ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: Algebra II Level 3
GRADE LEVEL: High School
CREATION DATE: November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11A, 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
Tests, quizzes, midterm
exam, and a cumulative
A. Equations and Inequalities
Benchmark 1:Use the order of operations and final exam.
formulas to evaluate algebraic expressions.
Optional forms of
Skill Set
assessment:
a.
Correctly implement the hierarchy of
Homework, projects,
P .E. M. D. A. S.
b.
Identify & demonstrate the use of the teacher observation in the
classroom, oral assessment,
Pythagorean Theorem to determine
performance assessment,
the sides of a right triangle.
groupactivities, or board
c.
Explain & demonstrate procedure of
work.
writing algebraic expressions in
correct form.
Benchmark 2: Determine the sets of
numbers to which a given number belongs
Skill Set
a. State a definition for the number sets
including real ®, rational (Q), irrational
(I), whole
W) ,integer (Z), and/or natural number( N)
b. Use Venn diagram to illustrate the
relationship between the sets of numbers
Algebra II-Integration,
Applications & Connections Glance / McGraw-Hill, 1998
Ti -81 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
Penncrest Math Office.
Instructional Strategies
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Optional instructional strategies
may include:
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:Use properties of real numbers
to simplify expressions
Skill Set
a. Explain the concept of ”absolute value”
using the commutative, associative,
identity,
inverse, and distributive properties.
Algebra II Level 3 – High School
Page 1
-1-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11A, 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
Benchmark 4:Represent and interpret data
graphically
Skill Set
a. Gather data by drawing line and circle
graphs
b. Use line plots, stem and leaf plots to
gather information
c. Explain & identify how points are plotted
on a grid.
d. Define & demonstrate the sign values of
the x-and-y coordinates from each of the
four quadrants that they lie.
Benchmark 5: Interpreting data using the
mean, median, mode, and range.
Skill Set
a. Define and explain the mean, median,
mode, and range.
b. Demonstrate & explain procedure of
computing the mean, median, mode, and
range.
Benchmark 6:Translate verbal expressions
and sentences into algebraic expressions and
equations.
Skill Set
a. Define & demonstrate the difference
between an equation and an inequality
b. Identify the components that make up an
equation: variables , numbers, equal signs,
as well as the less than and greater than
symbols.,etc
Algebra II Level 3 – High School
Page 2
-2-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11A, 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
Benchmark7:Recognize procedure of solving
equations for a specific variable using the
properties of equality.
Skill Set
a. Demonstrate & identify the properties of
reflexive, symmetric, transitive, and
substitution.
b. Explain procedure to determine a solution
set using the addition/subtraction and
multiplication/division properties of
equality.
Benchmark 8: Estimate solutions of
equations by building tables of values that are
generated from a graphing calculator
Skill Set
a. Explain & demonstrate the appropriate use
of the TI-82 graphing calculator to gain a
basic
understanding of how the device works.
b. Identify & apply the use of the graphing
calculator to a variety of problems.
Benchmark 9 Recognize compound
inequalities that contain “ and/or” statement
Skill Set
a. Explain & identify the relationship
between “ and” and “ or “ intersection”
b. Explain & identify the relationship
between “ or ‘ and “ union”.
Algebra II Level 3 – High School
Page 3
-3-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11A, 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 (I. E. P.).
Adaptations may include but not be limited
to extended time on tests and assignments,
preferential
seating, before- and-after school help, or modified
homework assignment
Approx. Time Allotment:
Enrichment Strategies
Remediation Strategies
Students may wish to
independently research
some of the topics, as
mentioned on the
Internet, and exploring
other software computer
programs to discover
how people live and
work in the business
world, as well as in
Remediation strategies may
include before-and/or -after
school help, extra-credit projects,
test corrections, &
Mu Alpha Theta tutoring...
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of
study.
Likewise, many of the
applications involve examples
that are multicultural in nature.
their own lives today. Using
some of the other topics that
were taught in the Algebra II
course, students will have the
opportunity to do a variety of
projects that will challenge
their intellect.
Algebra II Level 3 – High School
Page 4
-4-
November 2003
Essential Question, Concept or Theme: B. Permutations and Combinations
PA Standards: 2.11.A, 2.2.11.F, 2.5. 11. A -C
Benchmark/Skills
Benchmark 1:Recognize &
develop strategies for solving
permutation and combination
problems
Skill Set
a. Develop & demonstrate a
chart to show a step-by- step
procedure for solving problems
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, midterm exam, and
a cumulative final exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom, oral
assessment, performance
assessment, groupactivities, or
board work.
Benchmark 2: Demonstrate &
recognize problems that involve
linear and circular permutations,
and combinations.
Skill Set
a. Define & explain the difference
between permutation and
combination.
b. Identify & explain conditions
by which to define a
permutation as linear or
circular
c. Apply & demonstrate the use of
formulas to determine solutions for
permutation and combination
problems.
Algebra II Level 3 – High School
Approx. Time Allotment:
Page 5
Algebra II-Integration,
Applications & Connections Glance / McGraw-Hill, 1998
Ti -81 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 Penncrest
Math Office.
Instructional Strategies
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Optional instructional strategies
may include:
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
-5-
November 2003
Essential Question, Concept or Theme: B. Permutations and Combinations
PA Standards: 2.11.A, 2.2.11.F, 2.5. 11. A -C
Adaptations/Inclusion Techniques
Enrichment Strategies
Adaptations for students with special instructional
needs will be met in accordance with each student’s
Individualized Educational Plan (I. E. P.).
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
Adaptations may include but not be limited to
and exploring
extended time on tests and assignments,
other software computer
preferential
seating, before- and-after school help, or modified programs to discover how
people live and work in the
homework assignment
business world, as well as
in
their own lives today.
Using some of the other
topics that were taught in
the Algebra II course,
students will have the
opportunity to do a variety
of projects that will
challenge their intellect.
Algebra II Level 3 – High School
Page 6
Approx. Time Allotment:
Remediation Strategies
Remediation strategies
may include beforeand/or -after school help,
extra-credit projects, test
corrections, &
Mu Alpha Theta
tutoring...
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
-6-
November 2003
Essential Question, Concept or Theme: C. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.F,2.5.11.A-C,2.8.11.K,2.8.11.L,N,2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark 1: Identify functions through
graphing procedures.
Skill Set
a. Define and explain the following: ordered
pairs, coordinate system, Cartesian
coordinate
plane ,x-axis, y-axis, origin, quadrant,
relation, domain, range, mapping, function,
vertical line test, and a continuous function
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Benchmark 2: Determine values of functions
for a given set of data.
Skill Set
a. Use values from the domain to find values
for the range
Tests, quizzes, midterm
exam, and a cumulative
final exam.
Algebra II-Integration,
Applications & Connections Glance / McGraw-Hill, 1998
Optional forms of
assessment:
Ti -81 graphing calculators and
overhead view screen.
Homework, projects, teacher
observation in the classroom,
oral assessment,
performance assessment,
groupactivities, or board
work
Benchmark 3: Use graphing calculator to
determine graphs of linear equations
Skill Set
a. Explain & demonstrate the use of the
graphing calculator by drawing linear equations.
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 Penncrest
Math Office.
Instructional Strategies
Optional instructional strategies
may include:
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: Identify and graph by hand
equations that are linear.
Skill Set
a. Define & identify equations with dependent
and independent variables
b. Identify and demonstrate procedure for
graphing linear equations.
c. Identify and graph linear functions
Algebra II Level 3 – High School
Page 7
-7-
November 2003
Essential Question, Concept or Theme: C. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.F,2.5.11.A-C,2.8.11.K,2.8.11.L,N,2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Instructional Strategies
Benchmark 5: Write equations in standard
form.
Skill Set
a. Explain procedure of writing linear
equations in standard form.
Benchmark 6:Determine the x- and -y
intercepts of a line. Illustrate the ordered pair by
graphing equations.
Skill Set
a. Explain procedure for identifying problems
that involve the x- and -y intercepts
b. Demonstrate procedure that determines the
x- intercept by setting y = 0.
c. Demonstrate procedure that determines the
y- intercept by setting x = 0.
Benchmark 7:Determine the slope of a line.
Skill Set
a. Using formula to determine slope: m =
b. Demonstrate procedure that determine lines
that have a positive slope, negative
slope, zero
slope or undefined slope.
Benchmark 8: Use slope and a point to graph
an equation.
Skill Set
a Locate a point on the coordinate plane then
use the slope to identify the second point on the
graph.
Algebra II Level 3 – High School
Page 8
-8-
November 2003
Essential Question, Concept or Theme: C. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.F,2.5.11.A-C,2.8.11.K,2.8.11.L,N,2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Instructional Strategies
Benchmark 9: Determine & recognize that two
lines are parallel, perpendicular, or neither
Skill Set
a. Define and explain that parallel lines have
the same slope, and that perpendicular lines
have
slopes that are negative reciprocals..
Benchmark 10: Write an equation of a line that
is in the slope-intercept form .
Skill Set
a. Use formula: y = m x + b to write equations
of a line when the slope and a point are
given.
b. Explain and demonstrate the four- step
procedure to write a linear equation when
only two
points are given.
Benchmark 11: Write an equation of a line
using a different point-slope form.
Benchmark 12: Write equations of a line that
are parallel or perpendicular.
Skill Set
a. Explain problem solving techniques that
involve parallel lines that have the same
slope and
perpendicular lines that have slopes that are
negative reciprocals.
Algebra II Level 3 – High School
Page 9
-9-
November 2003
Essential Question, Concept or Theme: C. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.F,2.5.11.A-C,2.8.11.K,2.8.11.L,N,2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Instructional Strategies
Benchmark 13: Identify and graph special
functions.
a. Define and explain direct variation, constant
and identity variables.
b. Determine the greatest integer and / or
absolute value functions through problem
solving techniques.
Benchmark 14: Illustrate graphs of
inequalities in two variables.
Skill Set
a. Demonstrate procedure by shading the
solution set of two inequalities that are
represented by either a solid or broken line
which forms the boundaries of the graphs
depending on the inequalities involved.
Algebra II Level 3 – High School
Page 10
- 10 -
November 2003
Essential Question, Concept or Theme: C. Linear Relations and Functions
PA Standards: 2.1.11.A,2.2.11.F,2.5.11.F,2.5.11.A-C,2.8.11.K,2.8.11.L,N,2.8.11.O,P,Q,T
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s
Individualized Educational Plan (I. E. P.).
Adaptations may include but not be limited
to extended time on tests and assignments,
preferential
seating, before- and-after school help, or modified
homework assignment
Algebra II Level 3 – High School
Enrichment Strategies
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
and exploring
other software computer
programs to discover how
people live and work in the
business world, as well as
in their own lives today.
Using some of the other
topics that were taught in
the Algebra II course,
students will have the
opportunity to do a variety
of projects that will
challenge their intellect.
Page 11
Remediation Strategies
Remediation strategies may
include before-and/or -after
school help, extra-credit
projects, test corrections, &
Mu Alpha Theta tutoring...
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 11 -
November 2003
Essential Question, Concept or Theme: D. Systems of Linear Equations and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5. 11. A- C, 2.8. 11. F, G, H, 2.8.11.J, 2.8.11.K
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark 1:Solve systems of
equations by graphing.
Skill Set
a. Identify and demonstrate procedure
of finding the solution set of
overlapping regions
between two graphs.
b. Identify & demonstrate procedure of
finding problems that are consistent
or inconsistent
systems ,as well as those that are
dependent or independent systems.
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Tests, quizzes, midterm
exam, and a cumulative final
exam.
Algebra II-Integration,
Applications & Connections Glance / McGraw-Hill, 1998
Optional forms of
assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment,
performance assessment,
groupactivities, or board
work.
Ti -81 graphing calculators and
overhead view screen.
Benchmark 2:Use the substitution and
elimination methods to solve systems of
equations.
Skill Set
a. Explain & demonstrate the procedure
of using the substitution method.
b. Explain & demonstrate the procedure
of using the elimination method.
Instructional Strategies
Optional instructional strategies
may include:
Optional Resources:
Group work, or any variety of
Teacher resource materials
classroom activities such as “ List,
associated with the text.
Pass, Amass”, “Each one ,teach
Computer software applications for one”, etc.As suggested by the
classroom demonstration or
Professional Development
individual student exploration.
Coordinator.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Benchmark 3: Find values of 2nd order
determinants.
Skill Set
a. Define and explain problem solving
techniques that involve determinants,
elements, and second order determinants
by using a given form.
Algebra II Level 3 – High School
Page 12
- 12 -
November 2003
Essential Question, Concept or Theme: D. Systems of Linear Equations and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5. 11. A- C, 2.8. 11. F, G, H, 2.8.11.J, 2.8.11.K
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Instructional Strategies
Benchmark 4: Solve systems of
equations using Cramer’s Rule.
Skill Set
a. Explain & demonstrate procedure of
using Cramer’s rule.
Benchmark 5: Solve a system of three
equations in three variables.
Skill Set
a. Identify, locate, and explain problem
solving techniques that involve ordered
triple (x, y, z)
Algebra II Level 3 – High School
Page 13
- 13 -
November 2003
Essential Question, Concept or Theme: D. Systems of Linear Equations and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5. 11. A- C, 2.8. 11. F, G, H, 2.8.11.J, 2.8.11.K
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 (I. E. P.).
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
and exploring
other software computer
programs to discover how
people live and work in the
business world, as well as in
their own lives today. Using
some of the other topics that
were taught in the Algebra
II course, students will have
the opportunity to do a
variety of projects that will
challenge their intellect.
Remediation strategies may
include before-and/or -after
school help, extra-credit
projects, test corrections, &
Mu Alpha Theta tutoring...
Adaptations may include but not be limited to
extended time on tests and assignments,
preferential
seating, before- and-after school help, or
modified homework assignment
Algebra II Level 3 – High School
Page 14
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 14 -
November 2003
Essential Question, Concept or Theme: E. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A- C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 1: Add, subtract, multiply,
and divide polynomials.
Skill Set
a. Identify & explain techniques of
solving problems that involve like
terms, polynomial,
monomial, binomial, trinomial,
constant, coefficient, degree, and power.
b Explain & demonstrate rules for
multiplying and dividing exponents.
c. Explain & identify procedure of using
the distributive property with FOIL’s
method.
d. Demonstrate and explain the use of
the long division method for dividing
polynomials.
Benchmark 2:Use synthetic division to
divide polynomials.
Skill Set
a. Use the step-by-step process to
explain problem solving techniques of
synthetic division.
Benchmark 3: Represent an expression
with a negative exponent using an
equivalent expression with a positive
exponent.
Skill Set
a. Illustrate the given form.
Algebra II Level 3 – High School
Page 15
- 15 -
November 2003
Essential Question, Concept or Theme: E. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A- C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 4:Represents numbers in
scientific notation.
Skill Set
a. Recognize & demonstrate procedure
of writing numbers in scientific notation
form
Benchmark 5: Multiply and divide
exponents written in scientific notation
Skill Set
a. Explain & demonstrate that
multiplying and dividing exponents
can be written in scientific form.
Benchmark 6: Factor polynomials.
Skill Set
a. Demonstrate and explain the problem
solving technique that involve
greatest common factor,
perfect square trinomial, difference of
two squares, sum or difference of two
cubes, prime number, and prime
expression.
Benchmark 7: Use factoring to simplify
polynomial quotients.
Skill Set
a. Explain & demonstrate process of
factoring and dividing out common
factors.
Algebra II Level 3 – High School
Page 16
- 16 -
November 2003
Essential Question, Concept or Theme: E. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A- C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 8: Simplify radicals having
various indices .
Skill Set
a. Explain procedure that involve
problems of the various indices ( 2nd
root, 3rd root, 4th root,
etc.)
Benchmark 9: Simplify Radical
Expressions
Benchmark 10: Rationalizing
denominators of fractions that contain
radical expressions
Skill Set
a. Demonstrate & explain the process
by using a step-by-step technique.
Benchmark 11: Add , subtract ,
multiply , and divide radical expressions.
Skill Set
a. Explain techniques of problem
solving using like terms.
Benchmark 12: Write expressions with
rational exponents in simplified radical
form and vice versa.
Skill Set
a. Use standard form to demonstrate
process of reducing radicals to lowest
trems.
Algebra II Level 3 – High School
Page 17
- 17 -
November 2003
Essential Question, Concept or Theme: E. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A- C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 13: Evaluate expressions in
either exponential or radical form.
Skill Set
a. Explain and demonstrate procedure
of evaluating expressions in exponential
form.
b. Explain and demonstrate procedure
of evaluating expressions in radical
form.
Benchmark 14: Recognize & identify
equations and inequalities that contain
radicals.
Skill Set
a.
Explain and demonstrate the
technique of squaring terms that
are contained on both sides of an
equation
b.
Define and identify extraneous
solutions
Benchmark 15: Simplify square roots
containing negative radicands.
Skill Set
a. Rewrite the value of the square root
of negative one as the imaginary number,
(i)
b. Explain techniques of solving
problems using Imaginary numbers.
Algebra II Level 3 – High School
Page 18
- 18 -
November 2003
Essential Question, Concept or Theme: E. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A- C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 16: Solve quadratic
equations that have pure imaginary
solutions.
Skill Set
a. Use quadratic equations to determine
pure imaginary solutions.
Benchmark 17: Add , subtract , and
multiply complex numbers.
Skill Set
a. Demonstrate and illustrate technique
of writing complex numbers in the form
of a + bi
b. Define & identify “a” as the real part,
and “bi”as the imaginary part of a
complex number
c. Use a Venn diagram to illustrate the
relationship between complex, real,
imaginary
numbers, and all the subsets of real
numbers.
Benchmark 18: Simplify expressions
containing complex numbers in the
denominator.
Skill Set
a. Identify and explain procedure of
determining the complex conjugate for a
complex number.
Algebra II Level 3 – High School
Page 19
- 19 -
November 2003
Essential Question, Concept or Theme: E. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 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 (I. E. P.).
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
and exploring other
software computer
programs to discover how
people live and work in the
business world, as well as in
their own lives today. Using
some of the other topics that
were taught in the Algebra
II course, students will have
the opportunity to do a
variety of projects that will
challenge their intellect.
Remediation strategies may
include before-and/or -after
school help, extra-credit
projects, test corrections, &
Mu Alpha Theta tutoring...
Adaptations may include but not be limited to extended
time on tests and assignments, preferential seating,
before- and-after school help, or modified homework
assignment
Algebra II Level 3 – High School
Page 20
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 20 -
November 2003
Essential Question, Concept or Theme: F. 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
Benchmark 1: Identify techniques of writing functions
in quadratic form.
Skill Set
a. Explain and demonstrate process of writing
functions in the quadratic form
b. Define and identify quadratic, linear and constant
terms.
Assessment
Tests, quizzes,
midterm exam, and a
cumulative final
exam.
Optional forms of
assessment:
Homework, projects,
Benchmark 2: Graph quadratic functions
teacher observation
Skill Set
in the classroom,
a. Define and identify the shape of a parabola, the axis oral assessment,
of symmetry, vertex and the zero functions.
performance
assessment,
Benchmark 3: Solve quadratic equations by graphing
groupactivities, or
Skill Set
board work.
a. Demonstrate and identify the zero functions as the
x- intercepts
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Instructional Strategies
Algebra II-Integration,
Applications & Connections
- Glance / McGraw-Hill,
1998
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Ti -81 graphing calculators
and overhead view screen.
Optional instructional strategies
may include:
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.
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
Penncrest Math Office.
Benchmark 4: Solve quadratic equations by factoring
Skill Set
a. Use factoring techniques to determine the greatest
common factor, difference of two squares, and the
process of FOILs ”backwards” to factor expressions
that are in quadratic form
Benchmark 5: Solve quadratic equations by
completing the square.
Skill Set
a. Explain and demonstrate the process of completing
the square to write a quadratic equation.
Algebra II Level 3 – High School
Page 21
- 21 -
November 2003
Essential Question, Concept or Theme: F. 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
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Instructional Strategies
Benchmark 6: Solve quadratic equations by using the
quadratic formula: x=
Skill Set
a. Demonstrate and explain the use of the quadratic
formula to determine solutions.
Benchmark 7: Use the discriminant to determine the
nature of the roots of a quadratic equation.
Benchmark 8: Find the distance between any two
points on a line
Skill Set
a. Use formula to solve problems to find the distance
between any two points.
Benchmark 9: Find the midpoint of a line segment in
the coordinate plane.
Skill Set
a. Use formula to solve problems to find the
midpoint of a line segment.
Note: All other topics that are contained in this section will be
taught on an optional basis for the level 3 student...
Algebra II Level 3 – High School
Page 22
- 22 -
November 2003
Essential Question, Concept or Theme: F. 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 (I. E. P.).
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
and exploring other
software computer
programs to discover how
people live and work in the
business world, as well as in
their own lives today. Using
some of the other topics that
were taught in the Algebra
II course, students will have
the opportunity to do a
variety of projects that will
challenge their intellect.
Remediation strategies may
include before-and/or -after
school help, extra-credit
projects, test corrections, &
Mu Alpha Theta tutoring...
Adaptations may include but not be limited to extended
time on tests and assignments, preferential seating,
before- and-after school help, or modified homework
assignment
Algebra II Level 3 – High School
Page 23
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 23 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11A- C, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Benchmark 1: Determine
polynomial functions .
Skill Set
a. Define and identify polynomial
functions.
Benchmark 2: Identify general
shapes of the graphs of polynomial
functions
Skill Set
a. Define and identify the shapes of
graphs of polynomial functions
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, midterm exam,
and a cumulative final exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, groupactivities, or
board work.
Benchmark 3: Use the factor
theorem and the synthetic division
process to determine factors of
polynomials.
Skill Set
a. Demonstrate and explain the
procedure of dividing a
polynomial using synthetic
division by
other polynomials to determine
whether the polynomial is a
factor of the first polynomial.
Algebra II-Integration,
Applications & Connections Glance / McGraw-Hill, 1998
Instructional Strategies
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Ti -81 graphing calculators and
overhead view screen.
Optional instructional strategies
may include:
Optional Resources:
Group work, or any variety of
Teacher resource materials
classroom activities such as “ List,
associated with the text.
Pass, Amass”, “Each one, teach
Computer software applications for one”, etc. As suggested by the
classroom demonstration or
Professional Development
individual student exploration.
Coordinator.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Benchmark 4: Determine the number
of zeros that are contained in a
polynomial function.
Algebra II Level 3 – High School
Page 24
- 24 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11A- C, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Skill Set
a. Demonstrate the use of Descartes’
rule of signs to determine the number
of rational zero functions.
Benchmark 5:Use the rational zero
theorem to identify all possible
rational zeros of a polynomial
function
Skill Set
a. Locate and identify rational
solutions of polynomial functions
Benchmark 6:Solve equations that
are quadratic in form
Skill set
a. 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: Determine the inverse
of a function or a relation
Skill Set
a. Replace y with x and x with y in
the equation and solve for y to
find the inverse of a function
Algebra II Level 3 – High School
Page 25
- 25 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11A- C, 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 (I. E. P.).
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
and exploring other
software computer
programs to discover how
people live and work in the
business world, as well as in
their own lives today. Using
some of the other topics that
were taught in the Algebra
II course, students will have
the opportunity to do a
variety of projects that will
challenge their intellect.
Remediation strategies may
include before-and/or -after
school help, extra-credit
projects, test corrections, &
Mu Alpha Theta tutoring...
Adaptations may include but not be limited to extended
time on tests and assignments, preferential seating,
before- and-after school help, or modified homework
assignment
Algebra II Level 3 – High School
Page 26
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 26 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.A- C, 2.8.11.T ,2.11.11.A
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark 1: Demonstrate problems
that involve direct, inverse, and joint
varitions.
Skill Set
a. Define and identify problems about
direct, inverse, and joint variations.
Tests, quizzes, midterm exam,
and a cumulative final exam.
Benchmark 2: Simplify rational
expressions
Skill Set
a. Demonstrate and explain basic
algebraic manipulations to simplify a
rational expression .
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, groupactivities, or
board work.
Benchmark 3: Simplify complex
fractions.
Skill Set
a. Explain and identify the use of the
rule of multiplying a denominator
by its conjugate to
simplify complex fractions
Algebra II-Integration,
Applications & Connections Glance / McGraw-Hill, 1998
Ti -81 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 Penncrest
Math Office.
Instructional Strategies
Instructional strategies by the
teacher will include:
Lecture, demonstration, review,
graphing calculator activities.
Optional instructional strategies
may include:
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: Add and subtract
rational expressions.
Skill Set
a. Demonstrate procedure of rewriting
the expressions with a common
denominator, before
adding and/or subtracting rational
expressions.
Algebra II Level 3 – High School
Page 27
- 27 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.A- C, 2.8.11.T ,2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 6: Solve rational equations
and inequalities.
Skill Set
a. Identify process of multiplying
both sides of an equation by the
least common denominator
before solving for a particular
variable.
Note: All topics that are included in this section
will be taught to the level 3 students based upon
the opportunity of having the time to learn
about sequences and series...
Algebra II Level 3 – High School
Page 28
- 28 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.A- C, 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 (I. E. P.).
Students may wish to
independently research
some of the topics, as
mentioned on the Internet,
and exploring other
software computer
programs to discover how
people live and work in the
business world, as well as in
their own lives today. Using
some of the other topics that
were taught in the Algebra
II course, students will have
the opportunity to do a
variety of projects that will
challenge their intellect.
Remediation strategies may
include before-and/or -after
school help, extra-credit
projects, test corrections, &
Mu Alpha Theta tutoring...
Adaptations may include but not be limited to extended
time on tests and assignments, preferential seating,
before- and-after school help, or modified homework
assignment
Algebra II Level 3 – High School
Page 29
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications which connect the
math topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 29 -
November 2003