# ALG 2 pacing guide by xiaohuicaicai

VIEWS: 4 PAGES: 20

• pg 1
```									   Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary      Materials/
*teacher word          Resources
Student Learning Expectations (SLE)

1st Nineweeks
1. Enduring Understanding - A linear model can be used to represent relationships between data.
1a. Essential Question - How can a linear relationship be determined from a set of data?
DAP.6.AII.1                                        A. Find the equation and graph the regression      *draw a scatter plot                                     regression line
Find regression line for scatter plot, using       line for a scatterplot using appropriate           *use appropriate technology to calculate and graph the scatter plot
appropriate technology, and interpret the          technology.                                        regression line                                          correlation coefficient
correlation coefficient                            B. Interpret the correlation coefficient.          *use appropriate technology to calculate the correlation
coefficient and determine its significance

DAP.6.AII.2                                        Interpret and use the correlation coefficient to   *find the correlation coefficient using appropriate          correlation coefficient
Interpret and use the correlation coefficient to   assess the strength of the linear relationship     technology                                                   linear relationship
assess the strength of the linear relationship     between two variables.                             *interpret the correlation coefficient as it moves from -1
between two variables                                                                                 to 1

DAP.6.AII.4                                        Identify strengths and weaknesses of using         *use real-world data sets over a small interval to           extrapolate
Identify strengths and weaknesses of using         regression equations to approximate data.          calculate regression equation                                interval
regression equations to approximate data                                                              *approximate data using the regression equation              regression equation
*identify strengths and weaknesses of using the
Note: This SLE will be revisited later.                                                               regression to extrapolate (approximate) data

RF.1.AII.1                                         A. Determine, with and without appropriate         A.                                                           domain
Determine, with or without technology, the         technology, the domain and range of a relation     *know and use function notation                              range of function
domain and range of a relation defined by a        defined by a graph, a table of values, or a        *use a variety of mathematical notation to state the         relation
graph, a table of values, or a symbolic            symbolic equation, including those with            domain (i.e.: set-builder, interval, roster, sets, etc.)     function
equation including those with restricted           restricted domains.                                *evaluate functions for given values in their domain         set-builder notation
domains and whether a relation is a function       B. Determine whether a relation is a function.     *determine domain and range of a relation defined by a       interval notation
table (mapping) of values with and without technology        roster (set notation)
*determine domain and range of a relation defined by a       mapping
graph with and without technology                            function notation
*determine domain and range of a relation defined by a       evaluate
symbolic equation with and without technology
B.
*identify functions from mappings, tables or equations
*apply the vertical line test to graphs

rev. 5-2009                                                                                                                                                                                  1 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

RF.1.AII.9                                       Communicate real-world problems involving  *identify key information in a real-world problem                function
Apply the concepts of functions to real-world
1st Nineweeks (graphically, algebraically,
functions, graphically, algebraically,     *determine the format                                            reasonableness
situations                                       numerically and verbally.                         numerically or verbally) to represent the problem and its level of precision
solution
Note: This SLE will be revisited.                                                                  *evaluate the reasonableness of the solution
*communicate real-world problems graphically,
algebraically, numerically, and verbally
Note: Achieve includes solving literal equations and
solving problems that can be modeled using absolute
value, step, and other piece-wise defined functions.

1b. Essential Question - What are the effects of changing parameters on linear functions?
RF.1.AII.4                                       A. Recognize parent function (i.e.. y=x , y=x n   A.                                                        translation
Analyze and report, with and without             where n is a positive integer).                   *identify different parent functions                      reflection
appropriate technology, the effect of changing   B. Analyze and describe, with and without         B.                                                        coefficient
coefficients, exponents, and other parameters    appropriate technology, the effect of changing    *describe changes in slope and y-intercept from the       exponent
on functions and their graphs (linear,           coefficients, and other parameters on linear      parent graph                                              parameter
quadratic, and higher-degree polynomial)         functions and their graphs. (y=mx+b )             *describe changes in slope and y-intercept between two    parent function
C. Analyze and describe, with and without         linear functions                                          slope
Note: Only be concerned about linear             appropriate technology, the effect of changing    C.                                                        y-intercept
functions at this point in the curriculum.       coefficients, and other parameters on             *describe changes using the words translate, reflect,     translate
quadratic functions and their graphs. (y=a(x-     stretch or compress (shrink) including direction and      reflect
h) 2 + k )                                        units from the parent graph                               stretch
D. Analyze and describe, with and without         *describe changes using the words translate, reflect,     compress
appropriate technology, the effect of changing    stretch or compress (shrink) including direction and      transformation
coefficients, and other parameters on higher-     units between two quadratic functions                     linear functions
degree polynomial functions and their graphs.     D.                                                        quadratic functions
Note: Only be concerned about Parts A and         *describe changes using the words translate, reflect,     cubic functions
stretch or compress (shrink) including direction and      quartic functions
B with linear functions at this point in the
units from the parent graph                               higher-degree
curriculum.
*describe changes using the words translate, reflect,     polynomial functions
stretch or compress (shrink) including direction and
units between two higher-degree polynomial functions
Note: Achieve includes comparing to the parent graph
(linear, quadratic, square root, absolute value) as the
fundamental concept in this objective.

1c. Essential Question - How can the inverse of a linear function be determined?

rev. 5-2009                                                                                                                                                                          2 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary    Materials/
*teacher word        Resources
Student Learning Expectations (SLE)

RF.1.AII.3                                    A. Determine the inverse of a function.     A.                                                             inverse of a function
Determine the inverse of a function (Graph,   B. Graph, with and without appropriate
1st Nineweeks of an inverse and its notation f
*know the definition                                  -1
f -1 notation
with and without appropriate technology,      technology, functions and their inverses.    *determine the inverse of a function given a set of           exponential function
functions and their inverses)                                                              ordered pairs                                                 (Achieve)
*determine the inverse of a function algebraically            identity function
B.                                                            reflection
*know the identity function y=x and its graph                 Horizontal Line Test
*determine the inverse of a function graphically without      one-to-one
and with technology
Note: Achieve includes
-inverses which may not be functions (not one-to-one)
-explain why an inverse function would be only either
the positive or the negative part of the graph
-explain why the graphs of a function and its inverse
are reflections of each other over the line y=x
-show that when the inverse of a function is a function f -
1
(f(x))=x and f(f -1(x))=x
-inverses of exponential functions may be required
graphically but not in algebraic form

rev. 5-2009                                                                                                                                                                       3 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary      Materials/
*teacher word          Resources
Student Learning Expectations (SLE)

1st Nineweeks
2. Enduring Understanding - A function represents a unique relationship between a domain and range.
2a. Essential Question - How can special functions be represented graphically?
LEI.2.AII.1                                         A. Solve without and with appropriate            A.                                                        absolute value
Solve, with and without appropriate                 technology, absolute value equations and         *solve without appropriate technology absolute value      absolute value equation
technology, absolute value equations and            inequalities written in one variable and graph   equations written in one variable and graph solutions     inequalities
inequalities written in one or two variables, and   solutions.                                       *solve with appropriate technology absolute value         absolute value
graph solutions                                     B. Solve (graph), without and with appropriate   equations written in one variable and graph solutions     inequalities
technology, absolute value equations and         *solve without appropriate technology absolute value
inequalities written in two variables.           inequalities written in one variable and graph the
solution
*solve with appropriate technology absolute value
inequalities written in one variable and graph the
solution
B.
*solve (graph) without appropriate technology, absolute
value equations written in two variables
*solve (graph) with appropriate technology, absolute
value equations written in two variables
*solve (graph) without appropriate technology, absolute
value inequalities written in two variables
*solve (graph) with appropriate technology, absolute
value inequalities written in two variables

rev. 5-2009                                                                                                                                                                              4 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary        Materials/
*teacher word            Resources
Student Learning Expectations (SLE)

RF.1.AII.5                                     A. Graph, without and with technology,     A.                                                            piece-wise function
Graph, with and without appropriate            functions defined as piece-wise.
1st Nineweeks technology, graph functions with
*without appropriate                                          piece-wise function
technology, functions defined as piece-wise    B. Graph, without and with technology,         domain restrictions using open and closed circles         notation
and step                                       functions defined as step.                     *with appropriate technology, enter domain restrictions   step function
on the calculator                                         constant function
B.                                                        greatest integer function
*without appropriate technology, graph constant           greatest integer notation
functions
*without appropriate technology, evaluate expressions
using "greatest integer" notation
*without appropriate technology, create an appropriate
table of values and use the table to graph the step
function
*with appropriate technology, enter greatest integer
notation on the calculator
Note: Achieve includes writing an algebraic
representation for a given piece-wise defined function.

3. Enduring Understanding - Systems of linear equations and inequalities can be solved using multiple methods.
3a. Essential Question - What methods can be used to solve systems of linear equations and inequalities?
LEI.2.AII.2                                    Solve, without and with appropriate            *solve systems of linear equations in two variables       system of linear
Solve, with and without appropriate            technology, systems of linear equations with   graphically without appropriate technology                equations
technology, systems of linear equations with   two variables graphically and algebraically.   *solve systems of linear equations in two variables       solution set: Ø , (x, y) ,
two variables and graph the solution set                                                      graphically with appropriate technology                   or {(x,y)| y=mx+b}
*solve systems of linear equations in two variables       empty set
algebraically (i.e.. linear combination (elimination),
substitution, matrices) without appropriate technology
*determine the number of solutions

rev. 5-2009                                                                                                                                                                           5 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

LEI.2.AII.5                                                                                   A, B, C:
A. Apply linear equations and inequalities to                                                               linear programming
Apply, with or without technology, the             model real-world situations.
1st Nineweeksinformation
*identify the key                                                reasonableness
concepts of linear and absolute value              B. Apply absolute value equations and           *write the equations or inequalities to represent the
equations and inequalities and systems of          inequalities to model real-world situations.    situation algebraically and solve
linear equations and inequalities to model real-   C. Apply systems of linear equations and        *evaluate the reasonableness of the solution
world situations including linear programming      inequalities to model real-world situations,    Note: Achieve includes time/rate/distance, percentage
including linear programming.                   increase/decrease, ratio and proportion, mixture
problems, and break-even problems.

LEI.2.AII.3                                        A. Apply basic operations to matrices with      A. With and without appropriate technology:                 dimensions
Develop and apply, with and without                and without appropriate technology.             *add two matrices                                           scalar
appropriate technology, the basic operations       B. Find the inverse of a matrix with and        *subtract two matrices                                      associative
and properties of matrices (associative,           without appropriate technology.                 *multiply a matrix by a scalar                              commutative
commutative, identity, and inverse)                C. Investigate the properties (associative,     *multiply two matrices                                      identity
commutative, identity, and inverse) in          B.                                                          inverse of a matrix
relationship to matrices.                       *find the determinant of a matrix                           matrix
*find the inverse of a 2x2 matrix without appropriate       determinant
technology
*find the inverse of a 3x3 matrix with appropriate
technology
C.
*investigate with and without appropriate technology the
properties (associative, commutative, identity, and
inverse) in relationship to matrices

LEI.2.AII.4                                        A. Solve, systems of linear equations with      A.                                                          elimination
Solve, with and without appropriate                three variables using algebraic methods.        *solve systems of linear equations with three variables     substitution
technology, systems of linear equations with       B. Solve, with appropriate technology,          using algebraic methods (i.e.. elimination, substitution)   systems of equations
three variables using algebraic methods,           systems of linear equations with three          B.
including matrices                                 variables using matrices.                       *using appropriate technology, solve systems of linear
equations with three variables using matrices.
Note: Achieve suggests using systems of linear
equations limited to those with integer solutions and
small integral coefficients.

2nd Nineweeks
1. Enduring Understanding - Radical expressions and rational exponents represent a root of a quantity.
1a. Essential Question - How are radical expressions simplified?
rev. 5-2009                                                                                                                                                                           6 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary    Materials/
*teacher word        Resources
Student Learning Expectations (SLE)

Note: Be sure that
1st Nineweeks all computations are done with
• simplify radicals with different indices   different indices.
• rationalize denominators                      • solve equations that contain radicals or      *simplify radicals with different indices                rationalize
radical expressions                             solutions)                                      *rationalize denominators                                extraneous
expressions (check for extraneous solutions)
Note: Achieve includes the example:

x 2  6x  9         x  32     x3

1b. Essential Question - How can radical expressions be written and simplified using rational exponents?
PRF.4.AII.7                                     Convert between and among radical and           *convert the radical form of an algebraic expression to exponential form
Establish the relationship between radical      exponential forms of algebraic expressions.     its exponential form                                     (rational exponents)
expressions and expressions containing                                                          *convert the exponential form of an algebraic expression radical form
rational exponents                                                                              to its radical form
PRF.4.AII.8                                     Simplify variable expressions containing        *review laws of exponents                                variable expression
Simplify variable expressions containing        rational exponents using the laws of            *simplify variable expressions containing rational       laws of exponents
rational exponents using the laws of            exponents.                                      exponents using the laws of exponents
exponents

2. Enduring Understanding - A quadratic function is a second-degree polynomial represented graphically as a parabola.

2a. Essential Question - How are real, imaginary, and complex numbers related?
QEF.3.AII.2                                     Extend the number system to include the         *define the set of complex numbers                       conjugate
Extend the number system to include the         complex numbers.                                *find conjugates of complex numbers                      complex number
complex numbers                                 • define the set of complex numbers             *add, subtract, multiply, and divide complex numbers     pure imaginary numbers
• define the set of complex numbers             • add, subtract, multiply, and divide complex   *rationalize denominators                                "i"
• add, subtract, multiply, and divide complex   numbers                                         Note: Achieve Core includes "simplify powers of pure     rationalize
numbers                                         • rationalize denominators                      imaginary numbers (i.e. i5= i)"                          denominators
• rationalize denominators

rev. 5-2009                                                                                                                                                                       7 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary     Materials/
*teacher word         Resources
Student Learning Expectations (SLE)

QEF.3.AII.5                                       A. Develop and analyze, with and without    A.                                                              discriminate
Develop and analyze, with and without
1st Nineweeks with and without appropriate
*develop and analyze,
appropriate technology, quadratic relations by                                                              maximum value
appropriate technology, quadratic relations       graphing a parabolic relationship when given      technology, quadratic relations by graphing a quadratic   minimum value
• graph a parabolic relationship when given its   its equation.                                     relationship when given its equation (Note: this could    axis of symmetry
equation                                          B. Develop and analyze, with and without          include equations such as x=y2.)                          vertex
• write an equation when given its roots (zeros   appropriate technology, quadratic functions by    B.                                                        quadratic relations
or solutions) or graph                            writing an equation when given its roots (zeros   *develop and analyze, with and without appropriate        quadratic function
• determine the nature of the solutions           or solutions) or graph.                           technology, quadratic functions by writing an equation    roots
graphically and by evaluating the discriminate    C. Develop and analyze, with and without          when given its roots (zeros or solutions) or graph        zeros
• determine the maximum or minimum values         appropriate technology, quadratic functions by    C.                                                        solutions
and the axis of symmetry both graphically and     determining the nature of the solutions           *develop and analyze, with and without appropriate        nature of solutions
algebraically                                     graphically and by evaluating the discriminate.   technology, quadratic functions by determining the        parabolic relationship
D. Develop and analyze, with and without          nature (number and type) of the solutions graphically
appropriate technology, quadratic functions by    *know the discriminate as part of the quadratic formula
determining the maximum or minimum values         *develop and analyze, with and without appropriate
and the axis of symmetry both graphically and     technology, quadratic functions by determining the
algebraically.                                    nature (number and type) of the solutions by evaluating
the discriminate

D.
*develop and analyze, with and without appropriate
technology, quadratic functions by determining the
maximum or minimum values and the axis of symmetry
graphically
*develop and analyze, with and without appropriate
technology, quadratic functions by determining the
maximum or minimum values and the axis of symmetry
algebraically
Note: Achieve includes graphing the solution set of a
horizontal parabolas.

rev. 5-2009                                                                                                                                                                            8 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary        Materials/
*teacher word            Resources
Student Learning Expectations (SLE)

PRF.4.AII.2                                      With technology:
Analyze and sketch, with and without
A. Use appropriate            to:
1st Nineweeks technologyof a given polynomial
A. Analyze and sketch the graph of a given   *analyze and sketch the graph
polynomial function
end behavior
appropriate technology, the graph of a given     polynomial function.                             function                                                 multiplicity
polynomial function, determining the             B. Determine the characteristics of domain       *determine domain and range                              y-intercept
characteristics of domain and range,             and range, maximum and minimum points,           *determine maximum and minimum points                    symmetry
maximum and minimum points, end behavior,        end behavior, zeros, multiplicity of zeros, y-   *determine maximum and minimum values                    synthetic division
zeros, multiplicity of zeros, y-intercept, and   intercept, and symmetry.                         *distinguish between local (relative) and global         maximum point
symmetry                                         Without technology:                              (absolute) maximums and minimums                         maximum value
C. Determine domain, end behavior, zeros         *determine end behavior                                  maximum point
Note: This SLE will be revisited.                and multiplicity of zeros, y-intercept, and      *determine zeros and multiplicity of zeros               minimum value
symmetry.                                        *determine y-intercept                                   absolute/relative
*determine different types of symmetry                   maximum and
B. Without appropriate technology:                       minimums
*determine domain.                                       domain
*determine end behavior by using the leading coefficient range
and the degree of the polynomial.                        zeros
*determine zeros and multiplicity of zeros when
factorable to linear or quadratic factors.
*determine y-intercept.
*determine different types of symmetry.

RF.1.AII.5                                       A. Graph without and with technology,            A.                                                        piece-wise function
Graph, with and without appropriate              functions defined as piecewise.                  *without appropriate technology, graph functions with     piece-wise function
technology, functions defined as piece-wise      B. Graph without and with technology,            domain restrictions using open and closed circles         notation
and step                                         functions defined as step.                       *with appropriate technology, enter domain restrictions   step function
Note: At this point the emphasis is on Part      on the calculator                                         constant function
Note: At this point the emphasis is on           A.                                               B.                                                        greatest integer function
piece-wise functions.                                                                             *without appropriate technology, graph constant           greatest integer notation
functions
*without appropriate technology, evaluate expressions
using "greatest integer" notation
*without appropriate technology, create an appropriate
table of values and use the table to graph the step
function
*with appropriate technology, enter greatest integer
notation on the calculator
Note: Achieve includes writing an algebraic
representation for a given piece-wise defined function.

rev. 5-2009                                                                                                                                                                             9 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

RF.1.AII.4                                       A. Recognize parent function (i.e.. y=x , y=x n
A.
1st Nineweeks parent functions                                       translation
Analyze and report, with and without             where n is a positive integer).            *identify different                                            reflection
appropriate technology, the effect of changing   B. Analyze and describe, with and without         B.                                                      coefficient
coefficients, exponents, and other parameters    appropriate technology, the effect of changing    *describe changes in slope and y-intercept from the     exponent
on functions and their graphs (linear,           coefficients, and other parameters on linear      parent graph                                            parameter
quadratic, and higher degree polynomial)         functions and their graphs. (y=mx+b )             *describe changes in slope and y-intercept between two parent function
C. Analyze and describe, with and without         linear functions                                        slope
Note: At this point the emphasis is on           appropriate technology, the effect of changing    C.                                                      y-intercept
quadratics.                                      coefficients, and other parameters on             *describe changes using the words translate, reflect,   translate
quadratic functions and their graphs. (y=a(x-     stretch or compress (shrink) including direction and    reflect
h) 2 + k )                                        units from the parent graph                             stretch
D. Analyze and describe, with and without         *describe changes using the words translate, reflect,   compress
appropriate technology, the effect of changing    stretch or compress (shrink) including direction and    transformation
coefficients, and other parameters on higher-     units between two quadratic functions                   linear functions
degree polynomial functions and their graphs.     D.                                                      quadratic functions
Note: At this point the emphasis is on Parts      *describe changes using the words translate, reflect,   cubic functions
stretch or compress (shrink) including direction and    quartic functions
A and C with quadratic functions.
units from the parent graph                             higher-degree
*describe changes using the words translate, reflect,   polynomial functions
stretch or compress (shrink) including direction and
units between two higher degree polynomial functions
Note: Achieve includes comparing to the parent graph
(linear, quadratic, square root, absolute value) is the
fundamental concept in this objective.

rev. 5-2009                                                                                                                                                                      10 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary    Materials/
*teacher word        Resources
Student Learning Expectations (SLE)

RF.1.AII.3                                    A. Determine the inverse of a function.      A.                                                           inverse of a function
Determine the inverse of a function (Graph,   B. Graph, with and without appropriate
1st Nineweeks of an inverse and its notation f
*know the definition                                  -1
f -1 notation
with and without appropriate technology,      technology, functions and their inverses.     *determine the inverse of a function given a set of         exponential function
functions and their inverses)                                                               ordered pairs                                               (Achieve)
*determine the inverse of a function algebraically          identity function
Note: At this point the emphasis is on the                                                  B.                                                          reflection
inverse of a function. This SLE will be                                                     *know the identity function y=x and its graph               Horizontal Line Test
revisited in the 4th Nine Weeks.                                                            *determine the inverse of a function graphically without    one-to-one
and with appropriate technology
Note: Achieve includes
-Inverses which may not be functions (not one-to-one)
-Explain why an inverse function would be only either
the positive or the negative part of the graph
-Explain why the graphs of a function and its inverse
are reflections of each other over the line y=x
-Show that when the inverse of a function is a function f
-1
(f(x))=x and f(f -1(x))=x
-Inverses of exponential functions may be required
graphically but not in algebraic form

DAP.6.AII.3                                   Find the quadratic curve of best fit using    *draw a scatter plot                                        quadratic regression
Find the quadratic curve of best fit using    appropriate technology.                       *use appropriate technology to calculate the curve of       curve of best fit
appropriate technology                                                                      best fit                                                    scatter plot

DAP.6.AII.4                                   Identify strengths and weaknesses of using    *use real-world data sets over a small interval to          extrapolate
Identify strengths and weaknesses of using    regression equations to approximate data.     calculate regression equation                               interval
regression equations to approximate data                                                    *approximate data using the regression equation             regression equation
*identify strengths and weaknesses of using the
regression to extrapolate (approximate) data

rev. 5-2009                                                                                                                                                                    11 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary    Materials/
*teacher word        Resources
Student Learning Expectations (SLE)

1st Nineweeks
2b. Essential Question - How can various methods be used to solve quadratic equations?
QEF.3.AII.3                                     Analyze and solve quadratic equations with         *solve quadratic equations without appropriate           extracting the square
Analyze and solve quadratic equations, with     and without appropriate technology by              technology by graphing                                   root
and without appropriate technology, by          • factoring                                        *solve quadratic equations with appropriate technology   completing the square
• factoring                                     • graphing                                         by graphing                                              Quadratic Formula
• graphing                                      • extracting the square root (i.e.. The Square     *solve quadratic equations without appropriate           The Square Root
• extracting the square root                    Root Property)                                     technology by:                                           Property
• completing the square                         • completing the square                            - factoring                                              parabola
• using the quadratic formula                   • using the quadratic formula                      - extracting square roots
- completing the square
Note: Achieve includes quadratic equations involving

QEF.3.AII.4                                     A. Derive the quadratic formula.                   A.                                                       derive
Derive the quadratic formula and use it to      B. Use the quadratic formula to solve              *complete the square                                     quadratic formula
solve equations                                 equations.                                         *derive the quadratic formula
B.
*use the quadratic formula to solve equations

2c. Essential Question - How can quadratic functions be used to solve real-world problems?
QEF.3.AII.6                                     A. Apply the concepts of quadratic equations       *identify key information                                quadratic equation
Apply the concepts of quadratic equations and   and functions to model real-world situations by    *write an equation to represent the situation            reasonableness
functions to model real-world situations by     using appropriate technology when needed.          algebraically
using appropriate technology when needed        B. Communicate real-world problems                 *use the equation to find the unknown value
involving functions, graphically, algebraically,   *determine the reasonableness of the solution
numerically and verbally.

rev. 5-2009                                                                                                                                                                        12 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary       Materials/
*teacher word           Resources
Student Learning Expectations (SLE)

1st
3rd Nineweeks
1. Enduring Understanding - A relationship exists between a polynomial's factors, zeros, roots, and x-intercepts.
1a. Essential Question - How are a polynomial function and its factors related?
PRF.4.AII.1                                       Determine the factors of polynomials by           *review algebra I factoring techniques                     sum or difference of two
Determine the factors of polynomials by           • using factoring techniques including grouping   *factor polynomials by grouping                            cubes
• using factoring techniques including grouping   and the sum or difference of two cubes            *factor the sum or difference of two cubes                 synthetic division
and the sum or difference of two cubes            • using long division                             *apply the Rational Root (Zero) Theorem and analyze        polynomial
• using long division                             • using synthetic division                        results using technology                                   factor
• using synthetic division                                                                          *find factors using long division and synthetic division   Rational Root Theorem
Note: Achieve includes solving higher-order polynomial
equations

PRF.4.AII.3                                       Write the equation of a polynomial function       *determine a factor given a zero                           zero
Write the equation of a polynomial function       given its zeros.                                  *determine a zero given a factor                           polynomial function
given its roots (zeros)                                                                             *write the equation of a polynomial function given its     root
zeros                                                      factor
Note: include zeros of the form a+bi

1b. Essential Question - How can a graph be used to analyze a polynomial function?
PRF.4.AII.2                                       With technology:                                  A. Use appropriate technology to:                          polynomial function
Analyze and sketch, with and without              A. Analyze and sketch the graph of a given        *analyze and sketch the graph of a given polynomial        end behavior
appropriate technology, the graph of a given      polynomial function.                              function                                                   multiplicity
polynomial function, determining the              B. Determine the characteristics of domain        *determine domain and range                                y-intercept
characteristics of domain and range,              and range, maximum and minimum points,            *determine maximum and minimum points                      symmetry
maximum and minimum points, end behavior,         end behavior, zeros, multiplicity of zeros, y-    *determine maximum and minimum values                      synthetic division
zeros, multiplicity of zeros, y-intercept, and    intercept, and symmetry.                          *distinguish between local (relative) and global           maximum point
symmetry                                          Without technology:                               (absolute) maximums and minimums                           maximum value
C. Determine domain, end behavior, zeros          *determine end behavior                                    maximum point
and multiplicity of zeros, y-intercept, and       *determine zeros and multiplicity of zeros                 minimum value
symmetry.                                         *determine y-intercept                                     absolute/relative
*determine different types of symmetry                     maximum and
B. Without appropriate technology:                         minimums
*determine domain                                          domain
*determine end behavior by using the leading coefficient   range
and the degree of the polynomial                           zeros
*determine zeros and multiplicity of zeros when
factorable to linear or quadratic factors
*determine y-intercept
*determine different types of symmetry

rev. 5-2009                                                                                                                                                                              13 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

PRF.4.AII.4                                      Identify from a list of possible equations the
Identify the equation of a polynomial function
*use finite (first,
1st Nineweekssecond, third, etc.) differences to
equation of a polynomial function given its  identify linear, quadratic, or higher-order polynomial
finite differences
first differences
given its graph or table                         graph or table.                                  functions from a table                                    second differences
*use a graph to determine an equation of a polynomial     polynomial function
function                                                  linear
RF.1.AII.4                                   A. Recognize parent function (i.e.. y=x,             A.                                                        translation
Analyze and report, with and without         y=x n where n is a positive integer).                *identify different parent functions                      reflection
appropriate technology, the effect of changing
B. Analyze and describe, with and without            B.                                                        coefficient
coefficients, exponents, and other parametersappropriate technology, the effect of changing       *describe changes in slope and y-intercept from the       exponent
on functions and their graphs (linear,       coefficients, and other parameters on linear         parent graph                                              parameter
quadratic, and higher degree polynomial)     functions and their graphs. (y=mx+b )                *describe changes in slope and y-intercept between two    parent function
C. Analyze and describe, with and without            linear functions                                          slope
Note: The emphasis is on higher-degree       appropriate technology, the effect of changing       C.                                                        y-intercept
polynomials at this point in the curriculum. coefficients, and other parameters on                *describe changes using the words translate, reflect,     translate
quadratic functions and their graphs. (y=a(x-        stretch or compress (shrink) including direction and      reflect
units from the parent graph                               stretch
h) 2 + k )
*describe changes using the words translate, reflect,     compress
D. Analyze and describe, with and without
stretch or compress (shrink) including direction and      transformation
appropriate technology, the effect of
units between two quadratic functions                     linear functions
changing coefficients, and other
parameters on higher degree polynomial
*describe changes using the words translate, reflect,     cubic functions
functions and their graphs.
stretch or compress (shrink) including direction and      quartic functions
Note: The emphasis is on parts A and D at
units from the parent graph                               higher-degree
this point with higher-degree polynomial             *describe changes using the words translate, reflect,     polynomial functions
functions.                                           stretch or compress (shrink) including direction and
units between two higher-degree polynomial functions
Note: Achieve includes comparing to the parent graph
(linear, quadratic, square root, absolute value) is the
fundamental concept in this objective.

rev. 5-2009                                                                                                                                                                       14 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

1st Nineweeks
1c. Essential Question - How can polynomial function be used to solve real-world problems?
RF.1.AII.9                                      Communicate real world problems involving         *identify key information in a real-world problem         function
Apply the concepts of functions to real-world   functions, graphically, algebraically,            *determine the format (graphically, algebraically,        reasonableness
situations                                      numerically and verbally.                         numerically or verbally) to represent the problem and its level of precision
solution
*evaluate the reasonableness of the solution
*communicate real-world problems graphically,
algebraically, numerically, and verbally
Note: Achieve includes solving literal equations and
solving problems that can be modeled using absolute
value, step, and other piece-wise defined functions.

2. Enduring Understanding - Mathematical operations can be applied to functions.
2a. Essential Question - How can mathematical operations be applied to functions?
RF.1.AII.2                                      A. Evaluate functions.                            A.                                                        domain restrictions
Evaluate, add, subtract, multiply, and divide   B. Add, subtract, multiply and divide functions   *know and use function notation                           range restrictions
functions and give appropriate domain and       and give appropriate domain and range             B.                                                        function
range restrictions                              restrictions.                                     *combine functions by adding, subtracting, or             function notation
multiplying (i.e. polynomials)                            composition
*express division of two polynomials as a quotient and
include domain restrictions when appropriate
Note: Achieve includes composition of two functions.

rev. 5-2009                                                                                                                                                                        15 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

1st of polynomials.
3. Enduring Understanding - A rational function is a ratio Nineweeks
3a. Essential Question - How do you perform operations on rational expressions?
PRF.4.AII.6                                        A. Simplify rational expressions                   A.                                                       rational expression
Simplify, add, subtract, multiply, and divide      B. Add, subtract, multiply, and divide rational    *simplify rational expressions                           complex fractions
with rational expressions                          expressions                                        B.
*add and subtract rational expressions with common
denominators
*add and subtract rational expressions with unlike
denominators
*multiply and divide rational expressions (including
complex fractions)
Note: Achieve includes solving rational equations, and
solving problems that can be modeled with rational
functions.

3b. Essential Question - What are the characteristics of a rational function?
PRF.4.AII.5                                        Identify the characteristics of graphs of power    *graph power function                                    power function
Identify the characteristics of graphs of power    functions of the form f(x) = ax n , for negative   *examine end behavior of a power function                integral values
functions of the form f(x) = ax n , for negative   integral values of n , including domain, range,    *examine behavior of the function as x approaches zero   end behavior
integral values of n, including domain, range,     end behavior, and behavior at x = 0, and           from the left and right sides of the graph               domain
end behavior, and behavior at x = 0, and           compare these characteristics to the graphs of     *determine vertical and horizontal asymptotes            range
compare these characteristics to the graphs of     related positive integral power functions.         Note: Achieve includes rational functions with linear,   asymptote
related positive integral power functions                                                             quadratic, or monomial denominators and also graph
rational functions.

rev. 5-2009                                                                                                                                                                          16 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

1st
4th Nineweeks
1. Enduring Understanding - Exponential and logarithmic functions model extreme growth or decay.
1a. Essential Question - How do exponential relationships model rapid change?
ELF.5.AII.1                                   Recognize the graphs of exponential functions *identify exponential growth graphs                            exponential functions
Recognize the graphs of exponential functions distinguishing between growth and decay.      *identify exponential decay graphs                             growth
distinguishing between growth and decay                                                                                                                    decay

ELF.5.AII.2                                    A. Graph exponential functions without and        A.                                                        domain
Graph exponential functions and identify key   with technology.                                  *graph exponential functions without appropriate          intercepts
characteristics: domain, range, intercepts,    B. Identify key characteristics of exponential    technology                                                asymptotes
asymptotes, and end behavior                   functions, including domain, range, intercepts,   *graph exponential functions with appropriate             end behavior
asymptotes, and end behavior, without and         technology                                                range of functions
with technology.                                  B.
*identify key characteristics of exponential functions,
including domain, range, intercepts, asymptotes, and
end behavior, without appropriate technology
*identify key characteristics of exponential functions,
including domain, range, intercepts, asymptotes, and
end behavior, with appropriate technology

ELF.5.AII.3                                    A. Identify the effect that changes in the        A.                                                         parameters
Identify the effect that changes in the        parameters of the base have on the graph of       *identify an exponential function                          exponential function
parameters of the base have on the graph of    the exponential function without technology.      *identify the effect that changes in the parameters of the base
the exponential function                       B. Identify the effect that changes in the        base have on the graph of the exponential function
parameters of the base have on the graph of       without appropriate technology
the exponential function with technology.         B.
*identify the effect that changes in the parameters of the
base have on the graph of the exponential function with
appropriate technology
Note: Achieve includes explain or illustrate the effect
that changes in a parameter (a or c) or the base (b)
have on the graph of the exponential function f(x) = abx
+ c.

rev. 5-2009                                                                                                                                                                        17 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary   Materials/
*teacher word       Resources
Student Learning Expectations (SLE)

ELF.5.AII.4                                A. Recognize problems that can be modeled A.                                                              Change-of-Base
Recognize and solve problems that can be   using exponential functions.
1st Nineweeks that can be modeled using
*recognize problems                                             Formula
modeled using exponential functions        B. Solve problems that can be modeled using     exponential functions                                     logarithm
exponential functions.                          B.                                                        exponential function
C. Use technology to approximate solutions to   *solve exponential equations using logarithms             "e"
exponential equations.                          *apply the Change-of-Base Formula to approximate
solutions to exponential equations
*represent a real world problem using an exponential
equation and solve
C.
*use technology to approximate solutions to exponential
equations
Note: Achieve includes base e.

rev. 5-2009                                                                                                                                                                 18 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary    Materials/
*teacher word        Resources
Student Learning Expectations (SLE)

1st Nineweeks
1b. Essential Question - How can logarithmic functions be used to determine an unknown exponent?
RF.1.AII.3                                      A. Determine the inverse of a function.         A.                                                          inverse of a function
Determine the inverse of a function (Graph,     B. Graph, with and without appropriate          *know the definition of an inverse and its notation f -1    f -1 notation
with and without appropriate technology,        technology, functions and their inverses.       *determine the inverse of a function given a set of         exponential function
functions and their inverses)                                                                   ordered pairs                                               (Achieve)
*determine the inverse of a function algebraically          identity function
Note: This SLE was introduced in the 2nd                                                        B.                                                          reflection
Nine Weeks.                                                                                     *know the identity function y=x and its graph               Horizontal Line Test
*determine the inverse of a function graphically with and one-to-one
without appropriate technology
Note: Achieve includes
-inverses which may not be functions (not one-to-one)
-explain why an inverse function would be only either
the positive or the negative part of the graph
-explain why the graphs of a function and its inverse
are reflections of each other over the line y=x
-show that when the inverse of a function is a function f -
1
(f(x))=x and f(f -1(x))=x
-inverses of exponential functions may be required
graphically but not in algebraic form

ELF.5.AII.5                                    Establish the relationship between exponential *establish the relationship between exponential and          logarithmic functions
Establish the relationship between exponential and logarithmic functions without and with     logarithmic functions with and without appropriate           exponential functions
and logarithmic functions                      technology.                                    technology
*use the definition of a logarithm to convert between
exponential and logarithmic form
*find the inverse function of a given exponential or
logarithmic function
ELF.5.AII.6                                     Evaluate simple logarithms using the definition *evaluate simple logarithms using the definition (i.e. log logarithm
Evaluate simple logarithms using the definition (i.e. log 3 81 )                                3 81 )                                                     natural logarithm
(Ex. log 3 81 )                                                                                                                                            (Achieve)

ELF.5.AII.7                                     A. Use properties of logarithms to expand       *use properties of logarithms to expand logarithmic        expand
Use properties of logarithms to manipulate      logarithmic expressions.                        expressions                                                condense
logarithmic expressions                         B. Use properties to condense logarithmic       *use properties to condense logarithmic expressions
expressions.

rev. 5-2009                                                                                                                                                                        19 of 20
Arkansas Algebra II
Arch Ford/Northwest Arkansas Instructional Alignment
Algebra II
AR Department of Education
Essential Vocabulary     Materials/
*teacher word         Resources
Student Learning Expectations (SLE)

DAP.6.AII.5                                       A. Compute measures of spread (range,       A.                                                                 range of data
Compute and explain measures of spread
1st Nineweeks of spread (range, percentiles,
percentiles, variance, and standard deviation).
*compute measures
σ
percentiles
σ
(range, percentiles, variance, standard           B. Explain measures of spread (range,             variance, and standard deviation)                            variance 2, s2
deviation)                                        percentiles, variance, and standard deviation).   B.                                                           standard deviation , s
*explain measures of spread (range, percentiles,             mean µ , X- bar
variance, and standard deviation)                            measures of spread

DAP.6.AII.6                                       Describe the characteristics of a Gaussian        *sketch a Gaussian normal distribution                       Gaussian normal
Describe the characteristics of a Gaussian        normal distribution.                              *show the symmetry of the distribution                       distribution
normal distribution                                                                                 *locate the mean of the distribution                         standard deviation
*find the percent of data within one, two and three          distribution
standard deviations from the mean                            symmetry
mean

2. Enduring Understanding - Periodic functions can be used to describe natural relations.
2a. Essential Question - How can sine or cosine model specific phenomena such as frequency or amplitude?
RF.1.AII.6                                   Recognize periodic phenomena (sine or                  *given a graph determine if the graph exhibits periodic      periodic phenomena
Recognize periodic phenomena (sine or        cosine functions such as sound waves, length           behavior                                                     circular motion
cosine functions such as sound waves, length of daylight, circular motion)                          *given real-world situations (i.e.. sound waves, length of   sine function
of daylight, circular motion)                                                                       daylight, circular motion) determine if periodic behavior    cosine function
is displayed
RF.1.AII.7                                        Investigate and identify key characteristics of *investigate periodic functions                                period
Investigate and identify key characteristics of   periodic functions such as period, amplitude, *know and identify period, amplitude, maximum, and               amplitude
period functions and their graphs (period,        maximum and minimum from a graph or table. minimum from a graph or table of a periodic function                maximum
amplitude, maximum, and minimum)                                                                                                                                 minimum
periodic function

RF.1.AII.8                                        Apply frequency and amplitude to solve            *know and identify frequency and amplitude from a table frequency
Use basic properties of frequency and             problems that model real-world phenomena          of values or graph                                      amplitude
amplitude to solve problems                       (i.e. involving sound waves, tides,               *apply frequency and amplitude to solve problems
temperature, length of daylight, etc.)

rev. 5-2009                                                                                                                                                                              20 of 20

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