Chapter 7 Polynomial Box Problems Reflection

Need Extra Help or Computer Access for Tenmarks?
I will be in the computer lab room 108 for tutoring help every Tuesday and Thursday until 3 pm if you need help, want to work with someone else, or just use the computer to catch up on tenmarks.  The final exam is just around the corner.

Homework Consistency
About 1/4 of our class has completed all tenmarks assessments and had complete enough homework that I can tell they know the Fundamental Theorem of Algebra (7.4 complex coefficient problems).  But most of you have not.  In addition, there are review problems sprinkled in the homework, like Tangent Graphs, Law of Sines/Cosines, etc.  

Those of us not completing accurate graphs with labeled key features and step-by-step work for old material will not get full HW credit.  More importantly, you are not practicing old material to be ready for the final.

In other words, most of you need to do the most recent HWs and make up any old tenmarks assignments by Tuesday, including those "old" problems.

Analysis of where we are at in Chapter 7
Below is a chart I made for a workshop I am going to tomorrow but it is about our class, so take a look.  I reviewed the recent quizzes and HWs and scored each standard out of 4.  To get more 4's for synthetic division, I need to see how you do with the "complex" coefficient problems.   Word problem box problems and graphing generally looks good.  Numbers would be higher if I had more completed work, especially homework. 

Next Steps include more factoring to solve polynomials and moving on to Rational functions

Take a look.   The left column of the table is essentially a study guide of what you need to know:

:                                        

Essential Learning Outcome:  Model and Solve Real-Life Situations using Polynomials  -- >  “Box” Problems/Volume Applications in Context - Write polynomial, interpret graph, solve
Learning Targets and Relevant Problems                  I can…                                                                           STANDARD	Whole Class Observations
Numerically                                                                      CC9-12.A.APR.2   I can perform polynomial long division and synthetic division / substitution, and understand /can apply the factor and remainder theorems.  7.1 Synthetic Division Assessment (4 problems) and Poly Quiz #1 7.1 Problems Sets (HW)	85% of class consistently performing synthetic division accurately and understand the purpose of the  remainder theorem   Some clarity needed in evaluating using synthetic substitution Only 4 students at level 4 (Homework 7.4 needed to show Fundamental Theorem of Algebra (problems with complex coefficients )
Graphically                                                                       CC9-12.A.APR.3   Sketch the graph of polynomial functions by identifying zeros and understand the behavior near those zeros and as x approaches +/- infinity   7.2 Graphing Assessment 7.2 Problem Sets (HW) and mixed assessment problems	65% of class showing consistent graphical understanding.  Students without graphing calculators (a few non-HW completers) haven’t shown much understanding but seem to have partial understanding   Some students over relying on graphing calculator
Algebraically/Analytically                                                CC9-12.A.SSE.2      Recognize and rewrite polynomials as special products (FACTORS)        to find zeros of polynomial functions.  Examples:  Factor by grouping, Difference of Two Cubes, factor completely 7.3 Polynomials Application Quiz #3, 7.3/7.4 Problem Sets (HW) and mixed assessment problems	50% have shown strong factoring capabilities. Haven’t assigned many multi-step factoring problems but it came up in earlier chapters.   Need to assign more factor by grouping , factoring completely, and difference of squares/cubes.   Many common errors when depressed polynomial is NOT FACTORABLE (need to apply quad formula for irrational or complex solutions)
Making Sense of Problems/Model Using Mathematics    CC9-12.A.SSE.1  Write expressions to represent length, width, and height in a volume function and interpret the meaning of these expressions in a polynomial Apply appropriate tools strategically 7.3 Polynomials Assessment #3    HW 7.3/27-33 word problems	65% of class able to consistently set up/solve  volume problems leading to polynomials.   Box volume problems seem to be understood.  Some students not confident in setting up word problems from other contexts.  Solving process seems strong.

 

Other Comments:  ___________________ ______________________ # Exceeds ___   #Meets ____    #Nearly  ____    #Not Meeting _____      

__________________________________________________________________________________________________________________________

Wrapping up Ch5 and Moving on to Ch6

We are wrapping up our Trig. Applications chapter and this is a good time archive/file away our best work.  We will finish the Chapter 5 test Monday and scan our task work in the computer lab as well. 

Prepared for the test?
Be sure you know when and how to apply the Law of Cosines and how to sketch two distinct possible triangles for the ambiguous case of the Law of Sines.  I have posted some sample student work and worked out solutions for the 5R assignments.  Take a look, especially if you have not submitted those problems yet.  The solutions are on my MHS website at  http://www.mpsri.net/page.cfm?p=1567
Look under Chapter 5 resources. 

C-Period
Be sure to bring your solutions to the 6B applied problems we did a while back (also on my website if you need to see a copy). 

Feeling all set with Chapter 5?
Many of us have masted all the Trig. applications.  Two things you can do are:

(1)  Look over Section 5.5 - There are some other problems we will not cover this year but  you may see in Calculus.  Area with Law of Sines is just another application of the Law of Sines

(2)  Read ahead in Chapter 6.  We will be covering at least sections 6.1 and 6.2 this week.  Historically, Chapter 6 is a little tougher so you may want to read ahead and look over each section before coming to class.





    

The other Trig. Graphs

This week we will continue our graphing of the "other" trig functions and dig a little deeper into different ways to model real-world functions (not just the negative cosine models)

 3 Key  “Graded” Activities

·         HW 4.3b (Due next Class) - 206/11,13,17,22,24,27,29,39-45 AND Ch 4 Practice Quiz (will be assigned on Tuesday) 

·         Chapter 4 Quiz at the end of this week

·         Alternative Assessment (Starting this Week Due Next Monday)– Cool Trig. Graphing Mini-Project.   Those of you that already did it will earn full credit and get some extra feedback.

3 Key Resources

·          Graphs of Trigonometric Functions Yellow Reference Sheet  (use it while doing CW/HW)

·       ~Trig. Graphing Procedure Sine/Cosine Functions~

·       Sample solutions on my webpage (see link above) http://www.mpsri.net/page.cfm?p=1567    

Rule of 4_Real-World Problems

General
At this point we are shifting our angle and radian understanding to actual times and heights.  The purpose of the "leaf bobbing" and "ferris wheel" problems have been to transform your understanding of circular functions to actual situations that can be modeled with trigonometric functions. 

Hopefully, the graphing of the functions has been pretty straightforward  and the recognition of "four to five" different key times and heights connects to your understanding of the unit circle.

Key Products  

• 4.1 and 4.2 text assignments (especially #49) should be handed in with the last assignment sheet (this should show your understanding of the basic trigonmetric graphs).  Due Monday!
• Practice Task Handouts - The sinusoidal functions (see my website for some worked out solutions to one of the practice problems)
• Task (Tuesday or Weds).  You must complete these independently within one class period.  This will count as a test grade.
• Review packet problems (just for general review).  This does not relate to the task or Ch.4.

Understanding Numerically, Algebraically, and Graphically

• We have "solved" a couple of practice equations in class.  This basically involves what you already know solving using inverse operations then applying arcsine and arccosine to undo the function.
• We have not "evaluated" a lot of trig. functions in class but you will need to apply evaluating to our real-world trig. functions
• You do know how to apply unit circle reference angles and will need to apply that understanding to the actual repeating cycles of a trig. function to show proficient understanding on the task.  It all relates back to 180 +/- the reference angle or 360 - reference angle.  But we are not talking about angles anymore.

You are expected to look at the website tonight and see some worked out solutions if you are stuck on the task practice problems. 

Psyched about sinusoidals

General – You will be assessed on how well you can graph and interpret  sine and cosine functions tomorrow Quiz 4.1-4.2 (or Tuesday if you are in D-period)

Note:  Assignments 4.1 and 4.2 will be handed in tomorrow

Be sure you :

·         know the meaning of the coefficients of y = a sin b (x –c) + d

·         can determine the period, amplitude, and vertical shift

·         can graph sine an cosine functions using a table of values

3 Key Goals for this week

• Show you know the 4.1 – 4.2 material
• Apply trigonometry functions to real-world situations (sinusoidal relationships – see 4.7)
• Complete more challenging word problems/sample tasks to get ready for next week

 

For those of you who did not complete the New Year's Packet, I have created a second problem set.   You must complete the problems handed to you next class AND the New Year's refresher packet. 

 

For those you who did complete the packet.  You will be given the option of checking another students work once it is completed and/or completing less open-ended problems.

Any extra work completed can be used to raise an earlier homework grade from earlier in the year (the review packets really represent material learned eariler this year).  The new multiple choice problems will be posted on my website under the Ch.4 folder. 

Does the Functional New Year Start at (0,0) or (0,1)?

General - This should be my best blog post so far this year...  This upcoming week, we will be continuing to learn about the sine and cosine graphs, key features and what happens when we apply  “shifts”.  There are only 8 lessons left before the quarter is over so these next few weeks are really important.  Listed below are some key dates and upcoming assessments/tasks.  

3 Key Goals for this week

• Master the important features of sine and cosine graphs and their corresponding equations.
• Be able to describe what happens to our functions and  graphs when we starting changing the   a, b, c, and d’s of y = a sin(bx) +d and more importantly understand how these coefficients are related to real-world phenomenon
• Demonstrate that you have mastered previous algebraic and graphing skills (new year’s packet)  If you don’t show mastery (above 80%) on this packet you will receive more problems to do and mandatory time after school or during advisory to learn it and show it!

3 Key Products (this week)

·         New Year’s Packet (see rubric on the website) if you want to print rubric out and self-assess tonight please do!  Anyone who does gets a new non-sharpening pencil as a reward.   Sample solutions are posted for you on my MHS webpage.

• Homework 4.2 will be assigned next class and due Friday.
• Quiz 4.1 – 4.2 on Friday (day3)
• 
  
• Key Assessments  and Dates this Month (tentative…they may change a little)

• In class portfolio task on Monday  January 14^th, 2013 (worth a test grade)
• Mid year exam – Thursday January 24^th, 2013 (both C- and D-period)
• Trigonometry Art Project Due January 18^th, 2013 (General Instructions already on website)

Happy 2013!  Notice I wrote the correct date each time.