Download Plane Geometry CP Course Length - Morgan Hill Unified School

Morgan Hill Unified School District
Course Outline
Course Title:
Course Length:
Credits:
Grades:
Plane Geometry CP
One Year
10 credits
8 -12
Course Goals
• Students will be able to apply to properties of logic when developing mathematical
arguments.
• Students will be able to apply concepts developed through reasoning to real world
situations.
• Students will be able to interpret and apply spatial relationships.
• Students will be able to relate algebraic and geometric concepts.
Texts and Supplemental Instructional Materials
• Larson, Ron, Boswell, Laurie, Kanold, Timothy D., Stiff, Lee, Geometry. Boston:
McDougal Littell, 2007.
• Text resources
• Teacher made resources
• Manipulatives
• Scientific Calculator
Course Objectives by Essential Standards
Standard 1:
Students will be able to identify and give examples of undefined terms, axioms, theorems,
and inductive and deductive reasoning.
Standard 2:
Students will be able to write geometric proofs, including proofs by contradiction.
Standard 3:
Students will be able to construct and judge the validity of a logical argument.
Standard 4:
Students will be able to prove basic theorems involving congruence and similarity.
Standard 5:
Students will be able to prove triangles are congruent or similar and be able to use the
concept of corresponding parts of congruent triangles.
Standard 6:
Students will be able to use the Triangle Inequality Theorem.
Plane Geometry CP
Course #
2
Standard 7:
Students will be able to prove and use theorems involving the properties of parallel lines cut
by a transversal, the properties of quadrilaterals, and the properties of circles.
Standard 8:
Students will be able to derive, and solve problems involving perimeter, circumference, area,
volume, lateral area, and surface area of common geometric figures.
Standard 9:
Students will be able to compute volumes of prisms, pyramids, cylinders, cones, and spheres.
Standard 10:
Students will be able to compute areas of polygons including rectangles, scalene triangles,
equilateral triangles, rhombi, parallelograms, and trapezoids.
Standard 11:
Students will be able to determine how changes in dimensions affect the perimeter, area, and
volume of common geometric figures and solids.
Standard 12:
Students will be able to find and use measures of sides, interior and exterior angles of
triangles and polygons to classify figures and solve problems.
Standard 13:
Students will be able to prove relationships between angles in polygons using properties of
complementary, supplementary, vertical, and exterior angles.
Standard 14:
Students will be able to prove the Pythagorean Theorem.
Standard 15:
Students will be able to use the Pythagorean Theorem to determine distance and find missing
lengths of sides of right triangles.
Standard 16:
Students will be able to perform basic constructions with straightedge and compass such as
angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point
off the line.
Standard 17:
Students will be able to prove theorems using coordinate geometry, including the midpoint of
a line segment, distance formula, and various forms of equations of lines and circles.
Adopted by MHUSD Board: June 24, 2008
UC Approved Meets C Credit Requirement
Plane Geometry CP
Course #
3
Standard 18:
Students will be able to apply the basic trigonometric functions defined by the angles of a
right triangle. They will be able to use the elementary relationships between them, (e.g.
tan(x)= sin(x)/cos(x)).
Standard 19:
Students will be able to use trigonometric functions to solve for an unknown length of a side
of a right triangle, given an angle and a length of a side.
Standard 20:
Students will be able to use angle and side relationships in problems with special right
triangles such as 30-60-90 triangles and 45-45-90 triangles.
Standard 21:
Students will be able to prove and solve problems regarding relationships among chords,
secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
Standard 22:
Students will be able to illustrate the effect of rigid motions on figures in the coordinate plane
and space, including rotations, translations, and reflections.
Outline of Course
Major Units
Elements of Geometry
• Points, Lines, Planes
• Subsets of a line
• Introduction to deductive reasoning
• Proof in two column form
Angles and Perpendicular Lines
• Angles, and their measures
• Introduction to Theorems, Corollaries Concerning Angles
Parallel Lines and Planes
• Sufficient and Necessary Conditions for Parallel Lines
• Applications of Parallel Lines to Polygons
• Theorems and proofs for Parallel Lines
Congruent Triangles
• Concept of Correspondence Between Two Triangles
• Methods of Proving Congruent Triangles
• Corresponding Parts of Congruent Triangles
• Use of Corresponding Parts of Congruent Triangles for Extended Proofs
• Introduction of Auxiliary Lines
Adopted by MHUSD Board: June 24, 2008
UC Approved Meets C Credit Requirement
Plane Geometry CP
Course #
4
Applications of Congruent Triangles
• Parallelograms (Necessary and Sufficient Conditions for Parallelograms)
• Other Quadrilaterals (Rectangles, Rhombi, Squares, and Trapezoids)
• Triangle Inequalities
Similar and Regular Polygons
• Concept of Proportionality
• Properties of a Proportion
• Definition of a Similar Polygon (Similar Triangles and Proofs Involving Similar Triangles
• Definition of a Regular Polygon
• Area of Regular Polygons
• Angle Rules for Polygons
Right Triangles
• Pythagorean Theorem and its Applications
• Special Right Triangles
• Geometric Mean
• Trigonometric Ratios and basic applications
Circles
• Tangents, Arcs, and Chords
• Angles formed by segments in relation to a Circle
• Segments, lines, and rays in relation to a Circle
• Circumference and Area of Circles
Area and Volume of Solids including Spheres, Cones, Prisms, Cylinders, & Pyramids.
Coordinate Geometry
• Cartesian Plane
• Measurement of Segments in a Cartesian Plane
• Equations of a Line and its properties
• Slope of Line
Methods of Instruction
• Investigations/Explorations
• Group/Individual Activities
• Collaborative Learning (pairs/groups)
• Lecture/Discussion
• Use of Manipulatives/games
• Building Content Vocabulary
• Writing Assignments/Portfolio
• Audio Visual Materials
• Guest Speakers/Field Trips
• Notebook
Adopted by MHUSD Board: June 24, 2008
UC Approved Meets C Credit Requirement
Plane Geometry CP
Course #
5
Assessment methods and/or tools
Assessment methods include formative assessment, which will promote learning throughout the
course or summative assessments, such as benchmarks, final exams, which document student
progress toward meeting standards. These methods include:
• Homework and periodic checks of student work.
• Textbook and teacher generated tests and quizzes.
• Assessments periodically must include formal proofs.
• A variety of selected responses, which may include, but not limited to multiple-choice,
true/false, matching, and short answer fill-in items.
• Personal communication may include, but limited to, teacher/student conference and
interviews, teacher observation, classroom discussions, oral examinations, and journals
and logs.
• Peer activities may be used as an assessment for appropriate topics
• Essay assessments evaluating student’s knowledge, reasoning, and skills.
• Performance, e.g. student projects, performances, debates, and presentations.
Adopted by MHUSD Board: June 24, 2008
UC Approved Meets C Credit Requirement