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

6.5a	Trig Eq. Ineq. Lesson a	6.5a  314/2-16all	/5
6.5b	Trig Eq/Ineq. Lessonb	6.5b  315/35-43 odd,47     Assignments   6.4-6.5 checked 3/27/12	/5
6.6	Trig Eq./Inequalities in Quadratic Form	321/1-9 all, 17-19,34-36 [Practice]	/10
6R	Review	326/1-14 all,challenge 17-19 327/6,1113,16,20,23	/10 Accuracy

   Chapter 6 Test on Friday

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.

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.

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.

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.