Math Units Page

Lesson Purpose

The purpose of this lesson is for students to understand that the rules for factoring polynomials involve the simultaenous satisfaction of a very specific addition and multiplication calculation by using specific parts of the polynomial. This calculation is able to give the inverse result of a multiplication problem, and has direct application to may geometry questions. Finally, factoring a polynomial involves higher-order thinking skills that are helpful and analagous to the type of thinking required int he real world in order to solve complex problems involving more than one variable; particularly in the cases where recursive reasoning is necessary.

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Lesson Objectives

At the end of this lesson, students will be able to:

• Factor a polynomial expression
• Match factored binomial quantities with their corresponding polynomial expression

Student Target

“I can multiply two binomial quantities and multiplication to solve area problems in algebraic geometry.”

CCR Focus Standards

Algebra and Functions - Level E

• A.APR.1

  Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [NOTE: Emphasis should be on operations with polynomials.]

Supporting Standards

• A.CED.1

  Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*
  

• A.APR.6

  Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  

Standards for Mathematical Practice

• MP.2

  Reason abstractly and quantitatively. (MP.2)

• MP.7

  Look for and make use of structure. (MP.7)

KYAE Employability Standards

• E.1

  E.1 Effectively contribute to a team through cooperation, leadership, and giving and accepting critical feedback to work toward a common goal.

• E.6

  E.6 Identify and effectively use skills and materials needed for a particular task.