A.2a 
The student will perform operations on polynomials, including
a) applying the laws of exponents to perform operations on expressions;


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 sums and differences of polynomials.
 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).
 Find the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor.

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: Exponents  Expressions and Operations (PDF)  Using exponents (Word)
 Notes: Dividing Monomials (ppt)

Real World Lessons 

Practice 
 VDOE ESS: Exploring Exponents (pdf)
 VDOE ESS: Scientifically Speaking (pdf)
 Worksheet: Dividing Monomials CW (doc)
 Worksheet: Dividing Monomials HW (doc)

SelfAssessments 

Skills 
 JMU Pivotal Question: Monomial Division (doc)

Videos 
 Video: PH Zero and Negative Exponents
 Video: PH Dividing Expressions with Exponents
 Video: PH Raising a Quotient to a Power
 Video: PH Evaluating Exponential Expressions

Explore
Learning 
 Exponents and Power Rules  Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps.
 Dividing Exponential Expressions  Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.

Websites 
 Interactive
Notes: Dividing Polynomials by Monomials 
lessons and practice problems at Regentsprep.org
 Notes:
Rules for Exponents  displays all of the
rules for exponents at math.uww.edu

Old Website Links 

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