLOPXEy6FgyR6yl_DvtYm4eR5uC7g/edit

  6.5aTrig Eq. Ineq. Lesson a6.5a  314/2-16all      /5
  6.5bTrig Eq/Ineq. Lessonb 6.5b  315/35-43 odd,47    
Assignments   6.4-6.5 checked 3/27/12
    /5
   6.6Trig Eq./Inequalities in Quadratic Form321/1-9 all, 17-19,34-36 [Practice]    /10   
   6RReview 326/1-14 all,challenge 17-19
327/6,1113,16,20,23
      /10
Accuracy

   Chapter 6 Test on Friday

Wednesday, March 14, 2012

Course Selection and Pi Day thoughts

What an amazing Pi Day!  At the end of the day, I saw SG gift his Math for America slinky over to IM and really that is what the spirit of Pi Day is all about.  What goes around comes around at 3.14 times the diameter no less.

Course Selections for Juniors
Many of you should strongly consider taking AP Calculus next year or just calculus based on your interest and courseload.  The incentive of taking the AP exam and possibly getting college credits really gives you a step up for college.

Similarly, I would say you should consider taking a Physics class.  My understanding is that completion of the General Physics course can earn you up to 8 credits at URI and many other colleges.  It is just a nice follow up course to Trigonometry too.

I will have limited email access the weekend, but feel free to email me if you have questions.  In general, if you are maintaining an A or solid B and consistently doing HW you should consider AP Calculus.

Good luck tomorrow and be nice to the sub.  You basically should be putting your recent HW into your folders with scores, taking out most of the old assignments (except tests) and then taking your quiz and handing it to him.  Calculators are not needed for this exam.

Sunday, March 11, 2012

Week of 3/12/12 - More Identities and some Trigonometric Equations

Last Week
Based on last week's quiz results, we got off to a great start on Chapter 6.  We were well above our goal of 80% or more getting a B or better on the quiz for both classes.  The only room for improvement was with the tangent sum problem, just the final step of rationalizing the denominator.  Thanks to students who posted to the blog last week.  Everyone who posted may skip the 6.2 HW.  If you already did the 6.2 HW, we will figure out a different reward.  Section 6.2 is not a major emphasis, but there may be a question or two that will pop onto a quiz or the Chapter test. 

On the Horizon
Pi Day! on Wednesday.  This week we will work on the Double Angle and Half-Angle Identitities and transition into some Trigonometric Equation solving.

For our next class
We previewed section 6.3 and you should be reading pgs. 297-300.  The best thing to do before your next class would be to focus on these problems:

HW 6.3a 302/7-10 [Practice] and Class Exercises 302/1,3,5,12,14   
These are all double angle problems.  In class Friday, I said to focus on the double angles, and these are your best bet.
Question #12 will be the biggest challenge.

We will address both the double angle and half-angle identities next class.

One Pi Day Tribute Idea
Break out a new paper "pi" plate and create colorful unit circle with just the "pi/12" and "pi/8" angles and their multiples (which are not our memorized 30, 45, 60, 90 angles).  You will find that many of this week's problems involve those 15-degree and 22.5-degree angles.  Or you could draw the familiar 30, 45, 60, 90 mutliples and just color the pi/12 and pi/8 multiples that are not co-terminal with the familar angles.

Maybe the blog followers who read this and bring in a prepared pi plate will earn a reduced HW reward.  It has to be accurate, colorful, and done before your first class this week.  Spread the word for the non-followers.

Sunday, March 4, 2012

Previewing Trigonometric Identities and using our Textbook

General
This week we will be starting a new Trigonometric Identity Chapter which will involve deriving some key angle formulas and applying them to find exact values.  The early part of the chapter will involve a lot of memorizing and applying some relatively long identities and you will really need to be sure you have mastered much of the material from Chapter 3 (working with the unit circle, definition of all the trig functions and their reciprocals etc.)  To start off the week I want to see who is following this blog and who is actively reading their textbook and involve some students in actually creating the weekly assignment sheet and responding to some questions.

Three Key Things
  • I had mentioned to some D-period students that since they had completed their after test assignment more thoroughly than others, they may get an extra credit opportunity.  That opportunity is now if you go to the Ch. 6 draft assignment sheet and replace the ???? with the written objectives (find in your textbook) or names of the identities (find in textbook).  Each student to fill in an objective or key identity will be exempt from part of a future homework.  Access the draft assignment sheet by clicking the link below and it should let you make edits.   https://docs.google.com/document/d/1vUohN90Jrh5DBIpLOPXEy6FgyR6yl_DvtYm4eR5uC7g/edit
  • Secondly, for anyone who wants to answer any of the questions below by posting a comment to this blog, you may also receive reduced homework in the near future if you answer accurately.  [D- or C-Period:  Only one response per question, check comments before replying]
  • The assignment sheet is a "working assignment sheet" some of the problem sets may change but not by much and we are actually starting out with 6.2 which is not on the assignment sheet but will be announced in class.  Our first quiz for this Chapter will probably be Friday Day3.
Read through the Ch. 6 introduction and respond to these key questions:
1)  Describe what "dead reckoning" is for ship navigation and explain how you think this may have changed given more current technologies.

2)  How is a ship navigation angle reading convention different than the angle convention we use in Trigonometry class.

3)  Describe what a "knot" in terms of sailing navigation and provide a little history by doing some online research as to where the measurement of "knots" came from.

4)  What is a sextant and how is it used?

5)   What are the similarities and differences between the cos (A+/-B) and sin (A+/-B) Identities.

Good navigating has its rewards.  If you are posting, be sure to state the question # you are replying to.

Sunday, February 26, 2012

Week of 2/27/12 Chapter 5 Test Prep! Look Ahead to Ch. 6

General
We only have one section left in Ch. 5 (Area of a Triangle/Heron's Formula)!  So, we will spend one more day learning the new material and reviewing the other Trigonometry Applications.  This means the test will be on Tuesday for C-Period and Wednesday for D-Period.

Content Goal
Be able to understand all the trigonometry applications and when to use them based on what information we are given. 

Use the next couple of days to wrap up all that you have learned in Chapter 5 and create a small index card to write down key formulas you need to memorize.  Some solutions to the review assignments will be posted on my website at http://www.mpsri.net/page.cfm?p=1567   but will not be updated until Monday night.

Be sure you have completed the first two assignments before the test and the final assignment will be due the class after the test and should be self-graded based on accuracy (mulltiple choice answers will be posted).  Many problems are cumulative review problems and will set us up for Ch. 6.


Access to Google Document_Chapter 5 Assignment Sheet Link:  https://docs.google.com/document/d/166m_0ie0TDwZBQvxYEp4yIDEuEpm4UFO79cWyTBcsBc/edit

Monday, February 13, 2012

Week of 2/13/12 Following up our Projects_Peer Assessment_Ch5 Stuff

General
This week we will be completing some follow up activities related to our Art Project and Portfolio Task.  Specifically, we will look at someone else's feedback related to our project or providing feedback to them about their work.  While doing this, we will dig deeper into our own trig. graph knowledge, but more importantly, we will practice how we communicate our understanding of someone else's work.  In additions, we will incorporate someone else's feedback to improve our product.  Learning to communicate constructively and effectively is a very important skill to develop that will help you in all your classes and in life!  Also, reflecting about how your original ideas were communicated in your project should teach you a thing or two (or at the very least point out you did not follow directions!) about how to approach more open-ended projects.

Content Goal 
Be able to understand the difference between the Law of Sines (including the Ambiguous Case 5.3) and the Law of Cosines and apply those relationships to new situations (other sections of Chapter 5).

3 Key Products
  • Revised written "instructions" to describe how to create your graphs from the art project (due via e-mail Tuesday Night, 10 pm)
  • Textbook problems announced in class Ch.5  Handouts (due in folder last day of class this week)
  • Written Reflection about last week's task (submitted online or via email)   - You will be asked to submit a written reflection after you see your graded task.  Most likely, you will see your graded task Thursday or Friday. 

Sunday, February 5, 2012

Week of 2/6/12 Trigonometric Art and Using Triangles to Model and Measure

General - This week we will be demonstrating Mastery of our Trigonometric Function Knowledge by creating our own "art project" which involves drawing a picture using only Trig. Functions with specific domain/range restrictions.  Period C has already seen the sample student work and knows that they need to come to class Tuesday with a "rough draft" of their project on notebook paper and Period D will see the preview Monday  Secondly, we will be starting Chapter 5 and the first two sections are comprised mainly of previously learned material that involves applying Right Triangle Trigonometry to model real-world phenomenon and perform indirect measurement.  Section 5.2 is about the Law of Sines which most of us mastered last year in Algebra II.  However, if you have not, there will be class time to learn practice, and help each other.

Finally, there will be a task Friday to assess our understanding of these principles.

Key Content Goal
Students will understand how to model real-life situations and use indirect measurement to find unknown heights, angles, etc.  Much of the Trigonometry we learn is applied in surveying, mapping, and developing computer models involving angle measurements and other related quantitites.  Much of this week's content can be found in Chapter 5, sections 5.1/5.2

3 Key Process Goals
  • Students will solve textbook problems and focus on using textbook examples as a learning resource
  • Students will work cooperatively to check their understanding.  If you took Algebra II honors, you have worked much more with Law of Sines compared to others in our class who took Algebra II last year.  If you have previously learned the Law of Sines you are expected to help out your classmates (I will be out Tuesday at a Professional Development).   If you do not know this content well, you will be expected to seek out help from classmates who are more familiar.
  • Students will be creating interesting products.  Your final "Art Project" is due on Friday as you come into class.  That same day you will be completing a full period task that will assess how well you can solve a real-world problem and demonstrate your ability to draw a diagram, apply relationship(s) and explain your understanding of the problem
3 Key Products
  • 5.1   248/2-11 Primes,14,15,18,24,27,30,33,34 Solutions must include a diagram, show formula, and worked out key steps to earn full credit  
  •  5.2 254/2-18 even, 20,22,23,24,26,29,31 [Possible Handout]
  • Art Project (individual rough draft due Tuesday (place in folders) and Final Project due Friday (You may work in Pairs or Independently)
Other Comments
  •  If you did poorly on the Ch. 4 Test, you are expected to make corrections to your exam and redo the Practice Test #4 problems that are similar to the ones you missed
  • You should use our "coloring technique" to highlight key features of your graph from the Ch. 4 test and create a table, if you did not originally
  • The art project is really an alternative assessment for you to show how well you know your Trig. graphs.  If you did poorly on the test, you this opportunity to balance out your grade and show what you know about Trig. Functions. 

Wednesday, February 1, 2012

3 More Things for Chapter 4

Just to address a few final questions and make sure you are prepared for tomorrow you get a bonus post this week.  My goal is to have about one weekly (usually on the weekend).  This post will address two questions and provide a link to a google document that has our more recent assignments (due tomorrow) and a short study guide.  But basically, be sure you can do anything from Chapter 4 but you probably will not have to graph inverse functions.

3 Things

  • One common question asked during class today and yesterday:  "Do I need to know how to do the inverses" Answer:  Yes, look back at that section, do the practice test problems, and the chapter review questions.  The key approach is to ask yourself when you see Arcsin (?)  is:   "What angle (or input) will result in a sine of ? "  Remember, to inverse something is to undo it.  We used it when we did the ferris wheel task when solving an equation for to determine an input time to find a height of 40 meters.
  • Second common question: "How do I decide what points to graph when there is a phase shift, etc."   Good question and the answer is you have to determine the period, use our "Rule of 4" and then think about what the phase shift does (adjusts your entire graph).  The first question of the review homework was a good one to address that.  When you practice you will find it involves do a little "fraction work".   Practice until you are confident.
  • Third thing - I experimented with a google document to write out all our recent assignments and it can be accessed at https://docs.google.com/document/d/1Ixg7oo1sDlLOmFiSPnAOpOgS5laJ4rvx7Su-839PluE/edit  It summarizes the objectives of what we have learned and lists the page/problem #'s.
Ultimately, I want to hand off more responsibility to you to use google documents or some other technology tool to create your own study guide and for us to track what is due.  Any volunteers?

Monday, January 30, 2012

First Full Week of Quarter Three "3 Key Things"

As we approach February and launch the Third Quarter - Here are 3 sets of 3 things to consider
 3 Key  “Graded” Activities
·         HW 4.3b (Due next Class) - 206/11,13,17,22,24,27,29,39-45 AND Ch 4 Practice Test
        Practice Test Answer Key will be posted at  http://www.mpsri.net/page.cfm?p=1567 
·         Chapter 4 Test on Thursday (Day 3)
·         Alternative Assessment (Starting this Week Due Next Tuesday)– Cool Trig. Graphing Mini-Project (Preview of the Project Expectations are posted at my Middletown Webpage (see link above). 
3 Key Resources
·         Graphs of Trigonometric Functions Reference Sheet  (use it while doing CW/HW)
·       ~Trig. Graphing Procedure Sine/Cosine Functions~
·         A new Google document assignment sheet will be added and linked to this page (but is not yet.  Our current assignment sheet can be found at ….(stay tuned) This Live Document can be accessed any time to see what you  should be working on.

3 Key Takeaways from Today’s class (Monday, January 30, 2012 – Day 3)
·         Our graphs have to show 6 ” key features” and  there should be a table of values showing our exact abscissa values (pi/4, pi/2, etc.) and important ordinates (fancy or mathematically precise words for (x,y) coordinates. 
·         We can use the graphing calculator to “check” the accuracy of our key features but must know how to adjust the window, table, tableset, etc.  This systematic approach to graphing Trig. functions will take practice but will pay off in the long run
·         There are two Algebraic forms of Trigonometric equations y = asinb(x-c) + d (when the b is “factored out”) and y = a sin(bx + c) which matches standard formats on our new reference sheet.  The “factored out” form  is better for identifying phase shifts and relating to earlier non-Trigonometry functions, shifts, etc.
  

Wednesday, January 25, 2012

Midyear Exam Reflection

Below are some thoughts about the mid term results.  Stop by and see me tomorrow if you want to see the test.  The actual exams will not be handed back, but you may take a peek.

Observations:

The good – Scores were generally high, mostly B’s and C’s and only a few A’s.  Pretty much the entire class was solid on inverses, graphing aspects of Trigonometric Functions, questions relating to the Unit Circle, and Domain, Range, Asymptotes.

The bad – Some of the open-ended answers and recognition of concepts learned earlier in the year.  Specifically, when analyzing an angle (like 188-degrees) we use a Reference Angle.  That is important vocabulary and matches the little yellow triangle we often had on the TV as a visual. Even functions are symmetrical about the y-axis.  Many of us missed this question.  Think about a parabola y = x^2. 

Do you recall what an odd function is symmetrical about?    And what is a good way of remembering that characteristic?  First new commenter who responds to those questions correctly starts of the new term with extra credit.

The Ugly – Solving polynomial equations (material from earlier in the year – try factoring first and check for zeros with your graphing calculators). 

Co-functions and the Domain/Range of Inverse Trig Functions– This is a pretty straightforward concept, we just need more practice.  

Expect some more HW problem coming soon.  We also need more practice with phase shifts.

See some of you Friday!  Good luck with any remaining exams.

Saturday, January 21, 2012

The Final Push Before the Midyear Exam

If you are reading this, you are most likely already prepared for the midyear exam.  However, you are probably likely to do just a little more to build some confidence. 

I always found that for math and science classes (especially in Engineering school) it just made me feel more confident to do problems and see that I am getting them right.  Also, you may just uncover one old problem that might force you to look up and old formula or just page through your old notes one more time (like say, an axis of symmetry problem for a quadratic).  Then, when you hit that problem on the actual exam you will feel happy (oh yeah, I remember x=-b/2a) instead of feeling anxious and losing confidence during the test.

So, remember that I did provide you with a page of answers to multiple choice problems (the day I gave out the pink topic sheet). 

If I were studying, I would open my textbook and put myself in "practice test mode".  Take out 4-5 pieces of paper, set aside an hour, and then just do each of those problems as if it were the final (hey it is cold and snowy out anyways).   I would pass over any of the problems I did not feel as confident about (good test taking skill) and then go back to them after finishing aobut 50  problems I do feel confident about.  I would then spend 15 minutes really focusing on those and then check all of my answers.  Then score your test and make any decisions about what else to study.

Good luck!  And if you don't have your Trig Midterm Review Book Problems answer sheets, I am sure one of your classmates will.  If not, email me and I will scan it and get you a copy.

ps.  This can be part of your final 50 HW problems as long as you show some evidence of calculations.

Tuesday, January 17, 2012

Even and Odd Intervals

The following are a few student observations about graphing the secant and cosecent functions:

Re:  Secant/Cosecant Graphs-

The graphs of co-secant and secant graphs are both similar and different. 
1.       A co-secant graph is a shift of 90 degrees or pi/2 to the right of a secant graph. 
2.       The asymptotes for a secant graph cut through the center of the parabolic-structure of co-secant graphs. 
3.       The asymptotes for co-secant graphs cut through the center of a secant graph.
4.       When a sine graph's x-value is zero, the x-value for a secant graph is also zero. 
5.       When the x-value for a cosine graph is zero, the x-value of a co-secant graph is also zero. 
6.       All odd intervals of pi have the secant graphs opening downward. 
7.       All odd intervals of 3pi/2 have co-secant graphs opening downward. 
8.       All even intervals of pi have secant graphs opening upwards. 
9.       All even intervals of  3pi/2 have co-secant graphs opening upwards
Question:  Is there an algebraic way of modeling

"all odd intervals of"

"all even intervals of"

Hint:  It may involve k's and Z's

First commenters may receive extra credit.  Post a comment!  and now the wikipedia is going dark at midnight!

Monday, January 16, 2012

Ferris Wheel_Intial Post

We have had a great year in Trigonometry so far and are getting very close to the midyear exam.  As the year has developed, I see more and more how important it is to use visuals to describe certain concepts and how great it is to see how you (my students) describe your understanding in writing.  I plan to use this blog to provide roughly a weekly update (T = one week, probably each weekend)  about what we learned, any updates about assignments etc. and to preview what is on the horizon.  Ideally, it can also be a place to share good links and also hear your thoughts and descriptions about what you have learned.  In fact those of you that did not e-mail me last week will be our first commenters!  Stay tuned.

To borrow a Trigonometry model, much of what we learn in mathematics is cyclical (it just gets more sophisticated), and as we go through each week we can learn more and more how all the ideas are related.

Last Week
 We got back our graded HEP5 tasks.  The Ferris Wheel problem really helped me see who understands the relationships between circles, sine/cosine graphs, and how time and height are modeled using a trigonometry function. 

Everyone seemed to master the "vertical shift" considering the Ferris Wheel was on top of a building and we had to choose a "middle" height and think about whether cosine or sine could be used to model the changing height over time.

Sine versus Cosine.    After we all completed our tasks, there was  a learning opportunity to see how either sine or cosine model could be used to model the height at any time ( negative cosine was the most used model because it started at "the bottom").  The graded task transitioned nicely into the idea of a "cofunction", realizing that sine and cosine are the same function, just shifted by a quarter turn (or 90-degrees or pi/2 for you radian purists).

Problem Solving - The most unfamiliar step of the task was using the graph to see how often the ferris wheel was at 40-meters above the ground.  This was a great question to recognize the value of our graphical knowledge to estimate how often and when that height occurs and how to use the graphing calculator to find the "actuals".  That solving step is just like a systems of equations problem with a horizontal line.  The intervals between the 40's ended up happening about every 3 minutes (lower parts of the wheel) and 11 minutes (the longer part of the rotation).  Not just a coincidence that 11+3 = 14 minutes, the period of rotation for the Ferris Wheel.

This Week
We are in exam preparation mode.  Using our pink topic sheet as a guide, we can review mixed problems to prepare for the exam.  Making sure you hit each topic at least 4 times (to follow a topic mastery "rule of 4").  Most of what we learned 2nd quarter can be found in Section 6 of the Algebra2/Trig Page. of http://www.regentsprep.org/    It is up to you to do problems and check yourself.  Keep enough evidence of showing your work to be able to show me and another student you have fully prepared yourself.  Your completed work should be organized and placed into your folder by the Monday of exam week.  (This Friday, is even better!) 

50 questions is a minimal expectation (and your final HW assignment).  Those of you who are struggling should do more and seek out help for anything you don't understand.

Inverse Functions
One new concept that we will hit this week is the graphing inverse functions.  Since you will be at the regentsprep website, take a look at the lesson page for that topic.  One reason I assign this website as a review is so you can re-learn or teach yourself any concepts that you may be struggling with.  That is what you will be doing in college!

Ok - stop reading now and (1) Scan/upload your tasks  (2) attempt the mixed multiple choice Trigonometry problems at the end of Section 6 then (3) check your solutions on the website. 

If you finish that, page through each of the topics in Section 6 and attempt the practice pages highlighted in the classroom.

Good luck!