A.2b 
The student will perform operations on polynomials, including
b) adding, subtracting, multiplying, and dividing polynomials.


Essential Knowledge and Skills 
 Model sums, differences, products, and quotients of polynomials with concrete objects and their related pictorial representations.
 Relate concrete and pictorial manipulations that model polynomial operations to their corresponding symbolic representations.
 Find products of polynomials. The factors will have no more than five total terms (i.e. (4x+2)(3x+5) represents four terms and (x+1)(2x2 +x+3) represents five terms).

Essential Understandings 
 Operations with polynomials can be represented concretely, pictorially, and symbolically.
 Polynomial expressions can be used to model realworld situations.
 The distributive property is the unifying concept for polynomial operations.


Vertical Articulation 
 SOL 7.16  apply properties w/ real numbers: a) commutative and associative properties for add/multi; b) distributive property; c) add/multi identity properties; d) add/multi inverse properties; e) multi property of zero
 SOL 8.15  c) identify properties of operations used to solve equations
 SOL AII.3  perform operations on complex numbers/express results in simplest form using patterns of the powers of i/ID field properties for complex numbers

Instructional Materials 
 VDOE ESS Lesson: Multiplying Polynomials Using Algebra Tiles  Expressions and Operations (PDF)  Multiplying polynomials (Word)
 Modeling: Multiplying Polynomials with Algebra Tiles (ppt)
 Student Notes (doc)
 Multiplying and Dividing Polynomials (ppt)
 Activity: Illuminations  Multiplying with Algetiles  select Expand tab

Real World Lessons 

Practice 
 VDOE ESS: Multiplying Polynomials Using Algebra Tiles (pdf)
 Worksheet: Multiplying and Dividing Polynomials CW (doc)
 Worksheet: Multiplying and Dividing Polynomials HW (doc)
 ExamView Quiz: Multiplying a Monomial and a Polynomial
 ExamView Quiz: Multiplying Polynomials
 Prentice Hall Quiz
 ExamView Quiz: Special Products
 Prentice Hall Quiz  Special Products

SelfAssessments 

Skills 

Videos 
 Video: PH Multiplying a Monomial and a Polynomial
 Video: PH Multiplying Binomials with Distributive
 Video: PH Multiplying Binomials with FOIL
 Video: PH Application of Multiplying Polynomials
 Video: PH Multiplying a Trinomial and a Binomial
 Video: PH Squaring Binomials
 Video: PH Difference of Squares

Explore
Learning 
 None

Websites 
 Interactive Notes: Rules for Exponents  lessons and practice problems at Regentsprep.org
 Interactive Notes: Simplifying Polynomial Expressions  lessons and workout problems at Math.com
 Interactive: Algebra Tiles  math manipulative at matti.usu.edu that visualizes multiplying algebraic expressions using tiles. Choose the Algebra Tiles icon from the list.

Old Website Links 

Common Core
Standards 
7.EE.1 
8.EE.1 
NRN.1 
NRN.2 
ASSE.2 
ASSE.3a 
ASSE.3b 
ASSE.3c 
AAPR.1 
AAPR.4 
FIF.8a 
