Download Strath Haven High School Syllabus

Strath Haven High School Syllabus
Course Title:
Level:
Geometry
College Prep/Honors
Course Number: 3121/3142 Grade: 9-12
I.
Course Description/Overview
This course begins with an informal introduction to geometry, experimenting with drawings,
constructions, and geometry software. Using a theme of investigation before formalization, the course
examines congruence, similarity, parallel and perpendicular lines, the properties of polygons and
circles, perimeter and circumference, area, surface area, and volume. Students will also explore right
triangle trigonometry, as well as the formulas for midpoints, distance between points, and the equation
of a circle on the coordinate plane.
II.
Course Objectives
Recognize invariants in geometric figures.
Develop a literacy of mathematical proof.
Derive area formulas for polygons and the surface area and volume formulas for polyhedrons.
Understand how scaled figures represent mathematical similarity.
Determine well defined formulas and properties of curved figures.
Use right triangles and trigonometry to solve other geometric problems.
Develop the fundamentals of coordinate geometry including midpoint, distance and transformation.
III.
Course Content
A.
Introduction to Geometry
Key Concepts/Skills
Visualize geometric objects well enough to draw them.
Use clear language to draw shapes.
Distinguish between drawing a figure and constructing a figure.
Use hand construction tools, including paper folding
Recognize invariants and use geometry software to test for invariants
Apply the Midline Conjecture
Search for numerical and spatial invariants
Make conjectures and use software to experiment with geometric models
B.
Congruence and Proof
Key Concepts/Skills
Develop literacy and tests pertaining to congruent figures.
Identify congruent relationships that result from parallel lines cut by a transversal.
Write and represent a deductive proof including triangle congruence proofs.
Prove that the sum of the angle measures of a triangle is 180o
Recognize the difference between experimentation and deduction.
Derive and apply the Perpendicular Bisector Theorem.
Apply the Isosceles Triangle Theorem to prove parts of a figure are congruent.
Classify quadrilaterals.
Understand the meaning of converse.
Understand the meaning of always, sometimes, and never in mathematics.
C.
Dissections and Area
Key Concepts/ Skills
Prove the midline theorem using cuts and rearrangement.
Devise and follow algorithms to dissect and rearrange a figure into an equal area figure.
Prove and calculate the area of a parallelogram, or a triangle, and of a trapezoid.
Prove the Pythagorean Theorem and use it to determine missing lengths in figures.
Find the surface area of solids by visualizing their nets.
Estimate the volumes of solids.
Use formulas for the volumes of certain solids.
D.
Similarity
Key Concepts/Skills
Apply scale factor to make similar figures.
Decide whether two figures are well scaled copies of each other.
Use a scale factor to approximate distances in blue prints and maps.
Identify dilation as an enlargement or reduction by looking at the scale factor.
Describe the effect of the choice for center of dilation on the resulting dilation.
Describe and use the ratio method and the parallel line method to make dilations.
Decide how lines parallel to a side of a triangle split the other two sides.
Identify corresponding parts of similar triangles.
Use the AA, SAS, and SSS tests for similarity in triangles.
Explore the relationship in the areas of a polygon and the scaled copy of that polygon.
E.
Circles
Key Concepts/Skills
Approximate the area and perimeter of irregular shapes.
Find the area of regular polygons.
Derive theorems about arcs, chords, inscribed angles, secants and tangents of circles.
Look for invariants in circles including the power of a point with respect to a circle.
Develop and apply the area and circumference formulas of a circle.
F.
Using Similarity and a Trigonometric Introduction
Key Concepts/Skills
Use similar triangles to find unknown lengths.
Use similarity to prove theorems.
Use the sine, cosine, and tangent functions and their inverses to solve triangles.
Solve a triangle given SAS and find the area.
Calculate probability using a comparison of areas.
G.
Coordinate Geometry
Key Concepts/Skills
Calculate the midpoint and distance of the segment given the endpoints.
Write equations of lines with given characteristics.
Apply transformations to figures and the graphs of functions in the coordinate plane.
IV.
Types of Student Assessments and Evaluations
Quizzes, tests, oral presentations, and graded homework.
V.
Grading Policy
Grades are based on a point system. Averages are calculated by dividing the total points earned by
the student by the total number of possible points. Final grades are determined as follows: first
marking period (40%), second marking period (40%), and final exam (20%).
VI.
Homework
Homework is given on a regular basis. Most assignments are due the next day.
VII
Resources
Graphing calculators (TI-Nspire recommended), rulers, protractors, compasses, graph paper and CME
Project: Geometry (CME Project Development Team)
SHHS Mission Statement: SHHS graduates will possess the ability to apply their knowledge and skills to: act as
responsible citizens engaged in their community, nation, and the world around them, exhibit intellectual curiosity and
aesthetic appreciation, demonstrate self-awareness and informed critical thinking, maintain personal integrity and healthy
decision-making in order to ensure success in post-secondary education, the workplace, and the home.
SHHS Respect Policy: All members of the school community are expected to be respectful of each other. Negative
comments about anyone’s race, nationality, religion, physical appearance or ability, intellectual capabilities, gender
identity, sexual orientation, work ethic, or character are unacceptable and will not be tolerated. Students are encouraged
to discuss any concerns with any adult in the building.