Mathematics
Curriculum Document for Algebra 2
Unit Title: Exploring Rational Functions
Time Frame: 10 blocks
Six Weeks:
Unit Number: 7
Curriculum
Enduring Understandings (Big Ideas):
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The student will know:
Simplifying math operations with a standard process helps
us communicate and solve real-world situations with
consistency.
Understanding how a parameter change affects the whole
helps us make predictions.
Solutions need to be evaluated for reasonableness.
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Rational functions are quotients of polynomials
Vertical asymptotes occur when the denominator is zero
Horizontal asymptotes occur as the graph approaches k
Extraneous solutions may exist in rational equations
The student will be able to:
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Model and make predictions using direct/inverse variation
Graph rational functions
Predict and use parameter changes on rational functions
Describe domain and range of rational functions (focus skill for PSAT
preparedness)
 Analyze various representations of rational functions (tables,
graphs, algebraic, verbal)
 Solve and determine reasonableness of solutions to rational
equations (algebraic, graph, table) and inequalities (graph and
table)
 Use rational functions to represent real-life situations
 Add, subtract, multiply, and divide rational functions
 Solve systems of rational equations/inequalities
 Determine reasonableness of solutions to systems of rational
equations/inequalities
Essential Questions:
 How is the whole picture affected when one aspect is altered?
 Why is it important to analyze effects of changing parameters?
Unit Title: Exploring Rational Functions
Unit Number 7
Revised Spring 2014
Page 1 of 4
Mathematics
Curriculum Document for Algebra 2
 What is a solution and what does it represent?
 Why do we follow certain procedures?
 How does recognizing patterns help us simplify expressions?
Student Understanding (student friendly TEKS):
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I can model and make predictions using direct/inverse variation. (taken from 2A.10G)
I can graph rational functions. (taken from 2A.4A)
I can predict and use parameter changes on rational functions. (taken from 2A.4B and 2A.10A)
I can describe domain and range of rational functions. (taken from 2A.10A and 2A. 10C)
I can solve and determine reasonableness of solutions to rational equations (algebraic, graph, table) . (taken from 2A.10C and 2A.10D)
I can solve and determine reasonableness of solutions to rational inequalities (graph and table). (taken from 2A.10C and 2A.10E)
I can use rational functions to represent real-life situations. (taken from 2A.10F)
I can add, subtract, multiply, and divide rational functions. (taken from 2A.10B)
I can analyze various representations of rational functions (tables, graphs, algebraic, verbal). (taken from 2A.10B)
I can solve systems of rational equations/inequalities. (taken from 2A.3B)
I can determine reasonableness of solutions to systems of rational equations/inequalities. (taken from 2A.3C)
TEKS:
(A2.3) Foundations for functions. The student formulates systems of equations and inequalities from problem situations, uses a variety
of methods to solve them, and analyzes the solutions in terms of the situations. The student is expected to:
(B) use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and
(C) interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.
(A2.4) Algebra and geometry. The student connects algebraic and geometric representations of functions. The student is expected to:
(A) identify and sketch graphs of parent functions, including linear (f (x) = x),
quadratic (f (x) = x2), exponential (f (x) = ax), and logarithmic (f (x) = logax) functions, absolute value of x (f (x) = |x|), square
root of x (f (x) = x), and reciprocal of x (f (x) = 1/x);
(B) extend parent functions with parameters such as a in f (x) = a/x and describe the effects of the parameter changes on
the graph of parent functions; and
(A2.10) Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods
to solve them, and analyzes the solutions in terms of the situation. The student is expected to:
(A) use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe
limitations on the domains and ranges, and examine asymptotic behavior;
(B) analyze various representations of rational functions with respect to problem situations;
Unit Title: Exploring Rational Functions
Unit Number 7
Revised Spring 2014
Page 2 of 4
Mathematics
Curriculum Document for Algebra 2
(C) determine the reasonable domain and range values of rational functions, as well as interpret and determine the
reasonableness of solutions to rational equations and inequalities;
(D) determine the solutions of rational equations using graphs, tables, and algebraic methods;
(E) determine solutions of rational inequalities using graphs and tables;
(F) analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or
quadratic function, and solve the problem; and
(G) use functions to model and make predictions in problem situations involving direct and inverse variation.
Targeted College Readiness Standards:
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IC1, IIB1, IIC1, IIC2, IID1, IID2, VIIB1, VIIB2, VIIC1, VIIC2, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIB1, VIIIB2, VIIIC1, VIIIC2, VIIIC3, IXA1,
IXA2, IXA3, IXB1, IXB2, IXC1, IXC2, IXC3, XA1, XA2, XB1, XB2, XB3
Targeted ELPs:
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1A, 1C, 1D, 1E, 1F, 1H, 2C, 2E, 2G, 2I, 3D, 3E, 3F, 3G, 3H, 3J, 4C, 4D
Academic Vocabulary:
 Asymptote
 Rational functions
Language of Instruction:
Denominator
Direct/Inverse variation
Domain
Extraneous solution
Horizontal
Inequality/ Equation
Numerator
Range
Transformation
Vertical
Instruction
Instructional Resources:
Textbook:
 Chapter 2 Section 5
 Chapter 8 Sections 1 (inverse only), 2-6
Engaging Mathematics: TEKS-Based Activities for Algebra II (Cheaper by the Dozen p. 227) (Spring Break p. 229)
Unit Title: Exploring Rational Functions
Unit Number 7
Revised Spring 2014
Page 3 of 4
Mathematics
Curriculum Document for Algebra 2
(Driving to South Padre p. 231) (Does it Vary? p. 233) (Variation in a Table p.235) (Where is the Line? p. 237) (Graphing
Rational Functions p. 239) (Zooming In p. 243)(Rodeo Rides p. 245) (You’re a Star p. 247) (Alike and Different p. 249)
Simplifying Rational Expressions
Rational Expressions Applications
Vertical Asymptotes Discovery Worksheet
Rational Equations Lab
Rational Inequalities
Algebra II End of Course Success- CCRS RC6
Algebra II End of Course Success- CCRS RC6 ANSWER KEY
Instructional Suggestions/Examples for PSAT preparedness
Technology:
Career Connections/Real Life Application:
Exemplar Lessons:
Research Based Instructional Strategies:
Assessment
Student self-assessment & reflection:
Portfolio – Student Template Rational
Portfolio – Teacher Template Rational
Critical Thinking Writing Examples
Unit Title: Exploring Rational Functions
Acceptable evidence or artifacts:
Performance Task Unit 7 #1
Performance Task Unit 7 #2
Unit Number 7
Revised Spring 2014
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