Mathematics Department
Geometry CPA
Course Syllabus
2015-2016
Instructor: Greg Aschoff
e-mail: gaschoff@westex.org
Phone: 973-228-1200 X839
A. Grading Policy – course work will be graded as follows:
a. Summative Assessments (test, quizzes, projects) – 90% of grade
b. Formative Assessments (homework) – 10% of grade
c. All grades should be verified in Genesis on a regular basis
B. Classroom
a. Rules of Conduct
i. Follow all rules as stated in student handbook
ii. Come prepared to class with all required materials
iii. No food or drinks in classroom
iv. No cell phone use in class
b. Required Material
i. Textbook
ii. Pencils
iii. Graphing calculator
iv. Three ring binder
c. Homework
i. All homework will be posted on the teacher’s school website
ii. Homework will not be accepted late unless the student has
been absent and/or has a medical excuse
iii. Missed homework should be made-up for understanding of
concepts
d. After School Help
i. Available Tuesdays, Wednesdays, Thursdays
ii. Will notify students if I cannot stay on a particular day
e. Attendance
i. Follow all rules as stated in student handbook
ii. One day to make up work for every day absent
iii. Work assigned prior to absence(s) will be due on the first day
back
f. Academic Integrity
i. Students are to hand-in their own work
1. Receiving assistance is different from copying
ii. Cheating will result in a zero on the assessment and a call
home to the parent
C. Course Description: Geometry CPA and Honors are college preparatory
courses which emphasize topics inherent to plane and solid geometry.
Knowledge of geometry will be developed with an emphasis on its logical
structure and problem solving with consideration of both the inductive and
deductive methods of reasoning as applied to formal proofs. Students will
also be introduced to probability concepts.
D. Course Objectives: This course has been designed with respect to and in
compliance with the expectations set forth in the New Jersey Common
Core State Standard. The course’s objective is to use inductive and
deductive reasoning to analyze, observe, and problem solve in order to
answer the following essential questions based on the New Jersey Common
Core State Standard Student Learning Objectives :
Congruence, Proof, and Construction
•
How can you use the undefined notion of a point, line, distance along a line
and distance around a circular arc to develop definitions for angles, circles,
parallel lines, perpendicular lines, and line segments?
•
How can you apply the definitions of angles, circles, parallel lines,
perpendicular lines, and line segments to describe rotations, reflections, and
translations?
•
How can you develop and perform rigid transformations that include
reflections, rotations, and translations using geometric software, graph paper,
tracing paper, and geometric tools, and compare them to non-rigid
transformations?
•
How can you use rigid transformations to determine, explain and prove
congruence of geometric figures?
•
How can you create proofs of theorems involving lines, angles, triangles,
and parallelograms?
•
How do you generate formal constructions with paper folding, geometric
software and geometric tools?
Similarity, Proof, and Trigonometry
•
How can you verify and use the properties of dilations, use the definition of
similarity to determine whether figures are similar, and establish the AA criterion
using similarity?
•
How do you prove theorems about triangles and use triangle congruence
and similarity to solve problems and prove relationships in geometric figures?
•
How can you develop and apply the definitions of trigonometric ratios for
the acute angles of a right triangle, the relationship between the sine and cosine
of complementary angles, and the Pythagorean Theorem on right triangles in
applied problems?
Extending to Three-Dimensions
•
How do you develop informal arguments to justify formulas for the
circumference of a circle, area of a circle, volume of a cylinder, pyramid, and
cone?
•
How can you solve problems using volume formulas for cylinders, pyramids,
cones, and spheres?
•
How do you identify the shape of a two-dimensional cross-section of a
three-dimensional figure and identify three-dimensional objects created by the
rotation of two-dimensional objects?
•
How can you use geometric shapes, their measures, and their properties to
describe objects?
•
How do you use density concepts in modeling situations based on area and
volume?
•
How can you solve design problems using geometric methods?
Circles and Expressing Geometric Properties through Equations
•
How can you identify and describe relationships among inscribed angles,
radii, and chords?
•
How do you generate proofs that demonstrate that all circles are similar?
•
How can you prove the properties of angles for a quadrilateral inscribed in
a circle and construct inscribed and circumscribed circles of a triangle, and a
tangent line to a circle from a point outside a circle, using geometric tools and
geometric software?
•
How do you use similarity to show 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?
•
How can you derive the formula for the area of a circular sector, the
equation of a circle, and the equation of a parabola?
•
How do you prove the slope criteria for parallel and perpendicular lines and
use them to solve geometric problems?
•
How do you construct formal proofs using theorems, postulates, and
definitions involving parallelograms?
•
How can you use the coordinate system to generate simple geometric
proofs algebraically and to compute perimeters and areas of geometric figures
using the distance formula?
•
How do you use geometric shapes, measures, and properties to model
multi-dimensional concepts in the context of real-world applications?
Applications of Probability
•
How can you describe events as subsets of a sample space (the set of
outcomes) using characteristics (or categories) of the outcomes, or as unions,
intersections, or complements of other events (“or,” “and,””not”)?
•
How do you use two-way frequency tables to determine if events are
independent and to calculate/approximate conditional probability?
•
How can you use everyday language to explain independence and
conditional probability in real-world situations?
E. TEXTS/RESOURCES
Geometry Concepts and Skills, Holt, Rinehart and Winston © 2007
TI-83/84 Plus calculator