College Algebra 2 / MAT 120 - Stratford Public Schools
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STRATFORD PUBLIC SCHOOLS
Stratford, Connecticut
“Tantum eruditi sunt liberi”
Only The Educated Are Free
College Algebra 2 / MAT 120
Harold Greist
7 - 12 STEM Coordinator
Angela Swanepoel Jillian Barnych
Bunnell HS Department Head Stratford HS Department Head
Janet Robinson, Ph.D. Linda A. Gejda, Ed.D.
Superintendent of Schools Assistant Superintendent
Approved January 25, 2021
1ACKNOWLEDGEMENTS
Board of Education Members
Allison DelBene-Chair
Amy Wiltsie-Vice Chair
Vinnie Faggella-Secretary
Andrea Corcoran
Janice Cupee
Bob DeLorenzo
Karen Rodia
Curriculum Writer
Jillian Barnych
2DISTRICT MISSION STATEMENT
.
The mission of the Stratford school community is to ensure that all students acquire the knowledge,
character, and 21st century skills to succeed through high quality learning experiences and community
partnerships within a culture of diversity and respect.
Portrait of a Stratford Graduate
● Responsible and Involved Citizen
○ Participate in and contribute with empathy and respect to the community.
○ Demonstrate knowledge of and respect for diverse cultures, identities, and perspectives.
○ Practice responsible digital and in person citizenship as a member of a community.
● Creative and Practical Problem-Solver
○ Define and analyze a problem/problems.
○ Select, evaluate, and apply appropriate resources/strategies necessary to find/generate a
solution(s) for problems.
○ Generate and critically evaluate the effectiveness of a solution.
● Informed and Integrative Thinker
○ Apply knowledge from various disciplines and contexts to real life situations.
○ Analyze, evaluate, and synthesize information from multiple and diverse sources to build
on and utilize knowledge.
○ Use evidence and reasoning to justify claims/solutions.
● Clear and Effective Communicator
○ Select and use communication strategies (questioning, clarifying, verifying, and
challenging ideas) and interpersonal skills to collaborate with others (peers, teachers,
community members, families) within a diverse community.
○ Demonstrate, adapt, and articulate thoughts and ideas effectively using/including oral,
written, multimedia, non-verbal, and/or a performance appropriate for a particular
audience.
○ Receive, understand and process information effectively and with consideration for others
through active speaking and listening.
● Self-Directed and Lifelong Learner
○ Apply knowledge to set goals, make decisions, and assess new opportunities.
○ Demonstrates initiative, reliability and concern for quality
results/solutions/resources/information within time constraints as applicable.
○ Demonstrate flexibility in thinking/problem-solving/etc. including the ability to incorporate
new ideas and revise.
3Grade X 1
: College Algebra 2 Curriculum
Unit: X Semester
Progression
Prior Course Students learned to…
● Define, analyze, and model using functions. (Including linear, quadratic,
exponential, and piecewise)
This Students will learn to…
Course ● Determine the roots of polynomials both graphically and algebraically.
● Graph polynomials and use technology to valid their findings.
● Apply their understanding of inverses to exponential and logarithmic functions.
● Solve equations in one variable; including exponential, logarithmic, and rational.
● Apply the definition of undefined expressions to determine excluded values of
rational expressions/functions.
● Graph rational functions and use technology to valid their findings.
Next Course Students will extend their work…
● By completing partial fraction decomposition of a rational expression
● By modeling with logarithmic functions
● By exploring direct and inverse variation
STUDENT LEARNING GOALS
Mathematics Standards
APR.B.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.
APR.B.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).
IF.C.7.C Graph polynomial functions, identifying zeros when suitable factorizations are available, and
showing end behavior.
BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values
of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology. Include recognizing even and odd functions from
their graphs and algebraic expressions for them.
IF.C.7.E Graph exponential and logarithmic functions, showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and amplitude.
BF.B.4 Find inverse functions.
BF.B.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship
to solve problems involving logarithms and exponents.
Page 1 of 6
4APR.D.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed
under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract,
multiply, and divide rational expressions.
REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
IF.C.7.D (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are
available, and showing end behavior.
REI.D.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.*
Mathematical Practice Standards (Appendix B)
MP1: Make sense of problems and persevere in solving them.
MP2: Reason abstractly and quantitatively.
MP3: Construct viable arguments and critique the reasoning of others.
MP4: Model with mathematics.
MP5: Use appropriate tools strategically.
MP6: Attend to Precision
MP7: Look for and make use of structure.
Interdisciplinary Standards Key Vocabulary
Technology Integration (Appendix C) Roots, factors, factor/remainder theorem,
21st Century Skills (Appendix D) multiplicity, end behavior, asymptote, excluded
values, domain, range, function composition, base,
argument
Enduring Understandings Essential Questions
● There are many functions used in the field of ● How can functions be used to model situations?
mathematics to model and make predictions. What are the real world implications of each
● The algebrical, graphical, and table of a attribute?
function all yield the same information. Each ● How can our understanding of rational numbers be
expression of the function has its benefits. applied to the understanding of rational functions?
● How does the algebraic equation of a function
relate to the graphical representation of a function?
Assessment Plan
Summative Assessment(s)/Performance Based Formative and Diagnostic Assessment(s)
Assessments including 21st Century Learning
Final exam provided by/required by SCSU
Page 2 of 6
5Learning Plan Components
Text
College Algebra with Integrated Review (7th Edition)
Author: Blitzer, Robert
Print Publisher: Pearson, 2017
ISBN: 978134469164
Accessible via student’s My Math Lab accounts
Electronic Khan Academy, Mathbits Notebook
Desmos,TI Graphing Calculator or App
Students will:
Unit 1 ● Graph, analyze, and model with Polynomial Functions.
Lessons Tasks / Additional Resources Technology
Activities
Students will be able to identify
graphs and equations of polynomials. Section 3.2 Khan Academy Desmos
Students will recall prior knowledge of
Mathbits Notebook
function properties to analyze graphs Polygraph TI Interactive App
for domain, range, extrema, Desmos
increasing, decreasing, etc. Introduction
Activity
Students will recall prior knowledge of
factoring and apply this
understanding to the relationship Desmos
between a factor and its root. Khan Academy
Students will factor polynomials in TI Interactive App
Mathbits Notebook
standard form to determine roots. Section 3.2
Students will create a polynomial Section 3.4
when given roots.
Students will discover and use the
multiplicity of roots and understand
their impact on the graph.
Students will understand and apply
the remainder/factor theorem to
produce factored form of seemingly Khan Academy Desmos
unfactorable polynomials.
Section 3.3 Mathbits Notebook TI Interactive App
(Will cover division of polynomials
using long division and synthetic
division)
Students will demonstrate their Section 3.2 Khan Academy
understanding by graphing a Desmos
polynomial given in standard form Section 3.3 Mathbits Notebook
and use technology to verify. TI Interactive App
Formative Activity:
https://teacher.desmos.co
m/activitybuilder/custom/5
61bd514fbd28d130f1f12c8
Page 3 of 6
6Students will be able to solve Section 3.6 Khan Academy Desmos
polynomial inequalities and express Mathbits Notebook TI Interactive App
the solution set(s) using interval
notation.
Students will:
● Apply their understanding of inverse functions to exponential and
Unit 2 logarithmic functions.
● Graph, analyze, and model with exponential/logarithmic Functions
● Solve exponential and logarithmic equations.
Lessons Tasks / Additional Resources Technology
Activities
Students will recall their work with
inverses and determine the inverse of Khan Academy Desmos
linear, quadratic, and square root
functions. Section 2.7 Mathbits Notebook TI Interactive App
Students will use composition to
verify functions are inverses.
Students will graph a basic
exponential growth function and use
the graphical symmetry of inverses to Section 4.1 Graphing Exponential WS Desmos
produce the graph of a logarithmic
function. Section 4.2 Graphing Logarithmic WS TI Interactive App
Graphs will be analyzed to derive Polygraph (Done in person or online
characteristics of exponential and Exploratory using Kami)
logarithmic functions. Activity via
Desmos Desmos Activity to
Students will graph exponential and Emphasize Function
logarithmic functions by hand and use Transformations
technology to verify.
Students will solve exponential and Section 4.1 Khan Academy Desmos
logarithmic functions graphically.
Section 4.2 Mathbits Notebook TI Interactive App
Students will recall prior knowledge of
properties of exponents to derive the
properties of logarithms. Section4.3 Khan Academy Desmos
Students will apply the properties of Mathbits Notebook TI Interactive App
logarithms to expand and condense a
logarithmic expression.
Students will solve exponential and
logarithmic equations; including those Khan Academy Desmos
involving the use of logarithmic Section 4.4
properties. Mathbits Notebook TI Interactive App
Page 4 of 6
7Students will:
● Apply the definition of undefined expressions to determine excluded
Unit 3 values of rational expressions/functions.
● Graph rational functions and use technology to valid their findings.
● Solve rational equations.
Lessons Tasks / Additional Resources Technology
Activities
Students will recall their prior
knowledge of rational numbers to Khan Academy Desmos
determine excluded values of a Section 3.5
rational expression. Mathbits Notebook TI Interactive App
Polygraph
Graphs of rational functions will be Exploration to
analyzed to introduce key vocabulary Introduce
and the link between the equation Vocabulary
and graphical representation.
Students will graph the parent
reciprocal function and apply their Section 3.5 Khan Academy
prior knowledge of function Desmos
transformations to graph basic Mathbits Notebook
rational functions. TI Interactive App
“Marbleslides” Activity
Students will apply their prior
knowledge of factoring expressions to Khan Academy
simplify rational expressions. (Can Desmos
include the use of factor theorem from Section P.6 Mathbits Notebook
Unit 1) TI Interactive App
Students will graph rational functions.
(Including vertical and horizontal
asymptotes, removable Desmos
discontinuities, and end behavior) Section 3.5 Khan Academy
TI Interactive App
Mathbits Notebook
Students will solve rational equations
and justify their solution; being Section 1.2; Additional Resource Desmos
mindful of extraneous solutions. objective 3
Khan Academy TI Interactive App
Mathbits Notebook
Summative Assessment Performance Task
Final exam provided by/required by SCSU Desmos “Job Application” Task
Student Sample
Page 5 of 6
8Page 6 of 6
9Appendix A: Sample Syllabus
Early College Course with SCSU MAT 120
Instructors: Jillian Barnych, Kathy O’Brien, Jim Stein
Course Description:
This course is a further study of Algebra and Mathematical Modeling. Functions covered will include linear,
quadratic, polynomial, rational, exponential, and logarithmic. The course will have an emphasis on
problem solving, real world applications, and appropriate use of technology.
Course Content:
Unit 1: Function Characteristics
● Definition of a function
● Multiple representations of a function
● Function notation
● Composition of functions
● Analyzing graphs of a function for function properties
● Applications of Functions
● Function Transformations
Unit 2: Linear Functions and Quadratic Functions
● Graphing of linear/quadratic functions
● Applications of Linear Equations (including inequalities)
● Piece - wise Functions
● Creating a scatterplot and utilizing regression to create a linear/quadratic/exponential model
● Solving linear/quadratic equations/inequalities algebraically and graphically
○ Including complex numbers
Unit 3: Polynomial Functions
● Characteristics of polynomials functions
● Solving higher degree equations by factoring
● Graphing polynomial functions
○ Including intercepts, multiplicity, end behavior, extrema
● Dividing polynomials (Long Division and Synthetic)
● Remainder/Factor Theorem
● Polynomial Inequalities
Unit 4: Exponential and Logarithmic Functions
● Characteristics of exponential functions
● Using exponential functions as mathematical models (including regression)
● Inverse Functions
10● Characteristics of logarithmic functions
● Properties of logarithms
● Solving exponential and logarithmic equations algebraically and graphically
Unit 5: Rational Functions
● Graphing parent reciprocal functions through transformations
● Graphs of rational functions
○ Including vertical and horizontal asymptotes, removable discontinuities, and end behavior
● Solving rational equations
Course Textbook: College Algebra with Integrated Review (7th Edition)
Author: Blitzer, Robert
Publisher: Pearson, 2017
ISBN: 978134469164
Course Grading Policy per Quarter/Marking Period
ONLINE HOMEWORK (5%) – Average on My Math Lab for School
● The purpose of these online homework assignments is to allow you to work at your own pace
through content covered in class.
● Many of these assignments are done outside of class
FORMATIVE ASSIGNMENTS (5%) – In-class assignments, problem sets, “check points”
● The purpose of these assignments are to provide opportunities to work towards mastery of the
content and standards being covered.
● Practice assignments will mostly be done during class time.
● These assignments are valuable in both the teacher and student to receive valuable feedback on
how we are doing!
PERFORMANCE ASSESSMENTS (90%) – Tests, quizzes, projects, and other demonstrations of learning
● The purpose of performance assignments are to demonstrate your mastery of the content and
standards being covered.
● Performance assignments make up the majority of your grade.
Overall Course Grading Policy/Weight
● Following the high school grading/weighting this course will be graded where each quarter/marking
period counts as 40% of the grade and the final exam (same exam as SCSU) will count as 20% of the
final grade for the course.
11Appendix B
8 Mathematical Practice Standards
MP1. Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem
and looking for entry points to its solution. They analyze givens, constraints, relationships, and
goals. They make conjectures about the form and meaning of the solution and plan a solution
pathway rather than simply jumping into a solution attempt. They consider analogous
problems, and try special cases and simpler forms of the original problem in order to gain
insight into its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the information
they need. Mathematically proficient students can explain correspondences between
equations, verbal descriptions, tables, and graphs or draw diagrams of important features and
relationships, graph data, and search for regularity or trends. Younger students might rely on
using concrete objects or pictures to help conceptualize and solve a problem. Mathematically
proficient students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the approaches of
others to solving complex problems and identify correspondences between different
approaches.
MP2. Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own,
without necessarily attending to their referents—and the ability to contextualize, to pause as
needed during the manipulation process in order to probe into the referents for the symbols
involved. Quantitative reasoning entails habits of creating a coherent representation of the
problem at hand; considering the units involved; attending to the meaning of quantities, not
just how to compute them; and knowing and flexibly using different properties of operations
and objects.
Appendix B – All Grades B1
12MP3. Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a
logical progression of statements to explore the truth of their conjectures. They are able to
analyze situations by breaking them into cases, and can recognize and use counterexamples.
They justify their conclusions, communicate them to others, and respond to the arguments of
others. They reason inductively about data, making plausible arguments that take into account
the context from which the data arose. Mathematically proficient students are also able
to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning
from that which is flawed, and—if there is a flaw in an argument—explain what it is.
Elementary students can construct arguments using concrete referents such as objects,
drawings, diagrams, and actions. Such arguments can make sense and be correct, even though
they are not generalized or made formal until later grades. Later, students learn to determine
domains to which an argument applies. Students at all grades can listen or read the arguments
of others, decide whether they make sense, and ask useful questions to clarify or improve the
arguments.
MP4. Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems
arising in everyday life, society, and the workplace. In early grades, this might be as simple as
writing an addition equation to describe a situation. In middle grades, a student might apply
proportional reasoning to plan a school event or analyze a problem in the community. By high
school, a student might use geometry to solve a design problem or use a function to describe
how one quantity of interest depends on another. Mathematically proficient students who can
apply what they know are comfortable making assumptions and approximations to simplify a
complicated situation, realizing that these may need revision later. They are able to identify
important quantities in a practical situation and map their relationships using such tools as
diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those
relationships mathematically to draw conclusions. They routinely interpret their mathematical
results in the context of the situation and reflect on whether the results make sense, possibly
improving the model if it has not served its purpose.
Appendix B – All Grades B2
13MP5. Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical
problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a
calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic
geometry software. Proficient students are sufficiently familiar with tools appropriate for their
grade or course to make sound decisions about when each of these tools might be helpful,
recognizing both the insight to be gained and their limitations. For example, mathematically
proficient high school students analyze graphs of functions and solutions generated using a
graphing calculator. They detect possible errors by strategically using estimation and other
mathematical knowledge. When making mathematical models, they know that technology can
enable them to visualize the results of varying assumptions, explore consequences, and
compare predictions with data. Mathematically proficient students at various grade levels are
able to identify relevant external mathematical resources, such as digital content located on a
website, and use them to pose or solve problems. They are able to use technological tools to
explore and deepen their understanding of concepts.
MP6. Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use
clear definitions in discussion with others and in their own reasoning. They state the meaning
of the symbols they choose, including using the equal sign consistently and appropriately. They
are careful about specifying units of measure, and labeling axes to clarify the correspondence
with quantities in a problem. They calculate accurately and efficiently, express numerical
answers with a degree of precision appropriate for the problem context. In the elementary
grades, students give carefully formulated explanations to each other. By the time they reach
high school they have learned to examine claims and make explicit use of definitions.
Appendix B – All Grades B3
14MP7. Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young
students, for example, might notice that three and seven more is the same amount as seven
and three more, or they may sort a collection of shapes according to how many sides the
shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in
preparation for learning about the distributive property. In the expression x2 + 9x + 14, older
students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an
existing line in a geometric figure and can use the strategy of drawing an auxiliary line for
solving problems. They also can step back for an overview and shift perspective. They can see
complicated things, such as some algebraic expressions, as single objects or as being composed
of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a
square and use that to realize that its value cannot be more than 5 for any real numbers x and
y.
MP8. Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for
general methods and for shortcuts. Upper elementary students might notice when dividing 25
by 11 that they are repeating the same calculations over and over again, and conclude they
have a repeating decimal. By paying attention to the calculation of slope as they repeatedly
check whether points are on the line through (1, 2) with slope 3, middle school students might
abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when
expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the
general formula for the sum of a geometric series. As they work to solve a problem,
mathematically proficient students maintain oversight of the process, while attending to the
details. They continually evaluate the reasonableness of their intermediate results.
Appendix B – All Grades B4
15Appendix C
5 Interdisciplinary Standards
IS1. Information Strategies
Students determine their need for information and apply strategies to select, locate, and access
information resources.
IS2. Information Use
Students evaluate, analyze, and synthesize information and data to solve problems, conduct
research, and pursue personal interests.
IS3. Information and Technology Application
Students use appropriate technologies to create written, visual, oral and multimedia products
that communicate ideas and information.
IS4. Literacy and Literary Appreciation
Students extract meaning from fiction and non-fiction resources in a variety of formats. They
demonstrate an enjoyment of reading, including an appreciation of literature and other
creative expressions.
IS5. Personal Management
Students display evidence of ethical, legal, and social responsibility in regard to information
resources and project and self-management.
Appendix C – All Grades C1
16Appendix D
21st Century Skills
TCS1. Use of Information
Use real-world digital and other research tools to access, evaluate, and effectively apply
information.
TCS2. Independence and Collaboration
Work independently and collaboratively to solve problems and accomplish goals.
TCS3. Communication
Communicate information clearly and effectively using a variety of tools/media in varied
contexts for a variety of purposes.
TCS4. Innovation and Adaptability
Demonstrate innovation, flexibility, and adaptability in thinking patterns, work habits, and
working/learning conditions.
TCS5. Problem Solving
Effectively apply the analysis, synthesis, and evaluative processes that enable productive
problem solving.
TCS6. Character
Value and demonstrate personal responsibility, character, cultural understanding, and ethical
behavior.
Appendix D – All Grades D1
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