# Deriving Continuous Compound Interest Formula Secondary Mathematics Curriculum

Document Sample

```					   Secondary Mathematics Curriculum Map                                                                                                                                                  1
Algebra II
Curriculum Map -- Algebra II -- Mathematics
First Quarter

ABSOLUTE VALUE AND INEQUALITIES
1. Essential Question: How can absolute value equations represent linear equations and inequalities?
1. Enduring                          Skills                         Objective(s)                                                     Learning Plan
Understanding:                                                                           Assessment                                         Instructional   Materials/         Essential
(Student Learning Expectations)                                                 Connection to Achieve Standards
Linear functions can                                                                                                                            Strategies    Resources         Vocabulary
be used to model LEI.2.AII.1                                      *I will solve linear                                                                     1.6, 1.7, 2.6,   absolute value
constant rates of Solve, with and without appropriate            absolute value                                                                           2.7, 2.8, and    equations,
change.       technology, absolute value equations and equations with one                                                                            supplement       inequalities
inequalities written in one or two variables, unknown and then
and graph solutions.                          graph that solution.
*I will solve absolute
value inequalities
with one or two
unknowns and then
graph that solution.

FUNCTIONS AND RELATIONS
2. Essential Question: How can linear relationships be determined?
2. Enduring                          Skills                                                                                      Learning Plan
Understanding:                                                    Objective(s)       Assessment                                         Instructional   Materials/             Essential
(Student Learning Expectations)                                            Connection to Achieve Standards
Linear functions can                                                                                                                        Strategies    Resources             Vocabulary
be used to model RF.1.AII.1                                   *I will determine if a                                                                   2.1                  domain, range,
constant rates of Determine, with or without technology, the relation is a function.                                                                                       relation, function
change.       domain and range of a relation defined by *I will determine
a graph, a table of values, or a symbolic domain and range of
equation including those with restricted  a relation from a
domains and whether a relation is a       graph, from a table of
function.                                 values, or an
equation.
*I will determine
domain and range of
a relation from a
graph, from a table,
or values, or an
equation with
restrictions.

07-15-10                                                                                 1
Secondary Mathematics Curriculum Map                                                                                 2
Algebra II
(continued)    RF.1.AII.4                                *I will analyze the          2.2, 2.3, 2.4   coefficients,
2. Enduring        Analyze and report, with and without      effect of changing                           translation,
Understanding:       appropriate technology, the effect of     coefficients,                                transformation,
Linear functions can   changing coefficients, exponents, and     exponents, and other                         reflection
be used to model      other parameters on functions and their   parameters on a
constant rates of    graphs                                    quadratic function
change.                                                   and its graph with or
without a calculator.
*I will report the end
effect of changing
coefficients,
exponents, and other
parameters of a
and its graph, with or
without a calculator

07-15-10                                                                             2
Secondary Mathematics Curriculum Map                                                                                                                             3
Algebra II
(continued) 2.      RF.1.AII.5                                    *I will create graphs          A.                                            2.7   piece-wise
Enduring         Graph, with and without appropriate           of piecewise-defined           *without appropriate technology, graph              function, step
Understanding:       technology, functions defined as piece-       functions with and             functions with domain restrictions using            function
Linear functions can   wise and step                                 without appropriate            open and closed circles
be used to model                                                    technology.                    *with appropriate technology, enter domain
constant rates of                                                                                 restrictions on the calculator
change.                                                                                      B.
*without appropriate technology, graph
constant 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.

DAP.6.AII.1                                   *I will find the line of                                                     2.5   regression line,
Find regressoin line for scatterplot, using   regression for scatter                                                             scatter plot,
appropriate technology, and interpret the     plots using a                                                                      correlation
correlation coefficient                       graphing calculator.                                                               coefficient
*I will find and
interpret the
correlation coefficient
of a scatter plot using
a graphing calculator.

DAP.6.AII.4                                *I will apply data                                                              2.5   regression
Identify strengths and weaknesses of using analysis and                                                                          equations
regression equations to approximate        probability to identify
strengths and
weaknesses of
regression equations
and to approximate
data.

07-15-10                                                                                   3
Secondary Mathematics Curriculum Map                                                                                                                                                      4
Algebra II
(continued)    DAP.6.AII.2                                     *I will apply the                                                                      2.5               correlation
2. Enduring        Interpret and use the correlation coefficient   correlation coefficient                                                                                  coefficient
Understanding:       to assess the strength of the linear            to assess the
Linear functions can   relationship between two variables.             strength of the linear
be used to model                                                      relationship between
constant rates of                                                    two variables.
change.

LINEAR EQUATIONS AND INEQUALITIES
3. Essential Question: How can matrices be used to solve real-world linear relationships?
3. Enduring                         Skills                                                                                              Learning Plan
Understanding:                                                   Objective(s)       Assessment                                                Instructional   Materials/          Essential
(Student Learning Expectations)                                                  Connection to Achieve Standards
Matrices can be                                                                                                                                 Strategies    Resources          Vocabulary
used to model linear LEI.2.AII.3                              *I will develop linear                                                                          4.1, 4.2, 4.4     dimensions
relationships     Develop and apply, with and without      equations and apply                                                                                               scalar
appropriate technology, the basic        basic operations and                                                                                              associative
operations and properties of matrices    properties of                                                                                                     commutative
(associative, commutative, identity, and matrices such as                                                                                                  identity
inverse)                                 associative,                                                                                                      inverse of a
commutative,                                                                                                      matrix
identity, and inverse                                                                                             matrix
with and without                                                                                                  determinant
appropriate
technology.

LEI.2.AII.4                                     *I will solve a system        Note: Achieve suggests using systems of                  3.6, 4.5, (3.5,   elimination
Solve, with and without appropriate             of equations with             linear equations limited to those with                   4.3 optional)     substitution
technology, systems of linear equations         three variables using         integer solutions and small integral                                       systems of
with three variables using algebraic            either algebraic              coefficients.                                                              equations
methods, including matrices                     methods or using
matrices

07-15-10                                                                                    4
Secondary Mathematics Curriculum Map                                                                                                                                                 5
Algebra II
FUNCTIONS AND INVERSE FUNCTIONS
4. Essential Question: How are domain and range related in functions?
4. Enduring                       Skills                                                                                             Learning Plan
Understanding:                                                 Objective(s)         Assessment                                              Instructional   Materials/        Essential
(Student Learning Expectations)                                            Connection to Achieve Standards
Functions can be                                                                                                                              Strategies    Resources        Vocabulary
used to model real RF.1.AII.9                              *I will apply the                    Note: Achieve includes solving literal                     continual        functions
world situations. Apply the concepts of functions to real concepts of functions                equations and solving problems that can                    application
world situations.                       to situations in the                 be modeled using absolute value, step,
real world.                          and other piece-wise defined functions.

SYSTEMS OF LINEAR EQUATIONS
5. Enduring      5. Essential Question: How can systems of linear equations and inequalities be solved?
Understanding:
Skills                                                                                            Learning Plan
Linear functions can
be used to model                                                    Objective(s)      Assessment                                              Instructional   Materials/      Essential
(Student Learning Expectations)                                                 Connection to Achieve Standards
constant rates of                                                                                                                              Strategies    Resources      Vocabulary
change.       LEI.2.AII.2                                *I will solve a system                                                                       3.1, 3.2       system of
Solve, with and without appropriate        of equations with two                                                                                       equations
technology, systems of linear equations    variables with or
with two variables and graph the solution. without using a
graphing calculator.
*I will graph a system
of equations with two
variables with or
without using a
graphing calculator.

LEI.2.AII.4                               *I will solve a system               Note: Achieve suggests using systems of                  3.6             system of
Solve, with and without appropriate       of equations with                    linear equations limited to those with                                   equations
technology, systems of linear equations   three variables using                integer solutions and small integral
with three variables using algebraic      either algebraic                     coefficients.
methods.                                  methods or using
matrices

07-15-10                                                                                5
Secondary Mathematics Curriculum Map                                                                                                                                                   6
Algebra II
LINEAR PROGRAMMING
6. Enduring      6. Essential Question: How can linear programming problems model real world situations?
Understanding:
QEF,                                                                                               Learning Plan
Linear inequalities
can be used to                                                     Objective(s)       Assessment                                              Instructional   Materials/        Essential
develop linear                                                                                                                                  Strategies    Resources        Vocabulary
programming models
LEI.2.AII.5                                *I will apply systems                Note: Achieve includes time/rate/distance,                1.6, 2.6, 3.3,   linear equations,
Apply, with or without technology, the     of linear equations,                 percentage increase/decrease, ratio and                   3.4              absolute value
concepts of linear and absolute value      absolute value and                   proportion, mixture problems, and break-                                   equations,
equations and inequalities and systems of inequalities for                      even problems.                                                             inequalities,
linear equations and inequalities to model modeling real world                                                                                             linear
real world situations including linear     situations including                                                                                            programming
programming .                              linear programming
with and without
technology.

07-15-10                                                                                  6
Secondary Mathematics Curriculum Map                                                                                                                                              7
Algebra II
Curriculum Map -- Algebra II -- Mathematics
Second Quarter
MATRICES
7. Enduring       7. Essential Question- How are the properties of matrices applied?
Understanding:
Skills                                                                                        Learning Plan
Matrices can be
used in problem                                                   Objective(s)          Assessment                                      Instructional     Materials/        Essential
(Student Learning Expectations)                                              Connection to Achieve Standards
solving.                                                                                                                              Strategies      Resources        Vocabulary
LEI.2.AII.3                                *I will create a matrix                                                                   4.1, 4.2, 4.4   Matrices,
Develop and apply, with and without        from real world data                                                                                      dimensions,
appropriate technology, the basic          and apply the basic                                                                                       scalar,
operations and properties of matrices      operations and                                                                                            associative,
(associative, commutative, identity, and   properties to it.                                                                                         commutative,
inverse)                                                                                                                                             identify, inverse
of a matrix,
determinant
SYSTEMS OF LINEAR EQUATIONS
8. Enduring     8. Essential Question- How can systems of linear equations be solved?
Understanding:
Linear systems of                     Skills                                                                                       Learning Plan
three variables can                                                   Objective(s)      Assessment                                       Instructional     Materials/       Essential
be used to develop        (Student Learning Expectations)                                             Connection to Achieve Standards
Strategies      Resources       Vocabulary
quadratic     LEI.2.All.4 Solve, with and without          *I will solve a system                                                                  3.6, 4.5,       Systems of
relationships.   appropriate technology, systems of linear of equations with                                                                          optional 3.5    equations
equations with three variables (coefficients three variables using                                                                   and 4.3
of a quadratic y=ax²+bx+ c) using algebraic either algebraic
methods, including matrices.                 methods or using
matrices

07-15-10                                                                                   7
Secondary Mathematics Curriculum Map                                                                                                                                            8
Algebra II
FUNCTIONS, RELATIONS, AND EQUATIONS
9. Enduring      9. Essential Question- How can quadratic equations and inequalities be solved and represented graphically?
Understanding:
can be represented                                               Objective(s)     Assessment                                            Instructional   Materials/       Essential
(Student Learning Expectations)                                           Connection to Achieve Standards
graphically as a                                                                                                                        Strategies    Resources       Vocabulary
parabola.      RF.1.AII.4                              *I will analyze the                                                                       5.1             Coefficients,
Analyze and report, with and without    effect of changing                                                                                        Exponents,
appropriate technology, the effect of   coefficients,                                                                                             Quadratic
changing coefficients, exponents, and   exponents, and other
other parameters on functions and their parameters on a
and its graph with or
without a calculator.

Analyze and solve quadratic equations with   quadratic equations             without appropriate technology by                    5.5, 5.6         equations,
and without appropriate technology by        and inequalities with           graphing. Solve quadratic                                             Completing the
• factoring                                  and without                     equations/inequalities with appropriate                               square,
• extracting the square root                 technology, by                  equations by : Factoring, extracting square                           formula,
• completing the square                      solving using                   roots, completing the square, using the                               translate,
• using the quadratic formula                appropriate methods.            quadratic formula. Note: Achieve                                      reflects, stretch ,
inequalities.

07-15-10                                                                               8
Secondary Mathematics Curriculum Map                                                                                     9
Algebra II
(continued)     QEF.3.AII.5                                   *I will analyze and          5.1, 5.6,5.7,   Quadratic
9. Enduring        Develop and analyze, with and without         develop quadratic            5.8, and page   relations,
Understanding:       appropriate technology, quadratic relations   relations with or            271             Parabolic
Quadratic functions   • graph a parabolic relationship when given   without technology.                          relationship,
can be represented    its equation                                  *I will graph a                              Discriminant,
graphically as a    • write an equation when given its roots      parabolic relationship                       Axis of
parabola.        (zeros or solutions) or graph                 when given its                               symmetry
• determine the nature of the solutions       equation with or
graphically and by evaluating the             without technology.
discriminant                                  *I will write a
• determine the maximum or minimum            quadratic equation
values and the axis of symmetry both          given its roots of
graphically and algebraically                 graph with or without
technology.
*I will determine the
equations graphically
with or without
technology.
*I will determine the
equations solutions
by evaluating the
discriminant with or
without technology.
*I will determine the
maximum and
minimum values of
with or without
technology.
*I will determine the
axis of symmetry of
both graphically and
algebraically with or
without technology.

07-15-10                                                                                 9
Secondary Mathematics Curriculum Map                                                                                                                                     10
Algebra II
(continued)     RF.1.AII.1                                     *I will determine if a          A.                                               Supplement   Vertical Line
9. Enduring        Determine, with or without technology, the     relation is a function.         *know and use function notation                               test, mapping,
Understanding:       domain and range of a relation defined by      *I will determine               *use a variety of mathematical notation to                    domain, range
Quadratic functions   a graph, a table of values, or a symbolic      domain and range of             state the domain (i.e.: set-builder, interval,
can be represented    equation including those with restricted       a relation from a               roster, sets, etc.)
graphically as a    domains and whether a relation is a            graph, from a table of          *evaluate functions for given values in their
parabola.        function                                       values, or an                   domain
equation.                       *determine domain and range of a relation
*I will determine               defined by a table (mapping) of values with
domain and range of             and without technology
a relation from a               *determine domain and range of a relation
graph, from a table,            defined by a graph with and without
or values, or an                technology
equation with                   *determine domain and range of a relation
defined by a symbolic equation with and
without technology
B.
*identify functions from mappings, tables or
equations
*apply the vertical line test to graphs

QEF.3.AII.2                                    *I will extend the              *define the set of complex numbers                     5.4    Complex
Extend the number system to include the        number system to                *find conjugates of complex numbers                           numbers ,
complex numbers                                include the complex             *add, subtract, multiply, and divide                          Rationalize
• define the set of complex numbers            numbers.                        complex numbers                                               denominator
• add, subtract, multiply, and divide          *I will perform                 *rationalize denominators
complex numbers                                operations of                   Note: Achieve Core includes "simplify
• rationalize denominators                     addition, subtraction,          powers of pure imaginary numbers (i.e. i5=
multiplication, and             i)"
division using
complex numbers.
*I will rationalize the
denominator of
complex numbers.

QEF.3.AII.6                                    I will apply the                                                                 5.8          Quadratic
and functions to model real world situations   functions to model                                                                            Quadratic
by using appropriate technology when           situations of the real                                                                        functions,
needed                                         world using                                                                                   conjugate, pure
appropriate                                                                                   imaginary
technology when                                                                               number
needed.
DAP.6.AII.3                                    *I will use technology                                                           5.8          Quadratic curve
Find the quadratic curve of best fit using     to find the line of best                                                                      of best fit,
appropriate technology                         fit for quadratic                                                                             scatter plot
equations.

07-15-10                                                                                    10
Secondary Mathematics Curriculum Map                                                                                                                                  11
Algebra II
9. Enduring      Derive the quadratic formula and use it to   equations and                                                                Supplements   formula
Understanding: solve equations                                   functions by deriving
can be represented                                                and using it to solve
graphically as a                                                equations.
parabola. I will
perform operations
subtraction,
multiplication, and
division using
complex numbers.

RF.1.AII.9                                   *I will apply the                                                            continual     Functions
Apply the concepts of functions to real      concepts of functions                                                        application
world situations                             to situations in the
real world.

RF.1.AII.5                                   *I will graph                  Note: Achieve includes writing an             Supplement    piece-wise
Graph, with and without appropriate          piecewise functions            algebraic representation for a given piece-                 function
technology, functions defined as piece-      with or without a              wise defined function.
wise and step                                graphing calculator.
*I will graph step
functions with or
without graphing
calculators

07-15-10                                                                                11
Secondary Mathematics Curriculum Map                                                                                                                                                  12
Algebra II
Curriculum Map -- Algebra II -- Mathematics
Third Quarter

RATIONAL EXPONENTS
13. Enduring       13. Essential Question- How can expressions with rational exponents be simplified?
Understanding:
Rational exponents                      Skills                                                                                      Learning Plan
represent the root of                                               Objective(s)     Assessment                                           Instructional   Materials/                Essential
(Student Learning Expectations)                                           Connection to Achieve Standards
a quantity.                                                                                                                            Strategies    Resources                Vocabulary
PRF.4.AII.8                              *I will analyze, then                                                                    6.1                      Rational
Simplify variable expressions containing simplify, variable                                                                                                exponents
rational exponents using the laws of     expressions
exponents                                containing rational
exponents using the
laws of exponents.

POWER FUNCTIONS
14. Enduring      14. Essential Question- How do the characteristics of positive and negative power functions relate to each other?
Understanding:
Relationships are                        Skills                                                                                             Learning Plan
present in                                                        Objective(s)      Assessment                                              Instructional     Materials/       Essential
(Student Learning Expectations)                                              Connection to Achieve Standards
polynomial functions                                                                                                                                Strategies      Resources       Vocabulary
between factors, root PRF.4.AII.5                                  *I will identify the              Note: Achieve includes rational functions                    6.2,           Power function
zeros and        Identify the characteristics of graphs of    characteristics of the            with linear, quadratic, or monomial                          Supplement     integral value
intercepts.       power functions of the form f(x) = ax^n, for positive and negative             denominators and also graph rational                         (negative      Domain,
negative integral values of n, including     integral values of                functions.                                                   exponents)     Range,
domain, range, end behavior, and behavior graphs of power                                                                                                  End behavior
at x = 0, and compare these characteristics functions with the
to the graphs of related positive integral   form f(x) = ax^n.
power functions                              *I will analyze the
characteristics of the
positive and negative
integral values of
power functions by
comparing domain,
range, end behavior
and behavior at
x = 0.

07-15-10                                                                                  12
Secondary Mathematics Curriculum Map                                                                                                                                                    13
Algebra II
POLYNOMIAL FUNCTIONS
15. Enduring         15. Essential Question- How are the factors of a polynomial function related?
Understanding:                            Skills                                                                                           Learning Plan
Relationships are                                                    Objective(s)        Assessment                                             Instructional   Materials/         Essential
present in               (Student Learning Expectations)                                            Connection to Achieve Standards
Strategies    Resources         Vocabulary
polynomial functions    PRF.4.AII.1                               *I will apply factoring             Note: Achieve includes solving higher-                    6.3, 6.4, 6.5    Difference of
between factors, root   Determine the factors of polynomials by   techniques to                       order polynomial equations                                                 cubes,
zeros and intercepts.   • using factoring techniques including    determine the factors                                                                                          synthetic
grouping and the sum or difference of two of polynomials.                                                                                                division,
cubes                                                                                                                                                    long division
• using long division
• using synthetic division

PRF.4.AII.2                                  *I will analyze graphs                                                                        6.2, 6.8      Domain
Analyze and sketch, with and without         of polynomial                                                                                               Range
appropriate technology, the graph of a       functions by                                                                                                Maximum point
given polynomial function, determining the   determining their                                                                                           Minimum point
characteristics of domain and range,         characteristics                                                                                             End behavior
maximum and minimum points, end              (domain, range,                                                                                             Zeros of a
behavior, zeros, multiplicity of zeros, y-   maximum, minimum,                                                                                           function
intercept, and symmetry                      zeros, end behavior,                                                                                        multiplicity of
y-intercept, and                                                                                            zeros
symmetry).                                                                                                  y-intercept
Symmetry

PRF.4.AII.3                                 *I will write the                  Note: include zeros of the form a+bi                        6.7, 6.9      Polynomial
Write the equation of a polynomial function equations of a                                                                                               function
given its roots                             polynomial function                                                                                          Roots, Zeros
given its roots.
PRF.4.AII.4                                  *I will identify the                                                                          6.9           Polynomial
Identify the equation of a polynomial        equation of a                                                                                               function, finite
function given its graph or table            polynomial function                                                                                         differences
given its graph or
table.
16. Enduring     16. Essential Question- How are relationships between radicals and rational exponents related?
Understanding:                      Skills                                                                                                  Learning Plan
Relationships exist                                             Objective(s)      Assessment                                                      Instructional    Materials/      Essential
Strategies     Resources      Vocabulary
expressions and
rational exponents.

07-15-10                                                                                   13
16. Enduring
Understanding:
Secondary Mathematics Curriculum Map
Relationships exist                                                                                                                                                       14
Algebra II
expressions and QEF.3.AII.1                                      *I will simplify               Note: Be sure that all computations are        7.1, 7.2, 7.6   Radicals
rational exponents. Perform computations with radicals            radicals with different        done with different indices.                   Supplement      Index
• rationalize denominators                    computations of                *simplify radicals with different indices                      Rationalize
radical expressions                           multiplication, and            *rationalize denominators
*I will rationalize the        radical expressions (check for extraneous
denominators of                solutions)
radicals.                      Note: Achieve includes the example:
*I will solve equations

x 2  6 x  9  x  3  x  3

RF.1.AII.2                                    *I will create                 Note: Achieve includes composition of          7.3             Domain and
Evaluate, add, subtract, multiply, and        combined functions             two functions.                                                 range
divide, and composite functions, and give     by evaluating,                                                                                restrictions,
appropriate domain and range restrictions     adding, subtracting,                                                                          composition
and dividing.                                                                                 functions,
*I will create                                                                                combined
composite functions                                                                           functions
and identify the
appropriate domain
and range
restrictions.

07-15-10                                                                                14
Secondary Mathematics Curriculum Map                                                                                                                                15
Algebra II
PRF.4.AII.7                                  I will analyze the                                                            7.1           Radical
Establish the relationship between radical   relationship between                                                                        expressions
expressions and expressions containing       rational exponents                                                                          Rational
expressions.

PRF.4.AII.8                                  *I will analyze                                                               6.1, 7.2      Rational
Simplify variable expressions containing     variable expressions                                                                        exponents,
rational exponents using the laws of         containing rational                                                                         variable
exponents                                    exponents by                                                                                expressions
simplifying using
laws of exponents.

RF.1.AII.3                                   *I will create the            Note: Achieve includes                          7.4, 7.5      Inverse of a
Determine the inverse of a function          inverse of a function         -Inverses which may not be functions (not                     functions, one-
(Graph, with and without appropriate         algebraically and             one-to-one)                                                   to-one
technology, functions and their inverses)    graphically, with and         -Explain why an inverse function would be
without technology.           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

RF.1.AII.9                                   I will apply quadratic        Note: Achieve includes solving literal          continual     Functions
Apply the concepts of functions to real      functions to real             equations and solving problems that can         application
world situations                             world situations              be modeled using absolute value, step,
and other piece-wise defined functions.

07-15-10                                                                             15
Secondary Mathematics Curriculum Map                                                                                                                                        16
Algebra II
Curriculum Map -- Algebra II -- Mathematics
Fourth Quarter

EXPONENTIAL FUNCTIONS
17. Enduring       17. Essential Question- How are growth and decay modeled with functions?
Understanding:                          Skills                                                                                   Learning Plan
Exponential and                                                  Objective(s)      Assessment                                         Instructional   Materials/        Essential
logarithmic functions       (Student Learning Expectations)                                         Connection to Achieve Standards
Strategies    Resources        Vocabulary
can be represented ELF.5.AII.1                               *I will analyze the                                                                     8.1, 8.2        Exponential
graphically.     Recognize the graphs of exponential     graphs of exponential                                                                                   functions,
functions distinguishing between growth functions and classify                                                                                  Growth,
and decay                               as growth or decay.                                                                                     Decay, Growth
factor, Decay
factor,
Compound
interest
ELF.5.AII.2                                *I will graph                                                                           8.1, 8.2, 8.3   Natural Base e,
Graph exponential functions and identify   exponential                                                                                             Continuous
key characteristics: domain, range,        functions.                                                                                              interest, Domain
intercepts, asymptotes, and end behavior   *I will identify the key                                                                                Range
characteristics of                                                                                      Intercepts
domain, range,                                                                                          Asymptotes
intercepts,                                                                                             End behavior
asymptotes, and end
behaviors of
exponential
functions.

07-15-10                                                                                  16
Secondary Mathematics Curriculum Map                                                                                                                             17
Algebra II
ELF.5.AII.3                                *I will identify the          Note: Achieve includes explain or illustrate   8.1, 8.2
Identify the effect that changes in the    effect that changes of        the effect that changes in a parameter (a
parameters of the base have on the graph   parameters or base            or c) or the base (b) have on the graph of
of the exponential function                have on the graph of          the exponential function f(x) = abx + c.
an exponential
function.

ELF.5.AII.4                               I will recognize               Note: Achieve includes base e .                  8.1,8.2, 8.3
Recognize and solve problems that can be problems that can be
modeled using exponential functions.     modeled using
exponential
functions.
I will solve problems
that can be modeled
using exponential
functions.

ELF.5.AII.5                                *I will analyze the                                                                8.4        Exponential
Establish the relationship between         relationship between                                                                          function
exponential and logarithmic functions      exponential and                                                                               Logarithmic
logarithmic functions.                                                                        function

07-15-10                                                                           17
Secondary Mathematics Curriculum Map                                                                                                                                                        18
Algebra II
LOGARITHMS
18. Enduring       18. Essential Question- How can logarithms be evaluated?
Understanding:                         Skills                                                                                             Learning Plan
Logarithmic                                                   Objective(s)                Assessment                                        Instructional          Materials/        Essential
functions are used to       (Student Learning Expectations)                                                  Connection to Achieve Standards
Strategies           Resources        Vocabulary
model growth and ELF.5.AII.6                                *I will evaluate simple                                                                                 8.4             logarithm,
decay.         Evaluate simple logarithms using the    logarithms using the                                                                                                    common log,
definition (Ex. log 3 81)               definitions.                                                                                                            natural log

ELF.5.AII.7                                *I will use the                                                                                     8.5, Activity   logarithm,
Use properties of logarithms to manipulate propertied of                                                                                       (Pg. 500)       common log,
logarithmic expressions                    logarithms to                                                                                                       natural log
manipulate
logarithmic
expressions.
RATIONAL FUNCTIONS
19. Enduring        19. Essential Question- How are operations with rational expressions applied and simplified?
Understanding:                          Skills                                                                                                 Learning Plan
Relationships are                                                       Objective(s)       Assessment                                               Instructional     Materials/        Essential
present in rational         (Student Learning Expectations)                                                Connection to Achieve Standards
Strategies      Resources        Vocabulary
functions between     PRF.4.AII.6                                   *I will apply                       Note: Achieve includes solving rational                        9.2, 9.3,9.4, Rational
factors, zeros and    Simplify, add, subtract, multiply, and divide arithmetic operations               equations, and solving problems that can                         9.5, 9.6    expressions,
asymptotes.        with rational expressions                     to simplify rational                be modeled with rational functions.                                          complex
expressions.                                                                                                     fractions

20. Enduring       20. Essential Question- How can periodic functions model real world problems?
Understanding:                           Skills                                                                                   Learning Plan
Periodic Functions                                                Objective(s)       Assessment                                         Instructional   Materials/                      Essential
can be used to            (Student Learning Expectations)                                         Connection to Achieve Standards
Strategies   Resources                       Vocabulary
model periodic      RF.1.AII.6                             *I will recognize                                                                        Supplement                     Periodic
phenomena.         Recognize periodic phenomena (sine or  phenomena that are                                                                                                      phenomena
cosine functions such as sound waves,  periodic such as                                                                                                        Sine function
length of daylight, circular motion)   sound waves, length                                                                                                     Cosine function
of daylight or circular
motions of sine or
cosine functions.

RF.1.AII.7                                     *I will evaluate                                                                                Supplement      Period functions
Investigate and identify key characteristics   periodic functions                                                                                              Period
of period functions and their graphs           and graphs to identify                                                                                          Amplitude
(period, amplitude, maximum, and               key characteristics.                                                                                            Maximum
minimum)                                                                                                                                                       Minimum

RF.1.All.8                              Use *I will apply the                                                                                  Supplement      Frequency
basic properties of frequency and           properties of                                                                                                      Amplitude
amplitude to solve problems                 frequency and
amplitude to solve
problems.

07-15-10                                                                                        18
Secondary Mathematics Curriculum Map                                                                                                                               19
Algebra II
DATA ANALYSIS AND PROBABILITY
21. Enduring          21. Essential Question- How do we interpret and represent data?
Understanding:        DAP.6.AII.5                             *I will compute                                                                         7.7    Range,
Use measures of       *Compute and explain measures of spread measures of spread                                                                             percentile,
central tendency      (range, percentiles, variance, standard and analyze the                                                                                variance,
and measures of       deviation)                              results.                                                                                       standard
dispersion to                                                                                                                                                deviation
describe data sets    DAP.6.AII.6                                *I will describe the                                                                 12.7   Gaussian
Describe the characteristics of a Gaussian characteristics of a                                                                        normal
normal distribution.                       Gaussian normal                                                                             distribution,
distribution.                                                                               mean, standard
deviation

INSTRUCTIONAL STRATEGIES / ASSESSMENT
Instructional Strategies                                                             Student Assessment
Include, but not limited to: Direct Instruction, Note taking,                           Include, but not limited to:          Teacher made
Questioning, Writing Prompts, Journaling, Graphic Organizers,                           authentic assessments (including rubrics), Peer Evaluation,
Use of Manipulatives, Cooperative Learning, Guided Practice,                            Self Evaluation, The Learning Institute ( TLI ) Formative
Independent study, Homework                                                             assessments (Quarterly), State End-of-Course (EOC)
Assessment

07-15-10                                                                                    19

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 119 posted: 1/18/2011 language: English pages: 19
Description: Deriving Continuous Compound Interest Formula document sample
How are you planning on using Docstoc?