Reflection: Vertical Alignment Polynomial Long Division and Solving Polynomial Equations - Section 2: Structured Discussion


As the Common Core embeds itself more deeply into our education system, I find that I can no longer assume that students have been exposed to and are comfortable with the Traditional Long Division Algorithm that I grew up with (and rely upon as a foundation to this section). These days it may be just as common to learn division with the Scaffolded/Recursive Algorithm or some other method. In addition, it’s not uncommon for me to discover that my students never really mastered division in the first place, regardless of what algorithm they were given.

My logic in assigning a “throw-back” homework assignment of long division problems is to uncover students’ comfort level with the standard algorithm.  If the students in front of me have mastered this procedure, I anchor my introduction of polynomial division to it.  If the majority of students have weak division skills, or use another algorithm, I focus on the logic of the process without presenting a parallel numeric problem.  

In any case, I present a single method of polynomial long division and assure my students that other algorithms exist for polynomials, just like multiple methods exist for numeric long division.  Eventually, students will ask me about “synthetic division” and I will remind them about this discussion of the existence of alternative methods.  Like with factoring, I prefer to introduce students to a single method that works for all polynomials.  When students in the class hear about another method from a sibling, friend, or Sal Khan, I let them show the class and lead a discussion about when the method can be used.

  What if They Don't Know How to do Long Division??
  Vertical Alignment: What if They Don't Know How to do Long Division??
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Polynomial Long Division and Solving Polynomial Equations

Unit 4: Polynomial Theorems and Graphs
Lesson 3 of 15

Objective: SWBAT relate polynomial long division to long division with integers and understand the Remainder Theorem.

Big Idea: Operations with polynomials are a lot like operations with integers.

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