Download Honors Geometry - Chillicothe City Schools

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Honors Geometry Syllabus
CHS Mathematics Department
Contact Information: Parents may contact me by phone, email or visiting the
school.
Teacher: Mr. Seth Moore
Email Address: [email protected]
Phone Number: (740) 702-2287 ext. 16227
Online: http://www.chillicothe.k12.oh.us/schools/chs/
CHS Vision Statement: Our vision is to be a caring learning center respected
for its comprehensive excellence.
CHS Mission Statement: Our mission is to prepare our students to serve
their communities and to commit to life-long learning
Course Description and Prerequisite(s) from Course Handbook:
Honors Geometry -272
State Course # 111200
Prerequisite: Students must have attained a “B+” or better in Algebra I and
teacher approval
Required Option Grade: 9-10
Weighted Grade Credit: 1
This course is design for the advanced math student. It will cover the
same topics as Geometry, with an accelerated pace and expectations of deeper
understanding. In-depth study of two and three-dimensional geometry
including representing problem situations using geometric models, deductive
reasoning, and geometry from an algebraic perspective. The fundamental
purpose of the course in Geometry is to formalize and extend students’
geometric experiences from the middle grades. Students explore more
complex geometric situations and deepen their explanations of geometric
relationships, moving towards formal mathematical arguments. Important
differences exist between this Geometry course and the historical approach
taken in Geometry classes. For example, transformations are emphasized
dearly in this course. Close attention should be paid to the introductory
content for the Geometry conceptual category found in the high school CCSS.
The Mathematical Practice Standards apply throughout each course and,
together with the content standards, prescribe that students experience
mathematics as a coherent, useful, and logical subject that makes use of their
ability to make sense of problem situations.
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Big Ideas/Purpose per Unit and Essential Questions/Concepts per Unit:
Defined below for clarity are the Big Ideas/Purpose of every unit taught
during this course and the essential questions/concepts to be learned to better
understand the Big Ideas/Purpose. A student’s ability to grasp, answer, and
apply the essential questions/concepts will define whether or not he or she
adequately learns the Big Ideas/Purpose and scores well on assessments
given for this course. The Common Core Standards can be found at
http://www.corestandards.org/the-standards.
 1st or 3rd 9 Weeks:
o Unit I: Proof and Parallel and Perpendicular Lines
 Big Idea #1: Prove theorems about lines and angles.
 Essential Question #1: Why is it important to be
able to prove theorems about lines and angles?
 Essential Question #2: How are vertical angles
proven congruent?
 Essential Question #3: What effect does a
perpendicular bisector have on a line segment?
 Essential Question #4: How is a point on a directed
line segment between two given points that
partition the segment in a given ration found?
 Big Idea #2: Prove parallel and perpendicular lines
 Essential Question #1: What can be proven
congruent when parallel lines are cut by a
transversal?
 Essential Question #2: How can the slope criteria
for parallel and perpendicular lines be used to
prove lines are parallel or perpendicular?
 Essential Question #3: How can the equation of a
line parallel or perpendicular to a given line that
passes through a given point be determined?
 Essential Question #4: How are lines proven to be
parallel?
o Unit II: Triangles
 Big Idea #1: Prove theorems about triangles and
congruency in triangles
 Essential Question #1: How are the interior angles
of a triangle proven to measure 180°?
 Essential Question #2: How are two triangles
proven congruent to one another?
 Essential Question #3: How are the base angles of
an isosceles triangle proven to be congruent?
 Essential Question #4: How can the definition of
congruence in terms of rigid motion be used to show
that two triangles are congruent if and only if
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corresponding pairs of sides and corresponding
pairs of angles are congruent?
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Big Idea #2: Understand and prove relationships in
triangles
 Essential Question #1: What are the similarities
and differences of a circumcenter, incenter,
orthocenter, and centroid?
 Essential Question #2:How is it proven that the
perpendicular bisectors, angle bisectors, medians,
or altitudes of a triangle all meet at a common
point?
 Essential Question #3: How is it proven that the
segment joining midpoints of two sides of a triangle
is parallel to the third side and half the length?
 Essential Question #4: How are inequalities used in
triangles and why are they important?
o Unit III: Quadrilaterals
 Big Idea #1: Classify and prove theorems about
quadrilaterals
 Essential Question #1: How are quadrilaterals
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classified and what are the properties of each?
Essential Question #2: How are opposite sides of a
parallelogram proven congruent?
Essential Question #3: How are opposite angles of a
parallelogram proven congruent?
Essential Question #4: How is it proven that the
diagonals of a parallelogram bisect each other?
Essential Question #5: How can properties,
theorems, corollaries, and definitions be used to
prove definitions of quadrilaterals?
Essential Question #6: How can coordinate
geometry be used to prove general relationships
about quadrilaterals?
2nd or 4th 9 Weeks:
o Unit IV: Similarity and Transformations
 Big Idea #1: Prove theorems involving similarity
 Essential Question #1: Given two figures, how can
the definition of similarity in terms of similarity
transformations decide if geometric figures are
similar?
 Essential Question #2: How can proportions, angle
measures, and properties be used to prove triangles
similar?
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Essential Question #3: How can congruence and
similarity criteria for triangles be used to solve
problems?
 Essential Question #4: How can the theorem a line
parallel to one side of a triangle divides the other
two proportionally be proven?
 Big Idea #2: Understand and apply transformations
 Essential Question #1: What is the effect of a
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translation, reflection, or rotation on a geometric
figure?
Essential Question #2: How can a composition of
transformations create a congruent figure?
Essential Question #3: Given two figures, how can
the definition of congruence in terms of rigid
motion be used to decide if they are congruent?
 Essential Question #4: How does a dilation affect a
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figure?
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Essential Question #5: Given the center and scale
factor, how can a dilation’s properties be verified
experimentally?
Big Idea #3: Understand similarity in terms of similarity
transformations
 Essential Question #1: In a dilation, why does a
line not passing through the center of the dilation
to a parallel line leave a line passing through the
center unchanged?
 Essential Question #2: In a dilation, why is a line
segment longer or shorter in the ratio given by the
scale factor?
 Essential Question #3: Given two figures, how is
the definition of similarity in terms of similarity
transformations used to decide if they are similar?
 Essential Question #4: How is are the properties of
similarity transformations used to establish the AA
criterion for two triangles to be similar?
o Unit V: Trigonometry and Circles
 Big Idea #1: Use the Pythagorean Theorem to solve right
triangles in applied problems
 Essential Question #1: How is the Pythagorean
Theorem and its converse derived and applied?
 Essential Question #2: How does the Pythagorean
Theorem apply to 45-45-90 and 30-60-90 triangles?
 Essential Question #3: How can the Pythagorean
Theorem be used to solve real world problems
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Big Idea #2: Understand and apply trigonometric ratios
 Essential Question #1: How is similarity used to
find the definitions of trigonometric ratios for acute
angles?
 Essential Question #2: How can the relationship
between the sine and cosine of complementary
angles be explained and used?
 Essential Question #3: How can the trigonometric
ratios be used to solve real world problems?
 Essential Question #4: How can trigonometric
ratios be applied to angles of elevation and angles
of depression?
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Big Idea #3: Understand and apply theorems about circles
 Essential Question #1: How can all circles be
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proven similar?
Essential Question #2: What are the relationships
among inscribed angles, radii, and chords? Include
the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is
perpendicular to the tangent where the radius
intersects the circle.
Essential Question #3: How are the inscribed and
circumscribed circles of a triangle constructed?
Essential Question #4: How are the properties of
angles for a quadrilateral inscribed in a circle
proven?
Essential Question #5: How can the fact that the
length of the arc intercepted by an angle is
proportional to the radius, and define the radian
measure of the angle as the constant of
proportionality both be derived using similarity?
Big Idea #4: Translate between the geometric description
and the equation of a circle.
 Essential Question #1: Given the center of a circle
and its radius, how can the equation of the circle be
derived?
 Essential Question #2: Given a circle in the
coordinate plane, how is its equation derived?
 Essential Question #3: How can completing the
square be used to find the center and radius of a
circle given by an equation?
o Unit VI: Area and Extending to Three Dimensions
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Big Idea #1: Visualize relationships between twodimensional and three-dimensional objects
 Essential Question #1: How are the shapes of twodimensional cross-sections of three-dimensional
objects identified?
 Essential Question #2: How are three-dimensional
objects generated by rotations of two-dimensional
objects identified?
Big Idea #2: Understanding and deriving area formulas
 Essential Question #1: How is an informal
argument for the formulas for the circumference of
a circle, area of a circle found?
 Essential Question #2: How is the formula for the
area of a sector derived?
Essential Question #3: How can coordinates be
used to compute perimeters and areas of polygons?
 Essential Question #4: How are concepts of density
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based on area and volume in modeling situations
applied to real world situations?
 Essential Question #5: How are geometric methods
applied to solve real world area design problems?
 Big Idea #3: Explain volume formulas and use them to
solve problems
 Essential Question #1: How is an informal
argument for the formulas for the volume of a
cylinder, pyramid, and cone found?
 Essential Question #3: How are volume formulas
for cylinders, pyramids, cones, and spheres used to
solve problems?
 Essential Question #3: How are geometric shapes,
their measures, and their properties used to
describe three-dimensional objects?
 Essential Question #3: How are geometric methods
applied to solve real world volume design
problems?
End of Course Exam
Textbook: Carter, J. A., & Cuevas, G. J. (2014). Glencoe Geometry (Common
Core Ed.). Columbus, OH: McGraw-Hill Companies.
Supplemental Textbook(s): Supplemental materials will be used throughout
the school year. However, no additional textbooks will be distributed to
students.
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Course Expectations
Class Rules
1.) Be punctual
2.) Be prepared for class
3.) Be respectful towards teachers/staff, class members, school property,
etc.
4.) Be honest
5.) Be observant of all class, school, and district rules and policies
6.) Be positive
1.)
2.)
3.)
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6.)
7.)
Procedures
Students will write and perform Bellringer, write the essential
question(s), and get materials ready the first 3 minutes of class
Students will request permission from the teacher, get their agenda
signed, and sign out on the back of the door to leave the classroom for
any reason
Students will turn in work at the appropriate time and place
Students will clean up after themselves as well as their group
members
Students will remain seated in their assigned seat unless otherwise
given permission
Students are responsible for getting their make-up work after an
absence
Students are responsible for scheduling make-up tests and quizzes
with the teacher
Course Material
 3-ring Binder with Dividers
 Loose Leaf College Ruled Paper
 Pencils
 Colored Pencils
 Graph Paper
 Scientific or Graphing Calculator (TI-84+is recommended)
 Compass
 Protractor
 Ruler
Grading:
Explaining the process of Mathematics is essential for success in this class
and standardized tests. Therefore, all work must be shown algebraically to
receive full credit.
Summative Unit Assessments
50%
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Assessments
Classwork
Homework
30%
10%
10%
Grading Scale
The grading scale for Chillicothe High School can be found in the student
handbook.
Late Work: Late work will be subject to the board adopted policy on
assignments that are turned in late (to be reviewed in class).
CHS TENTATIVE Course Schedule
This is an overview of what will be covered in this course at CHS for this
school year. Although, I would like to follow this plan verbatim this years’
tentative schedule is subject to change (at the teachers’ discretion).
1st or 3rd 9 Weeks:
Week 1: Beginning of the Year Pre-Assessment Exam
Weeks 1-3: Unit 1 Proof and Parallel and Perpendicular Lines
2.5 Postulates and Paragraph Proofs
2.6 Algebraic Proof
2.7 Proving Segment Relationships
2.8 Proving Angle Relationships
3.1 Parallel Lines and Transversals
Explore: Angles and Parallel Lines
3.2 Angles and Parallel Lines
3.3 Slopes of Lines
3.4 Equations of Lines
Extend: Equations of Perpendicular Bisectors
3.5 Proving Lines Parallel
3.6 Perpendiculars and Distance
Weeks 4-7: Unit 2 Triangles
4.1 Classifying Triangles
4.2. Angles in Triangles
4.3 Congruent Triangles
4.4 Proving Triangles Congruent –SSS,SAS
Extend: Proving Constructions
4.5 Proving Triangles Congruent – ASA, AAS
Extend: Congruence in Right Triangles
4.6 Isosceles and Equilateral Triangles
Explore: Congruence Transformations
4.7 Congruence Transformations
4.8 Triangles and coordinate Proof
Chapter 5 Explore: Construction Bisectors
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5.1 Bisectors of Triangles
Explore: Constructing Medians and Altitudes
5.2 Medians and Altitudes of Triangles
5.3 Inequalities in One Triangle
5.4 Indirect Proof
Explore: The Triangle Inequality
5.5 The Triangle Inequality
5.6 Inequalities in Two Triangles
Weeks 8-9: Unit 3 Quadrilaterals
6.1 Angles of Polygons
Extend: Angles of Polygons
6.2 Parallelograms
Explore: Parallelograms
6.3 Tests for Parallelograms
6.4 Rectangles
6.5 Rhombi and Squares
6.6 Trapezoids and Kites
2nd or 4th 9 Weeks:
Week 1-3: Unit 4 Similarity and Transformations
7.1 Ratios and Proportions
7.2 Similar Polygons
7.3 Similar Triangles
Extend: Proofs of Perpendicular and Parallel Lines
7.4 Parallel Lines and Proportional Parts
7.5 Parts of Similar Triangles
7.6 Similarity Transformations
7.7 Scale Drawings and Models
9.1 Reflections
9.2 Translations
Explore: Rotations
9.3 Rotations
Extend: Solids of revolution
Explore: Compositions of Transformations
9.4 Compositions of Transformations
9.5 Symmetry
Extend: Constructions with a Reflective Device
Explore: Dilations
9.6 Dilations
Extend: Establishing Triangle Congruence and Similarity
Week 4-6: Unit 5 Trigonometry and Circles
8.2 The Pythagorean Theorem and Its Converse
8.3 Special Right Triangles
Explore: Trigonometry
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8.4 Trigonometry
8.5 Angles of Elevation and Depression
10.1 Circles and Circumference
10.2 Measuring Angles and Arcs
10.3 Arcs and Chords
10.4 Inscribed Angles
10.5 Tangents
Extend: Inscribed and Circumscribed Circles
10.6 Secants, Tangents, and Angle Measures
10.7 Special Segments in a Circle
10.8 Equations of Circles
Week 7-9: Unit 6 Area and Extending to Three Dimensions
11.1 Areas of Parallelograms and Triangles
Explore: Areas of Trapezoids, Rhombi, and Kites
11.2 Areas of Trapezoids, Rhombi, and Kites
Extend: Population Density
11.3 Areas of Circles and Sectors
Explore: Investigating Areas of Regular Polygons
11.4 Areas of Regular Polygons and Composite Figures
Extend: Regular Polygons on the Coordinate Plane
11.5 Areas of Similar Figures
12.1 Representations of Three-Dimensional Figures
Extend: Topographic Maps
12.2 Surface Areas of Prisms and Cylinders
12.3 Surface Areas of Pyramids and Cones
12.4 Volumes of Prisms and Cylinders
Extend: Changing Dimensions
12.5 Volumes of Pyramids and Cones
12.6 Surface Area and Volumes of Spheres
12.7 Spherical Geometry
Extend: Navigational Coordinates
12.8 Congruent and Similar Solids
 End of Course Exam
Performance Based Section: Writing
Assignments/Exams/Presentations/Technology
One or more of the End of Unit Exams may be Performance Based. According
to the Ohio Department of Education, “Performance Based Assessments
(PBA) provides authentic ways for students to demonstrate and apply their
understanding of the content and skills within the standards. The
performance based assessments will provide formative and summative
information to inform instructional decision-making and help students move
forward on their trajectory of learning.” Some examples of Performance
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Based Assessments include but are not limited to portfolios, experiments,
group projects, demonstrations, essays, and presentations.
CHS Honors Geometry Course Syllabus
After you have reviewed the preceding packet of information with your
parent(s) or guardian(s), please sign this sheet and return it to me so that I
can verify you understand what I expect out of each and every one of my
students.
Student Name (please print):
________________________________________________________
Student Signature:
________________________________________________________
Parent/Guardian Name (please print):
________________________________________________________
Parent/Guardian Signature:
________________________________________________________
Date: ________________________________________________________