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MATRIX _

VIEWS: 57 PAGES: 5

									Course: Algebra 2                                         Austin ISD Curriculum Road Map                                                 2010 – 2011
                                                         th
                                                        4 Six week – January 4 – February 17 (31 days)

                                Concept (Big Idea): Square Root and Exponential Functions                                    Concept Pacing: 5 days
Enduring Understanding:                                                     Essential Questions:
Real-life applications can be represented and solved using square root       How are square root equations & inequalities different from the other types
(radical) equations and inequalities, and solved using a variety of methods    we have solved?
(some similar to quadratic methods)                                          What methods are most useful in solving square root equations &
                                                                               inequalities and how do we choose the best method?

Unit: Square Root Functions                                                                                                    Unit Pacing: 5 days
Vocabulary:   radical equation, radical inequality
Resources: DC Algebra II Assessment, SATEC, Holt

Matrix #        Established Goals                      Established Goals                    Students Will Know…                Students will be able to….
             TEKS Knowledge & Skill               TEKS Student Expectation
           2A.9: The student formulates   2A.9D: determine solutions of square root     essential vocabulary such as     solve radical equations and
  248      equations and inequalities     equations using graphs, tables, and           radical equation and radical     inequalities using a graph and a
           based on square root           algebraic methods;                            inequality                       table or using algebraic methods
           functions, uses a variety of   2A.9E: determine solutions of square root                                      determine if the solution or
 248A      methods to solve them, and     inequalities using graphs and tables                                           solutions of a square root equation
           analyzes the solutions in                                                                                     is extraneous
           terms of the situation.        2A.9F: analyze situations modeled by
                                          square root functions, formulate equations
  238
                                          or inequalities, select a method, and solve
                                          problems

                                                     Student Work Products/Assessment Evidence
                                                                            Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student
                           Performance Tasks
                                                                                               work samples, observations, etc.)
Algebra II Assessments (Charles A. Dana Center): I was going how fast?     Review Inverses and Square Roots, SATEC Algebra 2
                                                                           Just a Swingin’, SATEC Algebra 2, Radical Equations Matching Activity


                                                                        Learning Plan
Lesson/Activity/Module       Teacher Resource            Student Resource          Technology (Media,                  Other                 Assessment
        Name                                                                           website, etc.)
Square Root Functions     Algebra II Assessment        Dana Center I was going Graphing Calculators
                          Dana Center I was going      how fast? p. 227           Holt: power points
                          how fast?                    SATEC: Review Inverses
                          p. 228 – 230                 and Square Roots
                          SATEC: Review Inverses       SATEC: Just Swinging
                          and Square Roots             Reflect and apply
                          SATEC: Just Swingin’         Radical Equations
                          Radical Equations            Matching Activity
                          Matching Activity
                                                                          Page 1 of 5
Course: Algebra 2                                           Austin ISD Curriculum Road Map                                                    2010 – 2011
                                                           th
                                                          4 Six week – January 4 – February 17 (31 days)



                            Concept (Big Idea): Exponential Functions                                                   Concept Pacing: 11 days
Enduring Understanding:                                                           Essential Questions:
Exponential functions grow (eventually) faster than linear functions and do        In what ways is the exponential graph different from the other parent
not increase at a constant rate of change (like linear functions); they have         functions?
numerous applications in growth with populations ( and decay) and                  How does the symbolic notation of quadratic transformations (shifts,
monetary growth (loans, retirement plans, savings)                                   stretches, compressions) connect to the exponential graph?
Real-world problems involving growth, decay, and/or finances, can be               How are transformations of the exponential function similar to
modeled using exponential equations or inequalities and solved multiple              transformations of the quad & absolute value function? How are they
methods                                                                              different?
                                                                                   How does the function help to identify significant points to graph the
                                                                                     function?
                                                                                   How can exponential functions be used to analyze population growth/decay
                                                                                     and make real-life decisions surrounding population rates?
                                                                                   What methods can be used for exponential equations/ineqs and how do you
                                                                                     choose which method is best?
                                                                                   How do we know the answer makes sense?


Unit: Exponential Functions                                                                                                        Unit Pacing: 11 days
Vocabulary:   exponential function, base, asymptote, exponential growth, exponential decay
Resources: SATEC, Holt

Matrix        Established Goals                     Established Goals                          Students Will Know…                  Students will be able to….
  #       TEKS Knowledge & Skill               TEKS Student Expectation
          2A.4: The student             2A.4A: identify and sketch graphs of           Essential vocabulary such as               write and evaluate exponential
          connects algebraic and        parent functions, including linear (f(x) =     exponential function, base, asymptote,     expressions
                                                               2
          geometric representations     x), quadratic (f(x) = x ), exponential (f(x)   exponential growth and exponential         sketch (by hand) the graph of an
                                            x
  262     of functions.                 = a ), and logarithmic (f(x) = logax)          decay                                      exponential function with
                                        functions, absolute value of x (f(x) = |x|),   The similarities and differences of        significant points (intercepts,
                                        square root of x (f(x) = √x), and              transformations of exponential functions   asymptotes…) and proper shape
                                        reciprocal of x (f(x) = 1/x).                  compared to other functions such as        or direction
                                        2A.4B: extend parent functions with            quadratic and absolute value                  explain the parameter
                                        parameters such as a in f(x) = a/x and         the general form of an exponential         changes
  321                                   describe the effects of the parameter          equation and what each variable               and graph both the parent and
                                        changes on the graph of parent                 represents                                    transformed exponential
                                                                         x
                                        functions; exponential (f(x) = a ),                                                       function
          2A.11: The student            2A.11D: determine solutions of                 Essential vocabulary such as                  write a function that models
          formulates equations and      exponential and logarithmic equations          exponential growth and exponential         growth
  249
          inequalities based on         using graphs, tables, and algebraic            decay                                         and decay situations
          exponential and               methods                                                                                   be able to determine if the


                                                                               Page 2 of 5
Course: Algebra 2                                         Austin ISD Curriculum Road Map                                          2010 – 2011
                                                         th
                                                        4 Six week – January 4 – February 17 (31 days)

Matrix       Established Goals                   Established Goals                         Students Will Know…          Students will be able to….
  #       TEKS Knowledge & Skill             TEKS Student Expectation
         logarithmic functions, uses   2A.11E: determine solutions of                                                 exponential function shows
 247A    a variety of methods to       exponential and logarithmic inequalities                                       growth or decay without
         solve them, and analyzes      using graphs and tables                                                        graphing it
         the solutions in terms of     2A.11F: analyze a situation modeled by                                         be able to solve an exponential
         the situation                 an exponential function, formulate an                                          equation by using the same
 236                                                                                                                  base
                                       equation of inequality, and solve the
                                       problem



                                                      Student Work Products/Assessment Evidence
                                                                        Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student work
                         Performance Tasks
                                                                                                 samples, observations, etc.)
                                                                        Starbuck’s Exponential Growth; Graphing Exponential functions, SATEC Algebra
                                                                        2; Graphing Exponential Functions Parameter Changes, SATEC Algebra 2

                                                                          Learning Plan
Lesson/Activity/Module     Teacher Resource       Student Resource             Technology (Media, website, etc.)       Other           Assessment
        Name
Exponential Functions     Starbuck’s              Starbuck’s                                                                              Unit Test
                          Exponential Growth      Exponential Growth
                          SATEC: Graphing         SATEC: Graphing
                          Exponential Functions   Exponential Functions
                          SATEC: Graphing         SATEC: Graphing
                          Exponential Functions   Exponential Functions
                          Parameter Changes       Parameter Changes




                                                                           Page 3 of 5
Course: Algebra 2                                             Austin ISD Curriculum Road Map                                                     2010 – 2011
                                                             th
                                                            4 Six week – January 4 – February 17 (31 days)

                              Concept (Big Idea): Logarithmic Functions                                                   Concept Pacing: 14 days
Enduring Understanding:                                                             Essential Questions:
Logarithmic Functions, Inverses, & Transformations                                   In what ways is the logarithmic function similar to the exponential function?
 Logarithmic functions are inverses of exponential functions; they have                How are they different?
applications similar to that of the exponential functions; the graphing of log       How does the symbolic notation of quadratic transformations (shifts,
functions follows our predetermined rules of transformations for all parent            stretches, compressions) connect to the logarithmic graph?
functions                                                                            How are transformations of the logarithmic function similar to transformations
                                                                                       of the other parent functions? How are they different?
                                                                                     How does the function help to identify significant points to graph the
                                                                                       function?



Unit: Exponential Functions                                                                                            Unit Pacing: 7 days
Vocabulary:   asymptote, horizontal and vertical shifts, domain and range, logarithm, restricted domain, inverse functions
Resources: Holt, TEXTEAMS

Matrix #        Established Goals                      Established Goals                       Students Will Know…                  Students will be able to….
            TEKS Knowledge & Skill                TEKS Student Expectation
            2A.4: The student              2A.4A: identify and sketch graphs of          The relationship between the           Graph (without a calculator) the
            connects algebraic and         parent functions, including linear (f (x) =   exponential and logarithmic function   exponential and logarithmic parent
                                                                   2
            geometric representations      x), quadratic (f (x) = x ), exponential (f    graphs                                 function (with correct asymptotes
                                                   x
  262       of functions.                  (x) = a ), and logarithmic (f (x) = logax)    the asymptote of the exp and log       and intercepts)
                                           functions, absolute value of x (f (x) =       graphs and what they represent on
                                           |x|), square root of x (f (x) = x ), and      the graph
                                           reciprocal of x (f (x) = 1/x);
                                           2A.4B: extend parent functions with            The affects of “a” on the            Graph a logarithmic function, by
                                           parameters such as a in f(x) = a/x and          logarithmic graph                    hand, with a shift on the asymptote
  321
                                           describe the effects of the parameter          The affects of “h” & “k” on the      and x-intercept (horizontal & vertical)
                                           changes on the graph of parent                  horizontal & vertical shifts of      Identify the domain and range for a
                                           functions;                                      logarithmic functions                logarithmic graph that has been
                                                                                                                                transformed
                                           2A.4C: describe and analyze the                The relationship between the         Graph the inverse function given an
                                           relationship between a function and its         graph of an exponential and          exponential or log function
                                           inverse                                         logarithmic function                 Identify the domain and range for a
  327
                                                                                          The relationship between the         log or exp function and its inverse
                                                                                           domain and range of inverse
                                                                                           functions (exp & log)




                                                                                 Page 4 of 5
Course: Algebra 2                                          Austin ISD Curriculum Road Map                                                 2010 – 2011
                                                          th
                                                         4 Six week – January 4 – February 17 (31 days)

Matrix #      Established Goals                     Established Goals                     Students Will Know…                 Students will be able to….
           TEKS Knowledge & Skill              TEKS Student Expectation
           2A.11: The student            2A.11B: use the parent function to        -The affects of parameter changes      Graph a log function with parameter
           formulates equations and      investigate, describe, and predict the    (without a calculator)                 changes (without a calculator)
           inequalities based on         effects of parameter changes on the       - the limitations of domain and        Identify the domain and range of a
           exponential and               graphs of exponential and logarithmic     range on the log function (and its     transformed log function
  326      logarithmic functions, uses   functions, describe limitations on the    inverse)                               Restrict the domain to make a
           a variety of methods to       domain and range, and examine             - the definition of a restricted       function one-to-one and find its
           solve them, and analyzes      asymptotic behavior;                      domain                                 inverse
           the solutions in terms of                                               - the domain of a log function         - determine the reasonableness of a
           the situation                                                           (positive values of x for log x)       solution to exponential and log
                                         2A.11C: determine the reasonable          - the definition of a logarithm as     equations and inequalities
                                         domain and range values of exponential    related to exponents                   - solve log and exp equations &
                                         and logarithmic functions, as well as                                            inequalities using calculator and
  256                                    interpret and determine the                                                      algebraic methods
                                         reasonableness of solutions to                                                   - identify the relationship between
                                         exponential and logarithmic equations                                            logs and exponents
                                         and inequalities


                                                       Student Work Products/Assessment Evidence
                            Performance Tasks                                     Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student
                                                                                                     work samples, observations, etc.)
                                                                                  Quizzes, unit test, 6wks test, texteams: energy of earthquakes pg 166


                                                                      Learning Plan
Lesson/Activity/Module   Teacher Resource                Student Resource     Technology (Media, website, etc.)           Other              Assessment
Name
Inverse functions-       Holt 7-7, 7-8                                            Holt powerpoint 7.3
logarithms and           texteams: energy of
exponential functions    earthquakes pg 166;
& transformations        exploring inverseslogsexp




                                                                          Page 5 of 5

								
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