Module 6: Polynomials Expressions and Functions
Module Overview: In this module students learn how to multiply, add, and subtract polynomials using concrete models and analytic techniques.
They also learn how to factor quadratic trinomials using concrete models and analytic techniques. This work with polynomial expressions serves as
a bridge to introductory work with polynomial functions, laying the foundation for deeper study of quadratic functions in module 7 of this course
and general polynomial functions in Algebra II.
Essential Question:
Can two algebraic expressions that appear to be different be equivalent?
Prerequisite Skills and Knowledge:
finding factors of composite numbers, simplifying expressions, multiplying and dividing expressions with exponents
Tier III Vocabulary:
Monomial, Degree of a monomial, Polynomial, Binomial, Trinomial, Standard form of a polynomial, Degree of a polynomial
Common Core Standards for Mathematical Practices
Key
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of
others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
 ★ Modeling Standard
 *indicates a standard that appears in multiple modules
 + indicates a standard included to increase coherence
 PH Prentice Hall Algebra One textbook 2011
 BOLD indicates TN Common Core focus standards
abc indicates a part of a standard that appears in a different module
Common Core State Standards for Math Content
Students will be able to know or do
Activities/Resources
Cumberland County Algebra One Curriculum Guide 1
A-APR Arithmetic with Polynomial and Rational
Expressions

Accurately perform addition, subtraction,
and multiplication with polynomials.
A. Perform arithmetic operations on polynomial.
(Incorporate the classifying of polynomials
by degree and by term throughout the
module).
A-APR.A.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.
Classifying Polynomials
by degree and term
http://www.sparknotes.c
om/math/algebra1/polyn
omials/section1.rhtml
A-SSE Algebra Seeing Structure in Expressions

Decompose expressions and make sense of
the multiple factors and terms by
explaining the meaning of the individual
parts.

Understand how and why the following
three expression are equivalent based on
the distributive property
A. Interpret the structure of expressions.
A-SSE.A.1 Interpret expressions that represent a quantity
in terms of its context. ★
a.
b.
c.
d.
b. Interpret complicated expressions by viewing one
or more of their parts as a single entity. For
example, interpret P(1+r)n as the product of P and
a factor not depending on P.
o (x + y)(h + k).
o x(h + k) + y(h +k)
o xh + xk + yh + yk,
Task Arc for
Polynomials/Factoring(Be
gin and use individual
tasks as knowledge
progresses)
http://www.tncore.org/site
s/www/Uploads/MathTask
s_9.13/AlgebraITaskArc.p
df
A-SSE.A.2 Use the structure of an expression to identify
ways to rewrite it. For example, see x 4  y 4 as
x   y 
2 2
2 2
, thus recognizing it as a difference of
squares that can be factored as
x
2
 y2
 x
2

 y2 .
Cumberland County Algebra One Curriculum Guide 2
B. Write expressions in equivalent forms to solve
problems.

A.SSE.B.3 Choose and produce an equivalent form of an
expression to reveal and explain properties of the quantity
represented by the expression. ★
a. Factor a quadratic expression to reveal the zeros of the
function it defines.
A-APR Arithmetic with Polynomial and Rational
Expressions
B. Understand the relationship between zeros and factors
of polynomials.

A-APR.B.3 Understand zeros of polynomials when
suitable factorizations are available, and use the zeros to
construct a rough graph of the function defined by the
polynomial.

Factor quadratic equations and functions to
find and explain the meaning of the zeros.
o Given a quadratic function explain the
meaning of the zeros of the function.
That is if f(x) = (x – c) (x – a) then f(a)
= 0 and f(c) = 0.
o Given a quadratic expression, explain
the meaning of the zeros graphically.
That is for an expression (x – a) (x – c),
a and c correspond to the x-intercepts
(if a and c are real).
Factor quadratic and cubic polynomials in
which linear and quadratic factors are
available. For example, find the zeros of
(x-2)(x2-9).
Use the zeros and end behavior to sketch a
rough graph of the function.
Cumberland County Algebra One Curriculum Guide 3