ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: Algebra II, Level 2
GRADE LEVEL: High School
CREATION DATE: November 2003
No
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Benchmark/Skills
Benchmark 1: Students will use the order
of operations to evaluate expressions.
Skill Set
Correctly implement the hierarchy of
PEMDAS
Define and apply the following vocabulary:
parentheses, braces, brackets, and algebraic
expression
Benchmark 2: Students will use formulas
for problem solving.
Skill Set
Define and apply the following vocabulary:
formula, algebraic expression, Pythagorean
theorem, hypotenuse, legs.
Benchmark 3: Students will determine
the sets of numbers to which a given
number belongs.
Skill Set
State a definition for the number sets
including real (R), rational (Q), irrational
(I), whole (W), integer (Z), and/or natural
number (N)
Use a Venn diagram to illustrate the
relationship between the sets of numbers.
Aligned Materials/
Resources/Technology
Tests, quizzes, and a
Algebra II - Integration,
cumulative final exam.
Applications & Connections A,B,C, I, K. Covered on a
Glencoe/McGraw-Hill, 1998
Midterm exam.
TI-82, TI-83, or TI-83 Plus
graphing calculators and
Optional forms of assessment: overhead view screen.
Homework, projects, teacher
observation in the classroom, Optional Resources:
oral assessment, performance Teacher resource materials
assessment, group activities,
associated with the text.
or board work.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the
department coordinator’s
classroom.
Boxer Math
Approx. Time Allotment:
Assessment
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Benchmark 4: Students will use
properties of real numbers to simplify
expressions.
Skill set
Algebra II, Level 2
Page 1
-1-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Use the commutative property, associative
property, identity property, inverse property,
and/or distributive property to simplify an
expression or equation.
Benchmark 5: Students will translate
verbal expressions and sentences into
algebraic expressions and equations.
Skill set
Define and apply the following vocabulary:
variable, open sentence, equation, and
inequality
Benchmark 6: Students will solve
equations for a specific variable using the
properties of equality.
Skill set
Students will apply the reflexive,
symmetric, transitive, substitution,
addition/subtraction, and
multiplication/division properties of equality
to determine the solution set of an equation.
Benchmark 7: Students will use a
graphing calculator to estimate solutions
of equations by building tables of values.
Skill set
Demonstration basic understanding of the
use of the TI-82, 83, or 83-plus graphing
calculator
Benchmark 8: Solve problems containing
Algebra II, Level 2
Page 2
-2-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
absolute value and/or inequalities.
Skill set
Solve an inequality using the
addition/subtraction and
multiplication/division properties of
inequality
Solve compound inequalities using “and”
and “or” and relate “and” to “intersection”
and relate “or” to “union”.
Solve inequalities involving absolute value
and graph the solution set.
Algebra II, Level 2
Page 3
-3-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized
Educational Plan.
Enrichment Strategies
Remediation Strategies
Use enrichment workbook
associated with current textbook to
cover many optional topics such as
4X4 determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service offered
at Penncrest, or seek
professional tutoring outside
of the school day.
Multicultural/Interdisciplin
ary
Connection
The textbook contains many
applications that connect the
math topics to other fields of
study. Likewise, many of the
applications involve
examples that are
multicultural in nature.
-4-
November 2003
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Approx. Time Allotment:
Page 4
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.A-C,2.8.11.D, 2.8.11.K, 2.8.11.L.N, 2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Tests, quizzes, and a cumulative
Benchmark 1: Students will graph a
Algebra II - Integration,
final exam.
relation, state its domain and range
Applications & Connections
A,B,C, I, K. Covered on a Midterm - Glencoe/McGraw-Hill,
and determine if it is a function.
exam.
1998
Skill set
TI-82, TI-83, or TI-83 Plus
Define and apply the following
Optional forms of assessment:
graphing calculators and
vocabulary: ordered pairs, coordinate
Homework, projects, teacher
overhead view screen.
system, Cartesian coordinate plane, xobservation in the classroom, oral
axis, y-axis, origin, quadrant, relation,
assessment, performance
Optional Resources:
domain, range, mapping, function,
assessment, group activities, or
Teacher resource materials
discrete function, vertical line test,
board work.
associated with the text.
continuous function
Computer software
applications for classroom
demonstration or individual
Benchmark 2: Students will find
student exploration.
values of functions for given elements
Internet links suggested in the
of the domain.
text.
Videos available in the
Benchmark 3: Students will use
department coordinator’s
graphing calculator to graph linear
classroom.
equations.
Boxer Math
Skill set
Understand basic use of the TI-82, 83, or
83-plus graphing calculator
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Benchmark 4: Students will identify
and graph linear equations.
Skill set
Identify the dependent and independent
variable, linear equation, linear function
Algebra II, Level 2
Page 5
-5-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.A-C,2.8.11.D, 2.8.11.K, 2.8.11.L.N, 2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Write linear equations in standard form
Determine the intercepts of a line and
use them to graph an equation.
Determine the x-intercept by setting y =
0, determine the y-intercept by setting x
=0
Determine the slope of a line.
Approx. Time Allotment:
Instructional Strategies
Identify from a graph whether the line
has a positive slope, negative slope, zero
slope or undefined slope
Use the slope and a point to graph an
equation.
Locate a point on the graph on a
coordinate plane and use the slope to
identify a second point on the graph
Benchmark 5: Students will
determine whether two lines are
parallel, perpendicular, or neither.
Skill set
Understand that parallel lines have the
same slope, perpendicular lines have
slopes that are negative reciprocals.
Benchmark 6: Students will solve
problems by identifying and using a
pattern.
Benchmark 7: Students will write the
equation of a line.
Algebra II, Level 2
Page 6
-6-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.A-C,2.8.11.D, 2.8.11.K, 2.8.11.L.N, 2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Skill set
Write an equation of a line in slopeintercept form given the slope and one
or two points.
Approx. Time Allotment:
Instructional Strategies
Write an equation of a line in pointslope form given two points, or given
the slope and one point.
Write an equation of a line that is
parallel or perpendicular to the graph of
a given equation.
Parallel lines have the same slope;
perpendicular lines have slopes that are
negative reciprocals
Benchmark 8: Students will identify
and graph special functions.
Skill set
Identify and differentiate between direct
variation, constant, identity, step, and/or
absolute value functions.
Benchmark 9: Students will sketch
graphs of inequalities in two
variables.
Skill set
Shade the solution set; use solid or
broken line to form the boundary
depending on the type of inequality.
Algebra II, Level 2
Page 7
-7-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.A-C,2.8.11.D, 2.8.11.K, 2.8.11.L.N, 2.8.11.O,P,Q,T
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each student’s
Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised
to stay after school for
extra help, utilize the Mu
Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments, preferential
seating, after school help, or modified homework
assignments.
Algebra II, Level 2
Page 8
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
-8-
November 2003
Essential Question, Concept or Theme: C. Systems of Linear Equations and Inequalities
PA Standards:
2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.F,G,H, 2.8.11.J, 2.8.11.K
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Tests, quizzes, and a cumulative Algebra II - Integration,
Benchmark 1: Students will solve
final exam.
Applications & Connections systems of equations and
A,B,C, I, K. Covered on a
Glencoe/McGraw-Hill, 1998
inequalities by graphing.
Midterm exam.
TI-82, TI-83, or TI-83 Plus
Skill set
graphing calculators and overhead
Identify the solution set as the point of Optional forms of assessment:
view screen.
intersection or the overlapping region
Homework, projects, teacher
of the two graphs.
observation in the classroom,
Optional Resources:
Label systems as consistent or
oral assessment, performance
Teacher resource materials
inconsistent systems, dependent or
assessment, group activities, or associated with the text.
independent systems.
board work.
Computer software applications for
classroom demonstration or
individual student exploration.
Benchmark 2: Students will use the
Internet links suggested in the text.
substitution and elimination
Videos available in the department
methods to solve systems of
coordinator’s classroom.
equations.
Boxer Math
Benchmark 3: Students will solve
systems of equations by using
Cramer’s rule.
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Skill set
Find the values of 2nd order
determinants.
Know and apply Cramer's Rule.
Benchmark 4: Students will solve a
system of three equations in three
variables.
Ordered triple, (x,y,z)
Algebra II, Level 2
Page 9
-9-
November 2003
Essential Question, Concept or Theme: C. Systems of Linear Equations and Inequalities
PA Standards:
2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.F,G,H, 2.8.11.J, 2.8.11.K
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized Educational
Plan.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Enrichment Strategies
Remediation Strategies
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service offered
at Penncrest, or seek
professional tutoring outside
of the school day.
Page 10
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 10 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Benchmark 1: Students will
perform basic mathematical
operations with polynomials.
Skill set
Add, subtract, multiply and divide
polynomials.
Define and apply the following
vocabulary: like terms, polynomial,
monomial, binomial, trinomial,
constant, coefficient, degree, power.
Use the rules for multiplying and
dividing exponents
Use the distributive property and
FOIL method
Use the long division and synthetic
division method for dividing
polynomials
Assessment
Tests, quizzes, and a cumulative
final exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Aligned Materials/
Resources/Technology
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the department
coordinator’s classroom.
Boxer Math
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Benchmark 2: Students will
perform basic mathematical
operations involving exponents.
Skill set
Represent an expression with a
negative exponent using an
equivalent expression with a positive
exponent.
Represent numbers in scientific
notation.
Multiply and divide exponents
written in scientific notation.
Algebra II, Level 2
Page 11
- 11 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 3: Students will factor
polynomials.
Skill set
Factor polynomials using the
appropriate factoring method: greatest
common factor, perfect square
trinomial, difference of two squares,
sum or difference of two cubes.
Use factoring to simplify polynomial
quotients by factoring and dividing
out common factors.
Benchmark 4: Students will
simplify radicals and radical
expressions.
Skill set
Simplify radicals having various
indices (2nd root, 3rd root, 4th root,
etc.).
Simplify radical expressions.
Rationalize the denominator of a
fraction containing a radical
expression.
Benchmark 5: Students will
perform basic mathematical
operations with radicals.
Skill set
Add, subtract, multiply or divide
Algebra II, Level 2
Page 12
- 12 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
radical expressions.
Identify like terms
Write expressions with rational
exponents in simplified radical form
and vice versa.
Evaluate expressions in either
exponential or radical form.
Benchmark 6: Students will solve
equations and inequalities
containing radicals.
Skill set
Simplify by squaring both sides of an
equation.
Identify extraneous solutions.
Benchmark 7: Simplify square
roots containing negative
radicands.
Skill set
Rewrite
1 as the number i
Benchmark 8: Solve quadratic
equations that have pure imaginary
solutions.
Skill set
Apply the quadratic formula.
Take the square root of both sides of
an equation.
Algebra II, Level 2
Page 13
- 13 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 9: Students will add,
subtract, and multiply complex
numbers.
Write complex numbers in the form
a + bi
Identify “a” as the real part, and “bi”
as the imaginary part of a complex
number
Use a Venn diagram to illustrate the
relationship between complex, real,
imaginary numbers and all the
subsets of real numbers
Benchmark 10: Simplify
expressions containing complex
numbers in the denominator.
Determine the complex conjugate for
a complex number
Algebra II, Level 2
Page 14
- 14 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service
offered at Penncrest, or
seek professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 15
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 15 -
November 2003
Essential Question, Concept or Theme: E. Quadratic Functions and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Assessment
Benchmark 1: Students will write
functions in quadratic form.
Tests, quizzes, and a cumulative
final exam.
Skill set
Identify quadratic, linear and constant
terms
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Benchmark 2: Students will graph
quadratic functions.
Skill set
Identify the shape of a parabola, the
axis of symmetry, vertex and zeros.
Create a table of values and plot
coordinate pairs.
Use symmetry to identify additional
points on the graph.
Aligned Materials/
Resources/Technology
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the department
coordinator’s classroom.
Boxer Math
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Benchmark 3: Students will solve
quadratic equations using a variety
of methods.
Skill set
Solve quadratic equations by
graphing and identify the zeros as the
x-intercepts
Solve quadratic equations by
factoring. Use factoring techniques
to include greatest common factor,
difference of two squares, using FOIL
“backwards” to factor expressions of
2
2
the form x  bx  c or ax  bx  c
Solve quadratic equations by
Algebra II, Level 2
Page 16
- 16 -
November 2003
Essential Question, Concept or Theme: E. Quadratic Functions and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
completing the square.
Solve quadratic equations by using
the quadratic formula.
Use the discriminant to determine the
nature of the roots of a quadratic
equation.
Benchmark 4: Students will find
the sum and product of the roots of
quadratic equations.
Skill set
Use sum and product of roots to
identify the equation
Benchmark 5: Students will
determine the quadratic equation
that has given roots.
Skill sets
Use the formula fx  x  s1 x  s2 
Benchmark 6: Students will graph
quadratic functions and
inequalities of the form
y  ax  h 2  k
Benchmark 7: Students will find
the distance between two points in
the coordinate plane.
Benchmark 8: Students will find
the midpoint of a line segment in
Algebra II, Level 2
Page 17
- 17 -
November 2003
Essential Question, Concept or Theme: E. Quadratic Functions and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
the coordinate plane.
Benchmark 9: Students will write
equations for parabolas using the
2
formula fx  ax  h  k
Benchmark 10: Students will graph
parabolas without the aid of a
graphing calculator.
Skill set
Determine the focus, directrix, axis
of symmetry, and latus rectum using
appropriate formulas and
relationships based on the equation in
standard form.
Optional: Benchmark 11: Students
will solve systems of equations and
inequalities involving quadratics
graphically and algebraically.
Skill set
Use combination or substitution
methods to determine the solution set
algebraically.
Graph the system of equations with
the aid of a graphing calculator and
identify overlapping regions as the
solution set.
Algebra II, Level 2
Page 18
- 18 -
November 2003
Essential Question, Concept or Theme: E. Quadratic Functions and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service
offered at Penncrest, or
seek professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 19
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 19 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Benchmark 1: Students will evaluate polynomial
functions for a given domain value.
Benchmark 2: Students will identify general shapes
of the graphs of polynomial functions.
Benchmark 3: Students will find factors of
polynomials.
Skill set
Use the factor theorem and synthetic division to
determine whether a given polynomial is a factor of
another polynomial.
Benchmark 4: Students will perform a complete
analysis of a simple polynomial function and sketch
the graph of that function.
Skill set
Find the number and type of real zeros of a polynomial
function by using Descartes' rule of signs.
Use the rational zero theorem to identify all possible
rational zeros of a polynomial function.
Create a table of values by hand or with the aid of a
graphing calculator that can be plotted and a curve
sketched.
Use the complex conjugates theorem to identify any
additional complex zero given one complex zero.
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Tests, quizzes, and a
Algebra II - Integration,
cumulative final exam.
Applications &
Connections Optional forms of
Glencoe/McGraw-Hill,
assessment:
1998
Homework, projects,
TI-82, TI-83, or TI-83 Plus
teacher observation in the
graphing calculators and
classroom, oral assessment, overhead view screen.
performance assessment,
group activities, or board
Optional Resources:
work.
Teacher resource materials
associated with the text.
Computer software
applications for classroom
demonstration or individual
student exploration.
Internet links suggested in
the text.
Videos available in the
department coordinator’s
classroom.
Boxer Math
Assessment
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional
strategies may include:
Independent investigations,
Boxer Math applications,
group work, or any variety of
classroom activities such as
“List, Pass, Amass”, “Each
one, teach one”, etc. as
suggested by the Professional
Development Coordinator.
Benchmark 5: Students will perform a complete
analysis of a more complicated polynomial function
with the aid of a graphing calculator and sketch the
Algebra II, Level 2
Page 20
- 20 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Assessment
Aligned Materials/
Resources/Technology
Instructional Strategies
graph of that function.
Skill set
Use the graphing calculator to graph polynomial
functions and to approximate the real zeros.
Use a graphing calculator to determine maximum and
minimum values of a function within a specified range.
Benchmark 6: Students will solve equations that are
quadratic in form.
Skill set
Apply quadratic techniques to solve equations for
which the degree of the first term is twice the degree of
the second term, i.e. is quadratic in form.
Benchmark 7: Students will determine the
composition of functions.
Benchmark 8: Students will determine and graph
the inverse of a function or relation.
Skill set
Interchange x and y in the equation and solve for y to
find the inverse of a function, then graph it.
Use the graphing calculator to graph a function and its
inverse.
Reflect the graph of a function across the line y = x to
graph the inverse.
Algebra II, Level 2
Page 21
- 21 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Adaptations/Inclusion Techniques
Approx. Time Allotment:
Enrichment Strategies
Adaptations for students with special instructional Use enrichment workbook
needs will be met in accordance with each
associated with current
student’s Individualized Educational Plan.
textbook to cover many
optional topics such as 4X4
Adaptations may include but are not limited to
determinants, probability
extended time on tests and assignments,
topics, etc.
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 22
Remediation Strategies
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service
offered at Penncrest, or
seek professional tutoring
outside of the school day.
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 22 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A 2.11.11.A
Benchmark/Skills
Assessment
Benchmark 1: Students will graph
rational functions.
Tests, quizzes, and a cumulative
final exam.
Skill set
Determine the asymptotes for a
rational function by examining the
equation and end behavior of the
function.
Determine the values for which the
denominator of a rational function is
undefined.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Benchmark 2: Students will solve
problems involving direct, inverse,
and joint variation.
Benchmark 3: Students will
simplify rational expressions.
Aligned Materials/
Resources/Technology
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the department
coordinator’s classroom.
Boxer Math
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Skill set
Apply basic algebraic manipulations
to simplify a rational expression after
factoring the expression
Benchmark 4: Students will
simplify complex fractions.
Skill set
Use the rule of multiplying by the
inverse of the denominator to
simplify complex fractions.
Multiply numerator and denominator
Algebra II, Level 2
Page 23
- 23 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
by the common denominator of the
denominators within the complex
fraction.
Benchmark 5: Students will add
and subtract rational expressions.
Skill set
Rewrite the expressions with a
common denominator, then add or
subtract
Benchmark 6: Students will solve
rational equations and inequalities.
Skill set
Multiply both sides of the equation by
the least common denominator and
then solve for the variable.
Algebra II, Level 2
Page 24
- 24 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A 2.11.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service
offered at Penncrest, or
seek professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 25
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 25 -
November 2003
Essential Question, Concept or Theme: I. Sequences and Series
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.8.11.C, 2.11.11.D
Benchmark/Skills
Approx. Time Allotment:
Assessment
Benchmark 1: Students will
determine a specific term in an
arithmetic or geometric sequence,
or geometric series.
Tests, quizzes, and a cumulative
final exam.
Skill set
Define and apply the following
vocabulary: sequence, term,
arithmetic or geometric sequence,
common difference, series sigma,
summation notation.
Determine the nth term of an
arithmetic sequence
Determine the nth term of a
geometric sequence using
Determine the position of a given
term in an arithmetic or geometric
sequence.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Covered on a Midterm exam.
Aligned Materials/
Resources/Technology
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the department
coordinator’s classroom.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Benchmark 2: Students will
determine arithmetic and
geometric means.
Benchmark 3: Students will
determine the sum of an arithmetic,
or geometric series.
Determine the sum of an arithmetic
series
Determine the sum of a geometric
series using
Use sigma notation to express sums
Algebra II, Level 2
Page 26
- 26 -
November 2003
Essential Question, Concept or Theme: I. Sequences and Series
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.8.11.C, 2.11.11.D
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
of an arithmetic or geometric series.
Determine the sum of an infinite
geometric series.
Optional: Benchmark 4: Students
will iterate functions.
Algebra II, Level 2
Page 27
- 27 -
November 2003
Essential Question, Concept or Theme: I. Sequences and Series
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.8.11.C, 2.11.11.D
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service
offered at Penncrest, or
seek professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 28
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 28 -
November 2003
Essential Question, Concept or Theme: J. Permutations, Combinations and Probability
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.7.11.A,D,E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Tests, quizzes, and a cumulative Algebra II - Integration,
Benchmark 1: Students will solve
final exam.
Applications & Connections problems using the Fundamental
Glencoe/McGraw-Hill, 1998
Counting Principle.
Optional forms of assessment:
TI-82, TI-83, or TI-83 Plus
Skill set
Homework, projects, teacher
graphing calculators and
Illustrate fundamental counting principal observation in the classroom,
overhead view screen.
problems using a tree diagram
oral assessment, performance
Complete calculations involving
assessment, group activities, or Optional Resources:
factorials
board work.
Teacher resource materials
Identify independent and dependent
associated with the text.
events
Computer software applications
Solve problems by using the strategy of
for classroom demonstration or
solving a simpler problem.
individual student exploration.
Internet links suggested in the
text.
Benchmark 2: Students will solve
Videos available in the
problems involving linear and
department coordinator’s
circular permutations, and
classroom.
combinations.
Boxer Math
Skill set
Differentiate between permutations and
combinations.
Identify conditions that define a
permutation as linear or circular.
Apply formulas to determine
permutations and combinations.
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Benchmark 3: Students will
determine the probability of an event.
Apply formulas to determine probability
of success or failure.
Algebra II, Level 2
Page 29
- 29 -
November 2003
Essential Question, Concept or Theme: J. Permutations, Combinations and Probability
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.7.11.A,D,E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Find the probability of two or more
independent or dependent events.
Find the probability of mutually
exclusive or inclusive events.
Approx. Time Allotment:
Instructional Strategies
Benchmark 4: Students will
determine the odds of success and
failure of an event.
Examine the ratio of # of successes to #
of failures to determine the odds of
success or failure
Benchmark 5: Students will
differentiate between probability and
odds.
Algebra II, Level 2
Page 30
- 30 -
November 2003
Essential Question, Concept or Theme: J. Permutations, Combinations and Probability
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.7.11.A,D,E
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service
offered at Penncrest, or
seek professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 31
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 31 -
November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Benchmark/Skills
Benchmark 1: Students will perform
basic mathematical operations involving
matrices.
Skill set
Perform scalar multiplication on a matrix.
Add or subtract corresponding elements of a
matrix.
Determine whether two matrices can be
multiplied by verifying that the number of
columns in the first matrix is equal to the
number of rows in the second matrix.
Multiply matrices by using the row by
column method.
Set corresponding elements of two matrices
equal to one another and solve for any
variables.
Benchmark 2: Students will evaluate the
determinant of a 3 x 3 matrix.
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Tests, quizzes, and a
Algebra II - Integration,
cumulative final exam.
Applications & Connections Glencoe/McGraw-Hill, 1998
Covered on a Midterm exam. TI-82, TI-83, or TI-83 Plus
graphing calculators and
Optional forms of assessment: overhead view screen.
Homework, projects, teacher
observation in the classroom, Optional Resources:
oral assessment, performance Teacher resource materials
assessment, group activities,
associated with the text.
or board work.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the
department coordinator’s
classroom.
Boxer Math
Assessment
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-L. Lecture, demonstration,
review, graphing calculator
activities.
Optional instructional strategies
may include: Independent
investigations, Boxer Math
applications, group work, or any
variety of classroom activities such
as “List, Pass, Amass”, “Each one,
teach one”, etc. as suggested by the
Professional Development
Coordinator.
Skill set
Evaluate the determinant first by the method
of expansion by minors.
Evaluate the determinant by using the
graphing calculator.
Benchmark 3: Students will determine
the area of a triangle given the
coordinates of its vertices.
Benchmark 4: Students will write the
Algebra II, Level 2
Page 32
- 32 -
November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
identity matrix for any square matrix.
Benchmark 5: Students will determine
the inverse of a 2 x 2 matrix.
Benchmark 6: Students will solve systems
of linear equations by using inverse and
augmented matrices.
Optional Benchmark 7: Students will be
able to use a graphing calculator to
perform operations with matrices and
find determinants and inverses.
Algebra II, Level 2
Page 33
- 33 -
November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Benchmark/Skills
Algebra II, Level 2
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Page 34
Instructional Strategies
- 34 -
November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized
Educational Plan.
Approx. Time Allotment:
Enrichment Strategies
Remediation Strategies
Use enrichment workbook
associated with current textbook to
cover many optional topics such as
4X4 determinants, probability
topics, etc.
Students will be advised to
stay after school for extra
help, utilize the Mu Alpha
Theta tutoring service offered
at Penncrest, or seek
professional tutoring outside
of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Algebra II, Level 2
Page 35
- 35 -
Multicultural/Interdisciplin
ary
Connection
The textbook contains many
applications that connect the
math topics to other fields of
study. Likewise, many of the
applications involve
examples that are
multicultural in nature.
November 2003
Essential Question, Concept or Theme: L. Statistics
PA Standards: 2.6.11.A, 2.6.11.C, 2.6.11.D, 2.6.11.I
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 1: Students will be able to
represent and interpret data
graphically.
Skill set
Students will create and interpret the
following types of graphs: line graph,
circle graph, line plot, stem and leaf
plot, stem, leaf, back-to-back stem and
leaf plot
Benchmark 2: Find and use the mean,
median and mode to interpret data.
Skill set
Determine the mean, median, mode,
measure of central tendency, and
extreme values for a data set.
Benchmark 3: Students will model
data with a graph and linear equation.
Skill set
Draw scatter plots.
Find and use prediction equation.
Benchmark 4: Students will use a
graphing calculator to graph lines of
regression and to graph linear
inequalities.
Algebra II, Level 2
Page 36
- 36 -
November 2003
Essential Question, Concept or Theme: L. Statistics
PA Standards: 2.6.11.A, 2.6.11.C, 2.6.11.D, 2.6.11.I
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Skill set
Basic understanding of the use of the
graphing calculator.
Benchmark 5: Students will
determine the standard deviation for
a set of data.
Benchmark 6: Students will solve
problems involving normally
distributed data.
Benchmark 7: Students will use the
binomial expansion to find
probabilities.
Benchmark 8: Students will use
simulations to solve various
probability problems.
Skill set
Determine an unbiased sample.
Find margins of sampling error.
Test hypothesis by designing and
conducting experiments.
Algebra II, Level 2
Page 37
- 37 -
November 2003
Essential Question, Concept or Theme: L. Statistics
PA Standards: 2.6.11.A, 2.6.11.C, 2.6.11.D, 2.6.11.I
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each student’s
Individualized Educational Plan.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Students will be advised
to stay after school for
extra help, utilize the Mu
Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments, preferential
seating, after school help, or modified homework
assignments.
Algebra II, Level 2
Page 38
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 38 -
November 2003