Algebra II Curriculum Map - Muskogee Public Schools

Muskogee Public Schools
Curriculum Map
2009-20010
Course: Algebra II
Grade Level: 9-12
Nine-
Weeks
1 st Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
Standard 1: Number Systems and
Algebraic Operations - The student
will perform operations with rational,
radical, and polynomial expressions,
as well as expressions involving
complex numbers.
Academic Skills
Use a number line to graph and order
real numbers.
Identify properties of and use operations
with real numbers.
Evaluate algebraic expression.
Simplify algebraic expressions by
combining like terms.
Expected Strategies, Vocabulary &
Assessment
Vocabulary: Variable, Values, Variable
Expression, Evaluating the expression,
Unit Analysis, and Verbal Model.
Numerical Expression, Base of a power,
Exponent, Power, Algebraic Expression,
Mathematical Model, Terms of an
Expression, Coefficient, Like Terms,
Constant Term, Equivalent Algebraic
Expressions, and Identity.
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
2. Systems of Equations
a. Model a situation that can be
described by a system of equations or
inequalities and use the model to answer
questions about the situation.
b. Solve systems of linear equations and
inequalities using various methods and
tools which may include substitution,
Solve linear equations.
Use linear equations to solve real-life
problems.
Solve simple inequalities.
Solve compound inequalities.
Solve absolute value equations and
inequalities.
Use absolute value equations and
inequalities to solve real-life problems.
Equation, Linear Equation, Solution of an
equation in one variable, Equivalent
Equations, Algebraic Model, Linear
Inequality in One Variable, Solution of
an Inequality in One Variable, Graph of
an Inequality, Compound Inequality, and
Absolute value of a real number.

Nine-
Weeks
1 st Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
elimination, matrices, graphing, and
graphing calculators.
Academic Skills
Expected Strategies, Vocabulary &
Assessment
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
1. Functions and Function Notation
b. Add, subtract, multiply, and divide
functions using function notation.
d. Use algebraic, interval, and set
notations to specify the domain and
range of functions of various types.
Represent relations and functions.
Graph and evaluate linear functions.
Use the slope-intercept form of a linear
equation to graph linear equations.
Use the standard form of a linear
equation to graph linear equations.
Write Linear Equations.
Write direct variation equations.
Relation, Domain of a Relation, Range of
a Relation, Function, Ordered Pair,
Coordinate Plane, Equation in Two
Variables, Solution of an Equation in
Two Variables, Independent Variable,
Dependant Variable, Graph of an
Equation in Two Variables, Linear
Function, Function Notation, X and Y-
intercept, Slope-intercept Form, Standard
Form of a Linear Equation, Direct
Variation, and Constant of Variation.
Standard 3: Data Analysis and
Statistics - The student will use data
analysis and statistics to formulate
and justify predictions from a set of
data.
1. Analysis of Collected Data Involving
Two Variables
a. Interpret data on a scatter plot using a
linear, exponential, or quadratic
model/equation.
b. Identify whether the model/equation is
a curve of best fit for the data, using
various methods and tools which may
include a graphing calculator.
Use a scatter plot to identify the
correlation shown by a set of data.
Approximate the best-fitting line for a
set of data.
Scatter Plot, Positive, Negative, and
Relatively No Correlation,
Standard 2: 2 a and b (written above)
Graph linear inequalities in two
variables.
Linear Inequality in Two Variables,
Solution of an Inequality in Two

Nine-
Weeks
1 st Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
Academic Skills
Use linear inequalities to solve real-life
problems.
Expected Strategies, Vocabulary &
Assessment
Variables, and Half-planes.
Represent piecewise functions.
Use piecewise functions to model reallife
quantities.
Piecewise Function and Step Function.
Represent absolute value functions.
Use absolute value functions to model
real-life situations.
Vertex of an Absolute Value Graph
Standard 2: 2 a and b (written above)
Graph and solve systems of linear
equations in two variables.
Use linear systems to solve real-life
problems.
Use algebraic methods to solve linear
systems.
Use linear systems to model real-life
situations.
Graph a system of linear inequalities to
find the solutions of the system.
Use systems of linear inequalities to
solve real-life problems.
Solve linear programming problems.
Use linear programming to solve reallife
problems
Graph linear equations in three variables
and evaluate linear functions in two
variables.
Use functions of two variables to model
real-life situations.
Solve systems of linear equations in
three variables.
Use linear systems in three variables to
System of Two Linear Equations,
Solution of a System of Linear Equations,
System of linear inequalities in two
variables, Solution of a system of linear
inequalities, Graph of a system of linear
inequalities, Optimization, Linear
Programming, Objective Function,
Constraints, Feasible Region, Threedimensional
coordinate system, Z-axis,
Ordered Triple, Octants, Linear Equation
in Three Variables, Function of Two
Variables, System of Three Linear
Equations, and Solution of a System of
Three Linear Equations.

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
Academic Skills
model real-life situations.
Expected Strategies, Vocabulary &
Assessment
2 nd Nine
Weeks
Add and subtract matrices, multiply a
matrix by a scalar, and solve matrix
equations.
Use matrices in real-life situations.
Multiply two matrices.
Use matrix multiplication in real-life
situations.
Evaluate determinants of 2 3 2 and 3 3 3
matrices.
Use Cramer’s rule to solve systems of
linear equations.
Matrix, Dimensions of a Matrix, Entries
of a Matrix, Equal Matrices, Scalar,
Scalar Multiplication, Determinant,
Cramer’s Rule, and Coefficient Matrix.
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
1. Functions and Function Notation
a. Recognize the parent graphs of
polynomial, exponential, radical,
quadratic, and logarithmic functions and
predict the effects of transformations on
the parent graphs, using various methods
and tools which may include graphing
calculators.
2. Systems of Equations
a. Model a situation that can be
described by a system of equations or
Graph quadratic functions.
Use quadratic functions to solve real-life
problems.
Quadratic Function, Parabola, Vertex of a
Parabola, Axis of Symmetry of a
Parabola, and Standard Form.

Nine-
Weeks
2 nd Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
inequalities and use the model to answer
questions about the situation.
Academic Skills
Expected Strategies, Vocabulary &
Assessment
3. Quadratic Equations and Functions
a. Solve quadratic equations by
graphing, factoring, completing the
square and quadratic formula.
Factor quadratic expressions and solve
quadratic equations by factoring.
Find zeros of quadratic functions.
Solve quadratic equations by finding
square roots.
Use quadratic equations to solve real-life
problems.
Binomial, Trinomial, Factoring,
Monomial, Quadratic Equation in One
Variable, Zero of a Function, Square
Root, Radical Sign, Radicand, Radical,
Rationalizing the Denominator
Standard 1: Number Systems and
Algebraic Operations - The student
will perform operations with rational,
radical, and polynomial expressions,
as well as expressions involving
complex numbers.
3. Complex Numbers
*a. Recognize that to solve certain
problems and equations, number systems
need to be extended from real numbers
to complex numbers.
Note: Asterisks (*) have been used to
identify standards and objectives that
must be assessed by the local school
district. All other skills may be assessed
by the Oklahoma School Testing
Program (OSTP).
b. Add, subtract, multiply, divide, and
simplify expressions involving complex
numbers.
Solve quadratic equations with complex
solutions and perform operations with
complex numbers.
Apply complex numbers to fractal
geometry.
Imaginary Unit i, Complex Number,
Standard Form of a complex number,
Imaginary Number, Pure Imaginary
Number, Complex Plane, Complex
Conjugates, and Absolute Value of a
Complex Number
Standard 2: 3 a (written above)
b. Graph a quadratic function and
Solve quadratic equations by completing
equations the square.
Completing the Square

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
identify the x- and y-intercepts and
maximum or minimum value, using
various methods and tools which may
include a graphing calculator.
c. Model a situation that can be
described by a quadratic function and
use the model to answer questions about
the situation.
Academic Skills
Use completing the square to write
quadratic functions in vertex form.
Solve quadratic equations using the
quadratic formula.
Use the quadratic formula in real-life
situations.
Graph quadratic inequalities in two
variables.
Solve quadratic inequalities in one
variable.
Expected Strategies, Vocabulary &
Assessment
Discriminant of a Quadratic Equation,
Quadratic Inequality in Two Variables,
and Quadratic Inequality in One
Variable.
Write quadratic functions given
characteristics of their graphs.
Use technology to find quadratic models
for real-life data.
Best-fitting Quadratic Model
Use properties of exponents to evaluate
and simplify expressions involving
powers.
Use exponents and scientific notation to
solve real-life problems.
Scientific Notation
3 rd Nine
Weeks
Standard 1: Number Systems and
Algebraic Operations - The student
will perform operations with rational,
radical, and polynomial expressions,
as well as expressions involving
complex numbers.
2. Polynomial and Rational Expressions
a. Divide polynomial expressions by
lower degree polynomials.
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
Evaluate a polynomial function.
Graph a polynomial function.
Add, subtract, and multiply polynomials.
Use polynomial operations in real-life
problems.
Factor polynomial expressions.
Use factoring to solve polynomial
equations.
Divide polynomials and relate the result
to the remainder theorem and the factor
theorem.
Use polynomial division in real-life
Polynomial Function, Leading
Coefficient, Constant Term, Degree,
Standard Form of a Polynomial Function,
End Behavior, Factor by Grouping,
Quadratic Form, Polynomial Long
Division, and Synthetic Division.

Nine-
Weeks
3 rd Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
6. Polynomial Equations and Functions
a. Solve polynomial equations using
various methods and tools which may
include factoring and synthetic division.
Academic Skills
problems.
Find the rational zeros of a polynomial
function.
Use polynomial equations to solve reallife
problems.
Expected Strategies, Vocabulary &
Assessment
Use the fundamental theorem of algebra
to determine the number of zeros of a
polynomial function.
Use technology to approximate the real
zeros of a polynomial function.
Repeated solution
c. Given the graph of a polynomial
function, identify the x- and y-intercepts,
relative maximums and relative
minimums, using various methods and
tools which may include a graphing
calculator.
Analyze the graph of a polynomial
function.
Use the graph of a polynomial function
to answer questions about real-life
situations.
Local Maximum and Minimum.
Use finite differences to determine the
degree of a polynomial function that will
fit a set of data.
Use technology to find polynomial
models for real-life data.
Finite Differences
Standard 1: Number Systems and
Algebraic Operations - The student
will perform operations with rational,
radical, and polynomial expressions,
as well as expressions involving
complex numbers.
Evaluate nth roots of real numbers using
both radical notation and rational
exponent notation.
Use nth roots to solve real-life problems.
Use properties of rational exponents to
evaluate and simplify expressions.
Nth Root of A, Index of a Radical,
Simplest Form of Radical, and Like
Radicals.

Nine-
Weeks
3 rd Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
1. Rational Exponents
a. Convert expressions from radical
notations to rational exponents and vice
versa.
b. Add, subtract, multiply, divide, and
simplify radical expressions and
expressions containing rational
exponents.
Academic Skills
Use properties of rational exponents to
solve real-life problems.
Expected Strategies, Vocabulary &
Assessment
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
1. Functions and Function Notation
b. Add, subtract, multiply, and divide
functions using function notation.
c. Combine functions by composition.
e. Find and graph the inverse of a
function, if it exists.
Perform operations with functions
including power functions.
Use power functions and function
operations to solve real-life problems.
Power Function, Composition, Inverse
Relation, and Inverse Functions
Graph square root and cube root
functions.
Use square root and cube root functions
to find real-life quantities.
Radical Function
Standard 1:1 a and b (written above)
Solve equations that contain radicals or
rational exponents.
Use radical equations to solve real-life
problems.
Extraneous Solution
Standard 3: Data Analysis and
Use measures of central tendency and
Statistics, Mean, Median, Mode,

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
Statistics - The student will use data
analysis and statistics to formulate
and justify predictions from a set of
data.
* 2. Measures of Central Tendency and
Variability
a. Analyze and synthesize data from a
sample using appropriate measures of
central tendency (mean, median, mode,
weighted average).
b. Analyze and synthesize data from a
sample using appropriate measures of
variability (range, variance, standard
deviation).
Academic Skills
measures of dispersion to describe data
sets.
Use box-and-whisker plots and
histograms to represent data graphically.
Expected Strategies, Vocabulary &
Assessment
Measures of Dispersion, Range of Data
Values, Standard Deviation, Box-and-
Whisker Plot, Lower and Upper Quartile,
Histogram, Frequency of Data Values,
and Frequency Distribution.
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
5. Exponential and Logarithmic
Functions
a. Graph exponential and logarithmic
functions.
Graph exponential growth functions.
Use exponential growth functions to
model real-life situations.
Graph exponential decay functions.
Use exponential decay functions to
model real-life situations.
Use the number e as the base of
exponential functions.
Use the natural base e in real-life
situations.
Evaluate logarithmic functions.
Graph logarithmic functions.
Use properties of logarithms.
Use properties of logarithms to solve
real-life problems.
Exponent Function, Asymptote,
Exponential Growth Function, Growth
Factor, Exponential Decay Function,
Decay Factor, Common and Natural
Logarithm

Nine-
Weeks
4 th Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
Academic Skills
Expected Strategies, Vocabulary &
Assessment
Standard 1: Number Systems and
Algebraic Operations - The student
will perform operations with rational,
radical, and polynomial expressions,
as well as expressions involving
complex numbers.
1. Rational Exponents
a. Convert expressions from radical
notations to rational exponents and vice
versa.
b. Add, subtract, multiply, divide, and
simplify radical expressions and
expressions containing rational
exponents.
2. Polynomial and Rational Expressions
a. Divide polynomial expressions by
lower degree polynomials.
b. Add, subtract, multiply, divide, and
simplify rational expressions, including
complex fractions.
3. Complex Numbers
*a. Recognize that to solve certain
problems and equations, number systems
need to be extended from real numbers
to complex numbers.
Note: Asterisks (*) have been used to
identify standards and objectives that
must be assessed by the local school
district. All other skills may be assessed
by the Oklahoma School Testing

Nine-
Weeks
4 th Nine
Weeks
Content Area and PASS
Muskogee Academic Standards
Program (OSTP).
b. Add, subtract, multiply, divide, and
simplify expressions involving complex
numbers.
Academic Skills
Expected Strategies, Vocabulary &
Assessment
Standard 2: Relations and Functions -
The student will use the relationships
among the solution of an equation,
zero of a function, x-intercepts of a
graph, and factors of a polynomial
expression to solve problems involving
relations and functions.
1. Functions and Function Notation
a. Recognize the parent graphs of
polynomial, exponential, radical,
quadratic, and logarithmic functions and
predict the effects of transformations on
the parent graphs, using various methods
and tools which may include graphing
calculators.
b. Add, subtract, multiply, and divide
functions using function notation.
c. Combine functions by composition.
d. Use algebraic, interval, and set
notations to specify the domain and
range of functions of various types.
e. Find and graph the inverse of a
function, if it exists.
2. Systems of Equations
a. Model a situation that can be
described by a system of equations or
inequalities and use the model to answer
questions about the situation.
b. Solve systems of linear equations and

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
inequalities using various methods and
tools which may include substitution,
elimination, matrices, graphing, and
graphing calculators.
*c. Use either one quadratic equation
and one linear equation or two quadratic
equations to solve problems.
3. Quadratic Equations and Functions
a. Solve quadratic equations by
graphing, factoring, completing the
square and quadratic formula.
b. Graph a quadratic function and
identify the x- and y-intercepts and
maximum or minimum value, using
various methods and tools which may
include a graphing calculator.
c. Model a situation that can be
described by a quadratic function and
use the model to answer questions about
the situation.
4. Identify, graph, and write the
equations of the conic sections (circle,
ellipse, parabola, and hyperbola).
5. Exponential and Logarithmic
Functions
a. Graph exponential and logarithmic
functions.
b. Apply the inverse relationship
between exponential and logarithmic
functions to convert from one form to
another.
c. Model a situation that can be
described by an exponential or
logarithmic function and use the model
Academic Skills
Expected Strategies, Vocabulary &
Assessment

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
to answer questions about the situation.
6. Polynomial Equations and Functions
a. Solve polynomial equations using
various methods and tools which may
include factoring and synthetic division.
b. Sketch the graph of a polynomial
function.
c. Given the graph of a polynomial
function, identify the x- and y-intercepts,
relative maximums and relative
minimums, using various methods and
tools which may include a graphing
calculator.
d. Model a situation that can be
described by a polynomial function and
use the model to answer questions about
the situation.
7. Rational Equations and Functions
a. Solve rational equations.
b. Sketch the graph of a rational
function. c. Given the graph of a rational
function, identify the x- and y-intercepts,
vertical asymptotes, using various
methods and tools which may include a
graphing calculator.
d. Model a situation that can be
described by a rational function and use
the model to answer questions about the
situation.
Academic Skills
Expected Strategies, Vocabulary &
Assessment
Standard 3: Data Analysis and
Statistics - The student will use data
analysis and statistics to formulate
and justify predictions from a set of

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
data.
1. Analysis of Collected Data Involving
Two Variables
a. Interpret data on a scatter plot using a
linear, exponential, or quadratic
model/equation.
b. Identify whether the model/equation is
a curve of best fit for the data, using
various methods and tools which may
include a graphing calculator.
* 2. Measures of Central Tendency and
Variability
a. Analyze and synthesize data from a
sample using appropriate measures of
central tendency (mean, median, mode,
weighted average).
b. Analyze and synthesize data from a
sample using appropriate measures of
variability (range, variance, standard
deviation).
c. Use the characteristics of the Gaussian
normal distribution (bell-shaped curve)
to solve problems.
d. Identify how given outliers affect
representations of data.
3. Identify and use arithmetic and
geometric sequences and series to solve
problems.
Academic Skills
Expected Strategies, Vocabulary &
Assessment

Nine-
Weeks
Content Area and PASS
Muskogee Academic Standards
Academic Skills
Expected Strategies, Vocabulary &
Assessment