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

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ACKNOWLEDGEMENTS 

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

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DISTRICT MISSION STATEMENT

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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.

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Grade:

X College Algebra 2 Curriculum 1

Semester Unit: X Progression

Prior Course Students learned to… ● Define, analyze, and model using functions. (Including linear, quadratic,

exponential, and piecewise)

This Course

Students will learn to… ● 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.

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APR.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) 21st Century Skills (Appendix D)

Roots, factors, factor/remainder theorem, 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

mathematics to model and make predictions. ● The algebrical, graphical, and table of a

function all yield the same information. Each expression of the function has its benefits.

● How can functions be used to model situations? What are the real world implications of each attribute?

● How can our understanding of rational numbers be 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 Assessments including 21st Century Learning Final exam provided by/required by SCSU

Formative and Diagnostic Assessment(s)

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Learning Plan Components

Text College Algebra with Integrated Review (7th Edition)

Print Author: Blitzer, Robert Publisher: Pearson, 2017 ISBN: 978134469164

Electronic Accessible via student’s My Math Lab accounts Khan Academy, Mathbits Notebook Desmos,TI Graphing Calculator or App

Unit 1 Students will:

● Graph, analyze, and model with Polynomial Functions. Lessons Tasks /

Activities Additional Resources Technology

Students will be able to identify graphs and equations of polynomials. Students will recall prior knowledge of function properties to analyze graphs for domain, range, extrema, increasing, decreasing, etc.

Section 3.2 Polygraph Desmos Introduction Activity

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will recall prior knowledge of factoring and apply this understanding to the relationship between a factor and its root. Students will factor polynomials in standard form to determine roots. Students will create a polynomial when given roots. Students will discover and use the multiplicity of roots and understand their impact on the graph.

Section 3.2 Section 3.4

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will understand and apply the remainder/factor theorem to produce factored form of seemingly unfactorable polynomials. (Will cover division of polynomials using long division and synthetic division)

Section 3.3

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will demonstrate their understanding by graphing a polynomial given in standard form and use technology to verify.

Section 3.2

Section 3.3

Khan Academy Mathbits Notebook Formative Activity: https://teacher.desmos.com/activitybuilder/custom/561bd514fbd28d130f1f12c8

Desmos TI Interactive App

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Students will be able to solve polynomial inequalities and express the solution set(s) using interval notation.

Section 3.6 Khan Academy Mathbits Notebook

Desmos TI Interactive App

Unit 2

Students will: ● Apply their understanding of inverse functions to exponential and

logarithmic functions. ● Graph, analyze, and model with exponential/logarithmic Functions ● Solve exponential and logarithmic equations.

Lessons Tasks / Activities

Additional Resources Technology

Students will recall their work with inverses and determine the inverse of linear, quadratic, and square root functions. Students will use composition to verify functions are inverses.

Section 2.7

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will graph a basic exponential growth function and use the graphical symmetry of inverses to produce the graph of a logarithmic function. Graphs will be analyzed to derive characteristics of exponential and logarithmic functions. Students will graph exponential and logarithmic functions by hand and use technology to verify.

Section 4.1 Section 4.2 Polygraph Exploratory Activity via Desmos

Graphing Exponential WS Graphing Logarithmic WS (Done in person or online using Kami) Desmos Activity to Emphasize Function Transformations

Desmos TI Interactive App

Students will solve exponential and logarithmic functions graphically.

Section 4.1 Section 4.2

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will recall prior knowledge of properties of exponents to derive the properties of logarithms. Students will apply the properties of logarithms to expand and condense a logarithmic expression.

Section4.3

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will solve exponential and logarithmic equations; including those involving the use of logarithmic properties.

Section 4.4

Khan Academy Mathbits Notebook

Desmos TI Interactive App

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Unit 3

Students will:

● Apply the definition of undefined expressions to determine excluded values of rational expressions/functions.

● Graph rational functions and use technology to valid their findings. ● Solve rational equations.

Lessons Tasks /

Activities Additional Resources Technology

Students will recall their prior knowledge of rational numbers to determine excluded values of a rational expression. Graphs of rational functions will be analyzed to introduce key vocabulary and the link between the equation and graphical representation.

Section 3.5 Polygraph Exploration to Introduce Vocabulary

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will graph the parent reciprocal function and apply their prior knowledge of function transformations to graph basic rational functions.

Section 3.5

Khan Academy Mathbits Notebook “Marbleslides” Activity

Desmos TI Interactive App

Students will apply their prior knowledge of factoring expressions to simplify rational expressions. (Can include the use of factor theorem from Unit 1)

Section P.6

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will graph rational functions. (Including vertical and horizontal asymptotes, removable discontinuities, and end behavior)

Section 3.5

Khan Academy Mathbits Notebook

Desmos TI Interactive App

Students will solve rational equations and justify their solution; being mindful of extraneous solutions.

Section 1.2; objective 3

Additional Resource Khan Academy Mathbits Notebook

Desmos TI Interactive App

Summative Assessment Performance Task Final exam provided by/required by SCSU

Desmos “Job Application” Task Student Sample

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Appendix 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

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● 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.

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Appendix B – All Grades B1

Appendix 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.

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Appendix B – All Grades B2

MP3. 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.

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Appendix B – All Grades B3

MP5. 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.

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Appendix B – All Grades B4

MP7. 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)(x

3 + x

2 + 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.

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Appendix C – All Grades C1

Appendix 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.

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Appendix D – All Grades D1

Appendix 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.

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