Name of Collaborative: CCGPS Advanced Algebra
Members of Collaborative Team: Mazzei, Turner, Bartlett, West, Marsh, Hutchins
Curriculum Area: Math
Unit Title: Polynomial Functions
Time Frame (Date): 4-5 weeks
Note: Each teacher keeps his/her own copy reflecting teacher’s unit plan
Desired Results
Content Standards ( # and brief description): Copy and paste from Picasso
Use complex numbers in polynomial identities and equations.
MCC9-12.N.CN.8 (+) Extend polynomial identities to the complex numbers.
MCC9-12.N.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials.
Interpret the structure of expressions
MCC9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.★
MCC9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.★
MCC9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single
entity.★
MCC9-12.A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Write expressions in equivalent forms to solve problems
MCC9-12.A.SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is
not 1), and use the formula to solve problems★
Perform arithmetic operations on polynomials
MCC9-12.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.
Understand the relationship between zeros and factors of polynomials
MCC9-12.A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the
remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
MCC9-12.A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the
zeros to construct a rough graph of the function defined by the polynomial.
Use polynomial identities to solve problems
MCC9-12.A.APR.4 Prove polynomial identities and use them to describe numerical relationships.
MCC9-12.A.APR.5 (+) Know and apply that the Binomial Theorem gives the expansion of (x + y)n in
powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined
for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a
combinatorial argument.)
Solve systems of equations
MCC9-12.A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically.
Represent and solve equations and inequalities graphically
MCC9-12.A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y =
f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately,
e.g., using technology to graph the functions, make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.★
Analyze functions using different representations
MCC9-12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.★
MCC9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available,
and showing end behavior.★
Essential Questions:
-How do we add, subtract, and multiply polynomials?
-How do we write a polynomial in standard or factored form?
-How do we divide polynomials?
-In which operations does closure apply?
-How can we apply Pascal’s Triangle to expand (x + y )n ?
-What is the Remainder Theorem and what does it tell us?
-What is the Factor Theorem and what does it tell us?
-What is the Rational Root Theorem and what does it tell us?
-How can we solve polynomials equations?
-Which sets of numbers can be solutions to polynomial equations?
-What is the Fundamental Theorem of Algebra and what does it tell us?
-What characteristics of polynomial functions can be seen on their graphs?
-What is the relationship between zeros and factors?
-How can we solve a system of a linear equation with a polynomial equation?
Content (Unpack Nouns from Standards):
Students will know…
Skills (Unpack Verbs from Standards):
Students will be able to…
Polynomials
Integers
Closure
Operations
Expressions
Terms
Factors
Coefficients
Binomial Theorem
Pascal’s Triangle
Identities
Remainder Theorem
Zeros
Fundamental Theorem of Algebra
Domain
Rate of Change
End behavior
System of equations
Inequalities
Constraints
Geometric series
Even function
Odd function
-Add, subtract, multiply, divide polynomials
-Rewrite expressions
-Interpret expressions as quantities
-Interpret parts of expressions
-Prove polynomial identities
-Describe numerical relationships
-Know and apply Binomial Theorem
-Expand Pascal’s Triangle
-Apply Remainder Theorem
-Identify zeros of polynomials
-Know the Fundamental Theorem of Algebra
-Relate the domain of a function to its graph
-Calculate and interpret rate of change of a function
-Graph functions expressed symbolically
-Graph polynomial functions, identify zeros, and
show end behavior.
-Show that the x-values of intersection points on a
graph represent solutions to a system.
-Solve a simple system.
-Create equations and inequalities in one variable.
-Create equations in two or more variables.
-Represent constraints by equations or inequalities.
-Derive the formula for the sum of a finite
geometric series.
-Recognize even and odd functions.
Essential Vocabulary: What critical vocabulary must be learned in order to master the content?
Polynomials
Integers
Closure
Operations
Expressions
Terms
Factors
Coefficients
Binomial Theorem
Pascal’s Triangle
Remainder Theorem
Factor Theorem
Rational Root Theorem
Fundamental Theorem of Algebra
Zeros
Constraints
End behavior
Geometric series
Even functions
Odd functions
Assessment Evidence
Summative
Not designed/developed as yet
(attach)
Formative
(build from Summative)
Quiz:
Quiz:
Quiz:
Quiz:
Quiz:
Operations with polynomials
Dividing polynomials (synthetic and long division)
Binomial theorem and Pascal’s triangle
Solving polynomial equations
Graphing polynomial functions and identifying characteristics
Learning Plan
Pacing Guide
(weekly or daily)
CCGPS Advanced
Algebra Spring 2014 Pacing Guide.docx
Engagement
(Highlight all that
apply)
Independent activities
Cooperative learning
Technology integration
Peer tutoring
Discussion
Learning Activities
What learning experiences and instruction will enable students to achieve the
desired results? Create a list with a brief description.
Pairing /small Groups
Hands on
Project
Visuals
Performance Task
Learning Stations
Whole group instruction
Lecture
Drawing/labelling
Game
Performance tasks will be used during this unit to reinforce concepts taught
in class.
“We’ve got to Operate”
“What’s your identity?”
“Divide and Conquer”
“Factors, Zeros, and Roots: Oh My!”
“Polynomial Patterns”
“Fascinating Fractals”
Visuals will be used throughout the unit to help students understand
vocabulary.
Differentiation
(Specialized
Instruction)
Integration of Literacy
Practice problems with varying levels of difficulty will be used throughout the
unit. Students will be grouped differently depending on the task. Teacher will
utilize mixed ability grouping when appropriate as well as same ability grouping
with assignment suited to group ability level. Enrichment/challenge activities
will be provided for gifted/acc students that understand content standards and
are ready to move forward or more in-depth. Remediation will be provided for
students needing extra assistance.
The performance tasks require students to read various real-world situations
and answer questions in regard to the scenarios. Students must write in
complete sentences to explain their answers as well as interpret information
from word problems.
Closing tasks will require students to answer the daily EQ’s using complete
sentences and citing examples from their notes and examples.
Students will create poster presentations summarizing work as well as creating
their own real-world practice problems.
Students will take turns critique each other’s work. Students will be required
to give valuable feedback relating to the standards, both positive and negative,
not just remarks such as “Good Job” or “Nice work”
Materials/Resources
Activities will be used for students to be able to practice using unit vocabulary
accurately and in correct context.
Holt Online textbook
Ga DOE frameworks learning tasks
Khan Academy
YouTube instructional video clips
Study Island
Will reflect on student progress throughout the unit in addition to keeping data
of student assessment scores.
Collaborative
Reflection
CAMPBELL HIGH SCHOOL UNIT PLAN TEMPLATE
Adopted from Kell HS
08/01/2011