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

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. 

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. 

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?

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.

  

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.

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.