ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: Geometry – Level 3
GRADE LEVEL: High School
CREATION DATE: November 2003
Essential Question, Concept or Theme: A. Points, Lines, Planes, and Angles
PA Standards: 2.1.11.A, 2.2.11.A, 2.2.11.B, 2.3.11.A, 2.3.11.B, 2.3.11.C, 2.5.11.B, 2.5.11.C, 2.8.11.D
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark #1 – The student will
demonstrate a knowledge and understanding
of points, lines, planes, angles, and their
relationships.
Skills:
a) Understand and use the three undefined
terms of geometry – point, line, plane
b) Draw representations of points, lines and
planes
c) Identify and name segments, rays,
distance
d) Identify and name angles; group angles
by type
e) Use the terms collinear, coplanar, and
intersection
f) Understand and apply basic postulates
involving points, lines, and planes.
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work,
group projects, graphing calc.
activities, individual projects,
midterm and final exams,
Truth Tables packet, and
Transformation Packet.
Page 1
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product (optional)
TI-83 or similar graphing
calculator (optional)
Geometry Sketchpad (optional)
Protractor, compass, and
straightedge
Numerous internet websites to
be recommended by teacher
Approx. Time Allotment:
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
-1-
November 2003
Essential Question, Concept or Theme: A. Points, Lines, Planes, and Angles
PA Standards: 2.1.11.A, 2.2.11.A, 2.2.11.B, 2.3.11.A, 2.3.11.B, 2.3.11.C, 2.5.11.B, 2.5.11.C, 2.8.11.D
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized Education
Plan.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Approx. Time Allotment:
Enrichment Strategies
Remediation Strategies
Students may pursue independent
study on any topic in the textbook.
Suggestions of topics and where to
research them will be made
throughout the school year. The
student will have an organizational
meeting with the teacher in order to
better prepare himself regarding how
to approach the study of his selected
topic. Examples of independent
study topics include: Lives and
Works of Famous Mathematicians,
Famous Problems, Careers in
Mathematics, other topics or
branches of mathematics (e.g.
Topology, Analysis, Linear
Programming, Tessellations,
Matrices, Logic and Truth Tables.)
Students may take advantage
of before- or after-school
help, supplementary problem
worksheets, Mu Alpha Theta
tutors, test corrections, and
extra credit projects.
Page 2
-2-
Multicultural/Interdisciplinary
Connection
November 2003
Essential Question, Concept or Theme: B. Deductive Reasoning
PA Standards: 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.4.11.D, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark #1 – The student will use
deductive reasoning to give logical
arguments.
Skills:
a) Recognize the hypothesis and
conclusion of a conditional
statement
b) State the converse, inverse, and
contrapositive of a conditional
statement
c) Use a counterexample to disprove a
conditional statement
d) Understand the meaning of if and
only if
e) Use properties from algebra and
properties of congruence in proofs
f) Use the Midpoint Theorem and the
Angle Bisector Theorem
g) Know the kinds of reasons that can
be used in proofs
h) Apply the definitions of
complementary and supplementary
angles
i) State and use the theorem about
vertical angles
j) Apply the definition and theorems
about perpendicular lines
k) Plan proofs and then write them in
two-column form (optional)
l) Plan and use the method of indirect
proof (optional)
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and quizzes,
homework assignments, board
work, group projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and Transformation
Packet.
Page 3
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites
to be recommended by
teacher
Instructional Strategies
-3-
November 2003
Essential Question, Concept or Theme: B. Deductive Reasoning
PA Standards: 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.4.11.D, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
m) Use truth tables to reveal the logic of
mathematical statements
Geometry, Level 3 – High School
Page 4
Approx. Time Allotment:
Instructional Strategies
-4-
November 2003
Essential Question, Concept or Theme: B. Deductive Reasoning
PA Standards: 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.4.11.D, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D
Adaptations/Inclusion Techniques
Enrichment Strategies
Adaptations for students with special instructional
needs will be met in accordance with each student’s
Individualized Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them
will be made throughout
the school year. The
student will have an
organizational meeting
with the teacher in order to
better prepare himself
regarding how to approach
the study of his selected
topic. Examples of
independent study topics
include: Lives and Works
of Famous
Mathematicians, Famous
Problems, Careers in
Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Adaptations may include but are not limited to
extended time on tests and assignments, preferential
seating, after-school help, or modified homework
assignments.
Geometry, Level 3 – High School
Page 5
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra
credit projects.
-5-
November 2003
Essential Question, Concept or Theme: C. Parallel Lines and Planes
PA Standards: 2.4.11.A, 2.4.11.B, 2.5.11.B, 2.5.11.C, 2.8.11.A, 2.8.11.D, 2.8.11.G, 2.9.11.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark #1 – The student will
demonstrate an understanding of
parallel lines and resultant situations
Skills:
a) Distinguish between intersecting,
parallel, and skew lines
b) State and apply the theorem about
the intersection of two parallel
planes by a third plane
c) Identify the angles formed when
two lines are cut by a transversal
d) State and apply postulates and
theorems about parallel lines
e) State and apply the theorems about
a parallel and a perpendicular to a
given line through a point outside
the line
f) Classify triangles according to
sides and angles
g) State and apply the theorem and
the corollaries about the sum of the
measures of a triangle
h) Recognize and name specific types
of convex polygons and regular
polygons
i) Find the measures of interior and
exterior angles of convex polygons
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Page 6
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
-6-
November 2003
Essential Question, Concept or Theme: C. Parallel Lines and Planes
PA Standards: 2.4.11.A, 2.4.11.B, 2.5.11.B, 2.5.11.C, 2.8.11.A, 2.8.11.D, 2.8.11.G, 2.9.11.A
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized Education
Plan.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Enrichment Strategies
Remediation Strategies
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them
will be made throughout
the school year. The
student will have an
organizational meeting
with the teacher in order to
better prepare himself
regarding how to approach
the study of his selected
topic. Examples of
independent study topics
include: Lives and Works
of Famous
Mathematicians, Famous
Problems, Careers in
Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take advantage
of before- or after-school
help, supplementary problem
worksheets, Mu Alpha Theta
tutors, test corrections, and
extra credit projects.
Page 7
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
-7-
November 2003
Essential Question, Concept or Theme: D. Congruent Triangles
PA Standards: 2.4.11.A, 2.4.11.B, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.G 2.9.11.B, 2.9.11.D
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark #1 – The student will
identify pairs of congruent triangles
Skills:
a) Identify corresponding parts of
congruent figures
b) Prove two triangles are congruent
by using the SSS, SAS, and ASA
Postulates
c) Deduce information about
segments and angles after proving
that two triangles are congruent
d) Apply the theorems and
corollaries about isosceles
triangles
e) Use the AAS and HL theorems to
prove that two triangles are
congruent
f) Prove that two overlapping
triangles are congruent (optional)
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework assignments,
board work, group projects,
graphing calc. activities,
individual projects, midterm and
final exams, Truth Tables
packet, and Transformation
Packet.
Page 8
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
-8-
November 2003
Essential Question, Concept or Theme: D. Congruent Triangles
PA Standards: 2.4.11.A, 2.4.11.B, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.G 2.9.11.B, 2.9.11.D
Adaptations/Inclusion Techniques
Enrichment Strategies
Adaptations for students with special instructional Students may pursue
needs will be met in accordance with each
independent study on any
student’s Individualized Education Plan.
topic in the textbook.
Suggestions of topics and
Adaptations may include but are not limited to
where to research them will
extended time on tests and assignments,
be made throughout the
preferential seating, after-school help, or
school year. The student
modified homework assignments.
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Geometry, Level 3 – High School
Page 9
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
-9-
November 2003
Essential Question, Concept or Theme: E. Quadrilaterals
PA Standards: 2.4.11.A, 2.4.11.B, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.9.11.A, 2.9.11.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark #1 – The student will
identify quadrilaterals by type and
name characteristics of each type.
Skills:
a) Use the definition and theorems
about parallelograms to name
characteristics of parallelograms
b) Prove that certain quadrilaterals
are parallelograms
c) Apply theorems about parallel
lines and the segment that joins
the midpoints of two sides of a
triangle
d) Identify the special properties of a
rectangle, rhombus, and square
e) Determine when a parallelogram
is a rectangle, rhombus, or square
f) Identify the properties of a
trapezoid and an isosceles
trapezoid
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework assignments,
board work, group projects,
graphing calc. activities,
individual projects, midterm and
final exams, Truth Tables
packet, and Transformation
Packet.
Page 10
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
- 10 -
November 2003
Essential Question, Concept or Theme: E. Quadrilaterals
PA Standards: 2.4.11.A, 2.4.11.B, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.9.11.A, 2.9.11.C
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 Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 11
Multicultural/Interdisciplinary
Connection
- 11 -
November 2003
Essential Question, Concept or Theme: F. Geometric Inequalities; Indirect Proof
Approx. Time Allotment:
PA Standards: 2.1.11.D, 2.1.11.E, 2.4.11.A, 2.4.11.B, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.A, 2.8.11.B, 2.8.11.C
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
Optional
Benchmark #1 – The student will express geometric
Assessments could include: TEXTBOOK: Geometry –
Lecture, demonstration, class
inequalities, and will understand and apply the concept teacher-produced tests and McDougall Littell,
review, group work,
of indirect reasoning
quizzes, homework
Houghton Mifflin, @1997.
cooperative learning, working
Skills:
assignments, board work,
BoxerMath Product
with manipulatives
a) Apply properties of inequality to positive numbers, group projects, graphing
TI-83 or similar graphing
(protractor, compass,
lengths of segments, and measures of angles
calc. activities, individual
calculator
straightedge, two- and threeb) State the contrapositive and inverse of a conditional projects, midterm and final Geometry Sketchpad
dimensional models of
statement
exams, Truth Tables
Protractor, compass, and
geometric figures), computer
c) Understand the relationship between logically
packet, and Transformation straightedge
programs (i.e. Sketchpad).
equivalent statements
Packet.
Numerous internet websites Strategy to be determined by
d) Draw correct conclusions from given statements
to be recommended by
the teacher. In addition, each
e) Write indirect proofs in paragraph form
teacher
student will be required to
f) State and apply theorems about inequalities in one
complete a major project each
triangle and inequalities in two triangles
marking period; the general
context of the project will be
assigned by the teacher,
however the specific topic
will be chosen by the student.
Geometry, Level 3 – High School
Page 12
- 12 -
November 2003
Essential Question, Concept or Theme: F. Geometric Inequalities; Indirect Proof
Approx. Time Allotment:
PA Standards: 2.1.11.D, 2.1.11.E, 2.4.11.A, 2.4.11.B, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.A, 2.8.11.B, 2.8.11.C
Multicultural/Interdisciplinary
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Connection
Adaptations for students with special instructional Students may pursue
needs will be met in accordance with each
independent study on any
student’s Individualized Education Plan.
topic in the textbook.
Suggestions of topics and
Adaptations may include but are not limited to
where to research them will
extended time on tests and assignments,
be made throughout the
preferential seating, after-school help, or
school year. The student
modified homework assignments.
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Geometry, Level 3 – High School
Page 13
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
- 13 -
November 2003
Essential Question, Concept or Theme: G. Similar Polygons
Approx. Time Allotment:
PA Standards: 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.A, 2.8.11.B, 2.8.11.C, 2.9.11.G, 2.9.11.J
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
Benchmark #1 – The student will
define and identify similar polygons
Skills:
a) Express a ratio in simplest form
b) Solve for an unknown term in a
proportion
c) Express a given proportion in
equivalent form
d) State and apply properties of
similar polygons
e) Prove triangles are similar using
the AA, SAS, and SSS similarity
postulates and theorems
f) Use similar triangles to deduce
information about segments or
angles
g) Apply the Triangle
Proportionality Theorem and the
Triangle Angle-Bisector Theorem
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework assignments,
board work, group projects,
graphing calc. activities,
individual projects, midterm and
final exams, Truth Tables
packet, and Transformation
Packet.
Page 14
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 14 -
November 2003
Essential Question, Concept or Theme: G. Similar Polygons
Approx. Time Allotment:
PA Standards: 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.A, 2.8.11.B, 2.8.11.C, 2.9.11.G, 2.9.11.J
Multicultural/Interdisciplinary
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Connection
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Education Plan.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Page 15
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
- 15 -
November 2003
Essential Question, Concept or Theme: H. Right Triangles
Approx. Time Allotment:
PA Standards: 2.1.11.A, 2.2.11.A, 2.2.11.B, 2.2.11.F, 2.5.11.B, 2.5.11.C, 2.8.11.A, 2.8.11.D, 2.9.11.A, 2.9.11.D, 2.10.11.B
Aligned Materials/
Benchmark/Skills
Assessment
Instructional Strategies
Resources/Technology
Benchmark #1 – The student will
understand and apply the basic
theorems of right triangles
Skills:
a) Determine the geometric mean
between two numbers
b) State and apply the relationships
that exist when the altitude is
drawn to the hypotenuse of a right
triangle
c) State and apply the Pythagorean
Theorem
d) State and apply the converse of
the Pythagorean Theorem
e) Determine the lengths of two
sides of a 45-45-90 triangle
f) Determine the lengths of two
sides of a 30-60-90 triangle
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework assignments,
board work, group projects,
graphing calc. activities,
individual projects, midterm and
final exams, Truth Tables
packet, and Transformation
Packet.
Page 16
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 16 -
November 2003
Essential Question, Concept or Theme: : H. Right Triangles
Approx. Time Allotment:
PA Standards: 2.1.11.A, 2.2.11.A, 2.2.11.B, 2.2.11.F, 2.5.11.B, 2.5.11.C, 2.8.11.A, 2.8.11.D, 2.9.11.A, 2.9.11.D, 2.10.11.B
Multicultural/Interdisciplinary
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Connection
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Education Plan.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Page 17
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
- 17 -
November 2003
Essential Question, Concept or Theme: I. Circles
PA Standards: 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.8.11.G, 2.9.11.A, 2.9.11.E, 2.9.11.F
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark #1 – The student will
understand, and apply theorems about
circles.
Skills:
a) Define a circle, sphere, and terms
related to them
b) Recognize circumscribed and
inscribed polygons and circles
c) Apply theorems that relate tangents
and radii
d) Define and apply properties of arcs
and central angles
e) Apply theorems about the chords of
a circle
f) Solve problems and prove
statements involving inscribed
angles
g) Solve problems and prove
statements involving angles formed
by chords, secants, and tangents
h) (optional)Solve problems involving
lengths of chords, secant segments,
and tangent segments
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Geometry, Level 3 – High School
Approx. Time Allotment:
Page 18
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 18 -
November 2003
Essential Question, Concept or Theme: I. Circles
PA Standards: 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.8.11.G, 2.9.11.A, 2.9.11.E, 2.9.11.F
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 Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 19
Multicultural/Interdisciplinary
Connection
- 19 -
November 2003
Essential Question, Concept or Theme: J. Areas of Plane Figures
PA Standards: 2.3.11.A, 2.5.11.A, 2.5.11.B, 2.9.11.A, 2.9.11.I
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark #1 – The student will
understand the concept of area, and will
calculate areas of polygons and circles
using the appropriate formula
Skills:
a) Find the area of squares, and
rectangles
b) Find the area of irregular rectangular
regions using the Area Addition
Postulate
c) Find the area of parallelograms,
triangles, and rhombuses
d) Find the area of trapezoids
e) Find the circumference and area of
circles
f) Find the arc length and area of a
sector of a circle
g) Find the areas of shaded regions
formed by inscribed and
circumscribed circles
h) Understand and apply the theorem
regarding ratio of areas in reference
to similar figures
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Geometry, Level 3 – High School
Page 20
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 20 -
November 2003
Essential Question, Concept or Theme: J. Areas of Plane Figures
PA Standards: 2.3.11.A, 2.5.11.A, 2.5.11.B, 2.9.11.A, 2.9.11.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 Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 21
Multicultural/Interdisciplinary
Connection
- 21 -
November 2003
Essential Question, Concept or Theme: K. Areas and Volumes of Solids
PA Standards: 2.3.11.A, 2.4.11.E, 2.5.11.A, 2.9.11.A, 2.9.11.I
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark #1 – The student will
understand the concepts of volume and
area of solids and will calculate volume
and area with appropriate formulas.
Skills:
a) Identify parts of prisms, pyramids,
cylinders, and cones
b) Find the lateral areas, total areas, and
volumes of right prisms and regular
pyramids
c) Find the lateral areas, total areas, and
volumes or right circular cylinders
and right cones
d) Find the area and volume of a sphere
e) State and apply the properties of
similar solids
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Geometry, Level 3 – High School
Approx. Time Allotment:
Page 22
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 22 -
November 2003
Essential Question, Concept or Theme: K. Areas and Volumes of Solids
PA Standards: 2.3.11.A, 2.4.11.E, 2.5.11.A, 2.9.11.A, 2.9.11.I
Adaptations/Inclusion Techniques
Enrichment Strategies
Adaptations for students with special instructional Students may pursue
needs will be met in accordance with each
independent study on any
student’s Individualized Education Plan.
topic in the textbook.
Suggestions of topics and
Adaptations may include but are not limited to
where to research them will
extended time on tests and assignments,
be made throughout the
preferential seating, after-school help, or
school year. The student
modified homework assignments.
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Geometry, Level 3 – High School
Page 23
Approx. Time Allotment:
Remediation Strategies
Multicultural/Interdisciplinary
Connection
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
- 23 -
November 2003
Essential Question, Concept or Theme: L.Transformations
PA Standards: 2.9.11.J, 2.9.11.H
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark #1 – The student will
recognize and understand basic
transformations
Skills:
a) Recognize and use the terms image,
preimage, mapping, one-to-one
mapping, transformation, isometry,
and congruence mapping
b) Locate images of figures by
reflection, translation, glide
reflection, rotation, and dilation
c) Recognize the properties of basic
mappings
d) Locate the images of figures by
composites of mappings
e) Recognize and use the terms identity
and inverse in relation to mappings
f) Describe symmetry of figures and
solids
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Geometry, Level 3 – High School
Page 24
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 24 -
November 2003
Essential Question, Concept or Theme: L.Transformations
PA Standards: 2.9.11.J, 2.9.11.H
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 Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 25
Multicultural/Interdisciplinary
Connection
- 25 -
November 2003
Essential Question, Concept or Theme: M. Introductory Trigonometry
PA Standards: 2.1.11.A, 2.2.11.A, 2.2.11.B, 2.2.11.E, 2.2.11.F, 2.3.11.A, 2.3.11.B, 2.9.11.H, 2.10.11.B
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Benchmark #1 – The student will
understand the six trigonometric
functions and use them to solve basic
right triangle problems
Skills:
a) Define the sine, cosine, and tangent
ratios and their reciprocals
b) Solve right triangle problems by
correct selection and use of the sine,
cosine, and tangent ratios
c) Use a trig table or scientific/graphing
calculator to find function values
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
Geometry, Level 3 – High School
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Page 26
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
- 26 -
November 2003
Essential Question, Concept or Theme: M. Introductory Trigonometry
PA Standards: 2.1.11.A, 2.2.11.A, 2.2.11.B, 2.2.11.E, 2.2.11.F, 2.3.11.A, 2.3.11.B, 2.9.11.H, 2.10.11.B
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 27
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
- 27 -
November 2003
Essential Question, Concept or Theme: N. (optional) Constructions
PA Standards: (optional) 2.9.11.A
Benchmark/Skills
Assessment
Benchmark #1 (optional) – The student
will use a compass and straightedge to
perform basic constructions
Skills:
a) Construct a segment of given length
b) Bisect an angle
c) Construct congruent angles
d) Construct a perpendicular bisector
e) Construct a perpendicular to a line at
a given point on the line
f) Construct a perpendicular to a line
through a point not on the line
g) Construct parallel lines
h) Construct a tangent to a circle from a
point on the circle
i) Construct a tangent to a circle from a
point outside the circle
j) Circumscribe a circle about a
triangle
k) Inscribe a circle in a triangle
l) Locate the incenter, circumcenter,
orthocenter, and centroid of a circle
(optional)
m) Divide a segment into a given
number of congruent segments
n) Given three segment, construct a
fourth segment so that the four
segments are in proportion
o) Construct the geometric mean of two
given segments
p) Optional: Construct a nine-point
circle
Assessments could include:
teacher-produced tests and
quizzes, homework
assignments, board work, group
projects, graphing calc.
activities, individual projects,
midterm and final exams, Truth
Tables packet, and
Transformation Packet.
Geometry, Level 3 – High School
Page 28
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
TEXTBOOK: Geometry –
McDougall Littell, Houghton
Mifflin, @1997.
BoxerMath Product
TI-83 or similar graphing
calculator
Geometry Sketchpad
Protractor, compass, and
straightedge
Numerous internet websites to be
recommended by teacher
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 28 -
November 2003
Essential Question, Concept or Theme: N. (optional) Constructions
PA Standards: (optional) 2.9.11.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 Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 29
Multicultural/Interdisciplinary
Connection
- 29 -
November 2003
Essential Question, Concept or Theme: O. (optional) Geometry in the Cartesian Plan
PA Standards: (optional) 2.2.11.C, 2.1.11.A, 2.4.11.A, 2.4.11.B, 2.8.11.J, 2.8.11.K, 2.9.11.L
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
As time allows:
Benchmark #1 (Optional) – The student Assessments could include:
TEXTBOOK: Geometry –
will graph linear equations on the
teacher-produced tests and
McDougall Littell, Houghton
Cartesian Plane, and
quizzes, homework
Mifflin, @1997.
will name the equation of a line, given
assignments, board work, group BoxerMath Product
specific information
projects, graphing calc.
TI-83 or similar graphing
Skills:
activities, individual projects,
calculator
a) State and apply the distance formula midterm and final exams, Truth Geometry Sketchpad
b) State and apply the general equation Tables packet, and
Protractor, compass, and
of a circle
Transformation Packet.
straightedge
c) State and apply the slope formula
Numerous internet websites to be
d) Determine whether two lines are
recommended by teacher
parallel, perpendicular, or neither
e) State and apply the midpoint formula
f) Identify the slope and y-intercept of
a line, given the equation
g) Draw the graph of the line specified
by a given equation
h) Write an equation of the line when
given either one point and the slope,
or two points
i) Determine the point of intersection
of two lines
j) Given a polygon, choose a
convenient placement of coordinate
axes and assign appropriate
coordinates
Optional: Understand the basic
properties of vectors
Geometry, Level 3 – High School
Page 30
Approx. Time Allotment:
Instructional Strategies
Lecture, demonstration, class
review, group work, cooperative
learning, working with
manipulatives (protractor,
compass, straightedge, two- and
three-dimensional models of
geometric figures), computer
programs (i.e. Sketchpad).
Strategy to be determined by the
teacher. In addition, each student
will be required to complete a
major project each marking period;
the general context of the project
will be assigned by the teacher,
however the specific topic will be
chosen by the student.
- 30 -
November 2003
Essential Question, Concept or Theme: O. (optional) Geometry in the Cartesian Plan
PA Standards: (optional) 2.2.11.C, 2.1.11.A, 2.4.11.A, 2.4.11.B, 2.8.11.J, 2.8.11.K, 2.9.11.L
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Education Plan.
Students may pursue
independent study on any
topic in the textbook.
Suggestions of topics and
where to research them will
be made throughout the
school year. The student
will have an organizational
meeting with the teacher in
order to better prepare
himself regarding how to
approach the study of his
selected topic. Examples of
independent study topics
include: Lives and Works of
Famous Mathematicians,
Famous Problems, Careers
in Mathematics, other topics
or branches of mathematics
(e.g. Topology, Analysis,
Linear Programming,
Tessellations, Matrices,
Logic and Truth Tables.)
Students may take
advantage of before- or
after-school help,
supplementary problem
worksheets, Mu Alpha
Theta tutors, test
corrections, and extra credit
projects.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after-school help, or
modified homework assignments.
Geometry, Level 3 – High School
Page 31
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
- 31 -
November 2003
Geometry, Level 3 – High School
Page 32
- 32 -
November 2003