Download Course Title: Geometry Grade: 8 Level: Honors I. Course Description

Course Title:
Level:
Geometry
Honors
Grade: 8
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 blueprints 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 weighted point system. Averages are calculated using a weighted system for 4
categories. Tests 40%, Quizzes 30%, Homework 15%, Other 15% (this category includes projects,
presentations, graded HW, etc.) The Final exam will count for 1/9th of the overall grade for the year but
will not impact the 4th marking period grade.
VI.
Homework
Homework is given on a regular basis. Most assignments are due the next day.
VII
Resources
Graphing calculators (TI-Nspire, TI-84, TI-83), rulers, protractors, compasses, graph paper, and text:
CME Project: Geometry (CME Project Development Team)
Note: This Syllabus mirrors the SHHS Geometry Syllabus. The grading policy has been adjusted for the SHMS 4 marking
period -180 day course length.