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A1-A-3-3

Page history last edited by Brenda Butz 6 years, 5 months ago

A1.A.3.3  Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.


In a Nutshell 

Students will factor polynomial expressions, including quadratics.  They will factor out the greatest common factor from polynomials of any degree and factor quadratics with a lead coefficient of one into two binomials.

Student Actions

Teacher Actions

  • Students will develop accurate and appropriate procedural fluency by finding the factors of a polynomial expression or quadratic equation.

  • Students will develop a deep and flexible conceptual understanding by comparing the quadratic equations and their graphs to see that the factors are solutions called x-intercepts (zeros) of the graphed equation.

  • Students will develop mathematical reasoning when they observe and explain how factoring is the reverse of distributing.

     

  • Use and connect mathematical representations by helping students discover the relationships between quadratic equations and their graphs, including those that model real-world situations.

  • Pose purposeful questions that guide students toward discovering factors of expressions.

  • Implement tasks that promote reasoning and problem solving by guiding students to interpret the mathematical relationship in the original context of the problem algebraically

     

Key Understandings

Misconceptions

  • Students will factor the greatest common factor from each term in a polynomial expression.

  • Students can identify the x-intercepts (roots) of the quadratic equation by factoring.

  • Students may forget to factor the greatest value possible from an expression before beginning to factor the polynomial.

  • Students may not take the real-world context for a quadratic relationship into account when giving solutions, causing them to include solutions that would not fit the situation.

  • Students may not identify the correct sign of the factors involved.

OKMath Framework Introduction

Algebra 1 Introduction

 

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