AFF Factoring to Find Zeros of Polynomials

Week of 12/22/14

Last week we extended our factoring prowess to analyze more sophisticated polynomial functions.

For example, we know that if we analyze p(x) below, we should first factor it (AFF!)  

In factored form, it will be clear that the first graph shown below does not match the given function. But the factored form will tell us the zeros we should expect to see.

In addition, last week we discussed the concepts of multiplicity.  We explored different graphs of polynomials that had repeated binomial factors linear factors raised to a power.  We can now analyze more complex behavior by inspecting the types of zeros (crossing or tangent).

We will discuss more graphing implications this week and after the holiday break.

 After the break we can also apply synthetic division as a solving tool.

Leftover goal which will be our focus this week

• Be able to make sense of word problems that lead to polynomial functions.         Then, persevere in solving them using factoring or other techniques.

Week of December 8th: Revisiting Sade and extending polynomial understanding to solve problems

General  Last week we improved our understanding of graphing polynomial functions and discussed key features of this function family including relative and absolute extrema.  In addition, we learned how to predict the end behavior of their graphs based on the degree and lead coefficient; and the relationship between the degree and number of turns we see on a polynomial graph.  This week we will extend what we learned about quadratic function solving techniques to solve problems involving polynomial functions.    
  

3 Key Learning Goals for the week

• Become and even smoother operator (factorer).  You will be asked to self-assess/rate your current understanding of factoring (GCF, DOT's, Factoring Completely, etc.) and apply similar techniques to rewrite polynomial expressions in a different form to solve problems. 
• Be able to make sense of word problems that lead to polynomial functions.  The persevere in solving them using factoring or other techniques.
• Address some misconceptions that showed up in the last two online assessments. Specifically,  there were some errors related to understanding exponent rules and writing expressions to represent volume algebraically.  These previously learned skills from other classes could be obstacles to doing well with our polynomial modeling and problem solving

Self Regulated Learning

My last post mentioned some of the characteristics of being a self-regulated learner.  One was that a self regulated learner identifies areas of strengths and weaknesses.  My teacher perspective is that graphing is, in general, a strength for our class.  Especially, problems that involve (FIF) interpreting functions, zeros, rates of change, domain and range etc.  However, the mixed tenmarks assessment results indicated that some of the problems reflecting the building function standard (FBF3), mainly transformations, were not as strong.  When I collect your paper homework next class be sure you can communicate any misconceptions related to transformation.  Previous paper pencil quizzes showed pretty strong understanding.  

Also, I need you to know how well you know your rules for exponents and can set up word problems.  If this is not a strength, there are some strategies and follow up activities you can do to improve your understanding.   

And of course, if you are not a smooth operator you need to improve your factoring.you

Self-Regulated Learning and tenmarks

Steppen into Trig is back up and running!  If you are currently in one of my Trig/Precalc. classes you are expected to join the blog (follow my posts).  In the past, I have updated it once each weekend so your responsibility is to mainly check in once each Sunday night to see what is up and coming for the week.  However, we may go further if we see opportunities for student/teacher or better yet student/student communication (about what we are learning in our class!)

You have done and seen a lot of www.tenmarks.com tracks and filled out your own tracking sheets this year.  This quality site allows to you to practice quality problems that can't really be created on a worksheet or copied from a textbook.  That is one great benefit, but I also want you to have and take more ownership in tracking what you know and need to know.   Tenmarks does a nice job of challenging you and giving you that "one more chance" to make corrections.  Those scores provide a consistent way for you to track where you are, and make decisions about what to do next.

The extra work I have put into familiarizing myself with tenmarks and giving your tracking sheets is to add one more tool to your toolbox to help you become a self-regulated learner.  Self-regulated learners take ownership in process of learning.

Self-Regulated Learners

·         Engage in self-observation (monitoring one’s activities), self-judgment (evaluation of one’s performance), and self-reactions (reactions to performance outcomes)

·         Identify academic strengths and weaknesses

·         Attribute their academic successes or failures to factors within their control (e.g. effort expended on a task, effective use of strategies)

  

     Next Steps:  In the upcoming Sunday night post I will talk about self-regulation and how it relates to the rubrics we have been using in class and give a good check-in/preview about how we are doing with Polynomials.