Reflection: Detailed Descriptions of our Puzzling Polynomials - Section 2: Describing Polynomials: Increasing and Decreasing


As students were working on part a, I took some time to observe their responses. I found that a lot of my students skipped indicating the regions where the graph is either increasing or decreasing. A few brave students attempted to respond and I really liked this creative answer: Student Work - Interesting Answer.   During their struggles through part A students would ask for help, I would tell them there is no right or wrong answer just write what you think. I would then prompt students to show me where the graph is increasing or decreasing. They had no problem doing this. Yet they still didn’t write anything!  So clearly, they just didn’t know HOW to write it.

I predicted that students would struggle over describing the regions, but I didn’t expect them to just flat out skip it. However, I still like that students had this mini-struggle before they learned interval notation for describing the regions. I think it helps students to have a greater appreciation for interval notation or at least understand WHY we need it.  

One of my students also came up with a great response that created an opportunity for a Favorite No. discussion:  Student Work - Favorite Wrong Answer.   It gave us a chance to discuss that common misconception. Just because a region in the graph is going off to the right it does not mean it is increasing. I asked students if anyone could come up with a counter-example. They did and drew it on the board.

  Student Work: "Favorite No" & Most Interesting
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Detailed Descriptions of our Puzzling Polynomials

Unit 2: Polynomial Functions and Equations
Lesson 4 of 15

Objective: SWBAT describe polynomial functions using accurate terminology, identify the number of turning points and state whether the functions are even or odd.

Big Idea: Students build on their intuitive understanding of increasing and decreasing functions and explore even/odd functions using a calculator.

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Math, polynomial functions, Precalculus and Calculus, Decreasing function, increasing function, Algebra 2, PreCalculus, even and odd functions, even function, odd function, interval notation
  50 minutes
even function
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