Download WISE English 12 -- Syllabus

Course title: Geometry
Course Description:
The course provides the student with the skills and knowledge of
concepts needed to solve mathematical and real world problems in
geometry. Students will used geometric models and measurement
to solve problems, explain processes and justify solutions. Topics
include right triangle theory, trigonometry, polygons and area, and
volume, coordinate geometry, and coordinate transformations.
Course Prerequisites:
There are no prerequisites for this course.
Major Objectives or Topics:
Use deductive reasoning to draw conclusions; Apply geometric
properties to solve problems; Compare, contrast and analyze
properties of geometric figures;
Use various techniques of measurement to calculate area,
circumference, perimeter, volume or two and three-dimensional
figures.
Materials:
Computer, internet access
Major Assignments Overview:
Using deductive reasoning
Venn Diagram project
Calculating volumes project
End of Course Test
Grading Procedures:
Each lesson will be graded based upon skill mastery. Students will
be asked to revise work until it meets the minimum requirements
outlined by the grading rubric on each lesson.
Submission Policy: Students are to complete course lessons in
orders. Each day a student may post either two new lessons, or 2
revisions, or a lesson and a revision in each course. Unless
permission to work on more than two lessons has been granted by
the teacher, students should only work on two lessons at a time.
Once a lesson is graded, students may move on to the next lesson
Communication: Students may communicate with their teacher
using the Teachermail. On the Student Desk, students will find
links to Guidance, Technical Help, and Transcripts.
Lessons:
Lesson 1: Naming Geometric Elements
Lesson 2: Inductive and Deductive Reasoning
Lesson 3: Conditional Statements and Venn Diagrams
Lesson 4: Supplementary and Complementary Angles
Lesson 5: Review: Synthesize Lessons 1-4
Lesson 6: Parallelism
Lesson 7: Polygons
Lesson 8: Similar Polygons
Lesson 9: Review: Synthesize Lessons 6-8
Lesson 10: Triangles
Lesson 11: Introduction to Trigonometry
Lesson 12: Pythagorean Theorem
Lesson 13: Special Right Triangles
Lesson 14: Review: Synthesize Lessons 10-13
Lesson 15: Circles: Chords, Radii, and Arcs
Lesson 16: Circles: Circumference and Arc Length
Lesson 17: Area of Circles and Sectors
Lesson 18: Area of Squares, Rectangles, and Rhombuses
Lesson 19: Review: Synthesize Lessons 15-18
Lesson 20: Area of Triangles, Parallelograms, and Trapezoids
Lesson 21: Areas of Polygons
Lesson 22: Surface Area and Volume of Spheres, Cylinders, and
Cones
Lesson 23: Area and Volume of Prisms and Pyramids
Lesson 24: Review: Synthesize Lessons 20-23
Lesson 25: The Cartesian Coordinate System and the Distance
Formula
Lesson 26: Transformations
Lesson 27: Proofs
Lesson 28: Review: Synthesize Lessons 25-27
Lesson 29: Course Review
Lesson 30: End of Course test
Course Outcomes and Virginia SOL Alignment
CompuHigh
Lesson
Lesson 1: Naming
Geometric Elements
Virginia SOL
G.1 The student will construct and
judge the validity of a logical
argument consisting of a set of
premises and a conclusion. This
will include
Lesson 2: Inductive and
Deductive Reasoning
a) identifying the converse,
inverse, and contrapositive of a
conditional statement;
Lesson 3: Conditional
Statements and Venn
Diagrams
b) translating a short verbal
argument into symbolic form;
c) using Venn diagrams to
represent set relationships; and
d) using deductive reasoning,
including the law of syllogism.
Lesson 12: The Cartesian
Coordinate System and the
Distance Formula
Lesson 8: Triangles
Lesson 22: Transformations
G.2 The student will use pictorial
representations, including
computer software,
constructions, and coordinate
methods, to solve problems
involving symmetry and
transformation. This will include
a) investigating and using formulas
for finding distance, midpoint, and
slope;
b) investigating symmetry and
determining whether a figure is
symmetric with respect to a line or
a point; and
c) determining whether a figure has
been translated, reflected, or
rotated.
Lesson 4: Supplementary
and Complementary Angles
Lesson 5: Parallelism
Lesson 6: Polygons
Lesson 4: Supplementary
and Complementary Angles
G.3 The student will solve practical
problems involving
complementary, supplementary,
and congruent angles that include
vertical angles, angles formed
when parallel lines are cut by a
transversal, and angles in polygons.
G.4 The student will use the
relationships between angles
formed by two lines cut by a
Lesson 5: Parallelism
transversal to determine if two
lines are parallel and verify, using
algebraic and
Lesson 23: Proofs
coordinate methods as well as
deductive proofs.
Lesson 6: Polygons
G.5 The student will
Lesson 22: Transformations
a) investigate and identify
congruence and similarity
relationships between triangles;
Lesson 23: Proofs
and
Lesson 8: Triangles
b) prove two triangles are
congruent or similar, given
information in the form of a figure
or statement, using algebraic and
coordinate as well as deductive
proofs.
Lesson 8: Triangles
Lesson 9: Introduction to
Trigonometry Lesson 10:
Pythagorean Theorem
G.6 The student, given information
concerning the lengths of sides
and/or measures of angles, will
apply the triangle inequality
properties to determine whether a
triangle exists and to order sides
and angles. These concepts will be
considered in the context of
practical situations.
G.7 The student will solve practical
problems involving right triangles
by using the
Pythagorean Theorem, properties
of special right triangles, and right
triangle
trigonometry. Solutions will be
expressed in radical form or as
decimal approximations.
G.8 The student will
a) investigate and identify
properties of quadrilaterals
involving opposite sides and
angles, consecutive sides and
angles, and diagonals;
b) prove these properties of
quadrilaterals, using algebraic and
coordinate methods as
well as deductive reasoning; and
c) use properties of quadrilaterals
to solve practical problems.
Lesson6: Polygons
Lesson 20: The Cartesian
Coordinate System and the
Distance Formula
Lesson 23: Proofs
Lesson 6: Polygons
G.9 The student will use measures
of interior and exterior angles of
polygons to solve problems.
Tessellations and tiling problems
will be used to make connections
to art, construction, and nature.
Lesson 12: Circles: Chords,
Radii, and Arcs
Lesson 13 Circles:
Circumference and Arc
Length
Lesson 14: Area of Circles
and Sectors
Lesson 20: The Cartesian
Coordinate System and the
Distance Formula
Lesson 21: Bisectors
Lesson 17: Surface Area and
Volume of Spheres,
Cylinders, and Cones
Lesson 18: Area and
Volume of Prisms and
Pyramids
G.10 The student will investigate
and solve practical problems
involving circles, using
properties of angles, arcs, chords,
tangents, and secants. Problems
will include finding arc length and
the area of a sector, and may be
drawn from applications of
architecture, art, and construction.
G.11 The student will construct a
line segment congruent to a given
line segment, the bisector of a line
segment, a perpendicular to a given
line from a point not on the line, a
perpendicular to a given line at a
point on the line, the bisector of a
given angle, and an angle
congruent to a given angle.
G.12 The student will make a
model of a three-dimensional
figure from a two-dimensional
drawing and make a twodimensional representation of a
three-dimensional object. Models
and representations will include
scale drawings, perspective
drawings, blueprints, or computer
simulations.
Lesson 17: Surface Area and
Volume of Spheres,
Cylinders, and Cones
Lesson 18: Area and
Volume of Prisms and
Pyramids
G.13 The student will use formulas
for surface area and volume of
three-dimensional objects to solve
practical problems. Calculators will
be used to find decimal
approximations for results.
G.14 The student will
Lesson 6: Polygons
Lesson 17: Surface Area and
Volume of Spheres,
Cylinders, and Cones
Lesson 18: Area and
Volume of Prisms and
Pyramids
a) use proportional reasoning to
solve practical problems, given
similar geometric
objects; and
b) determine how changes in one
dimension of an object affect area
and/or volume of
the object.