EL SEGUNDO UNIFIED
EL SEGUNDO HIGH SCHOOL
COURSE OF STUDY
Course Title: Geometry
Department: Mathematics
Grade Levels: 9-12
COURSE DESCRIPTION
GEOMETRY:
Geometry is a course that focuses on plane geometry; point, line, plane, geometric shapes. The geometric skills and concepts developed in this discipline are useful to all students. Aside from these skills and concepts, students will develop their ability with formal logical arguments and proofs in geometric settings and problems. Students will be exposed to the derivations in the outline.
Length: One year
Prerequisite for Enrollment: High School: A 70% or better in High School Algebra 1AB; Score 70% or better on the placement exam. Middle School: 90% or better in Algebra 1AB; Score 90% or better on the placement exam
Recommendation for Enrollment: Teacher recommendation
Type of Course: College preparatory (UC/CSU) and meets math graduation requirement.
COURSE OUTLINE AND STANDARDS
1.0: Students
demonstrate understanding by identifying and giving examples of undefined
terms, axioms, theorems, and inductive and deductive reasoning. (Integration of Core
Knowledge)
2.0: Students write
geometric proofs, including proofs by contradiction (Integration of Core Knowledge; Critical
Thinking/Problem Solving; Effective Communication)
3.0: Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
4.0: Students prove basic theorems involving congruence and similarity (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
5.0: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
6.0: Students know
and are able to use the triangle inequality theorem. (Integration of Core Knowledge)
7.0: Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
8.0: Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
9.0: Students compute the volumes and surface areas of prism, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. (Integration of Core Knowledge)
10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. (Integration of Core Knowledge)
11.0: Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
13.0: Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
14.0: Students prove the Pythagorean theorem. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
15.0: Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. (Integration of Core Knowledge)
16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. (Integration of Core Knowledge)
17.0: Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
18.0: Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. (Integration of Core Knowledge)
19.0: Students 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. (Integration of Core Knowledge)
20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30 degree, 60 degree, and 90 degree triangles and 45 degree, 45 degree, and 90 degree triangles. (Integration of Core Knowledge)
21.0: Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
22.0: Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. (Integration of Core Knowledge)
INSTRUCTIONAL METHODS
1. Lecture and Guided Practice
2. Investigations (Personal/Social Development)
3. Manipulatives
4. Class work and Homework
5. Individual work, and group work (Personal/Social Development)
6. Short term projects (Personal/Social Development)
7. Technology
EVALUATION/GRADING OF STUDENT WORK
1. Quizzes and Chapter tests (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
2. Semester exam (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
3. Comprehensive final exam (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
4. Homework and Classroom participation (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)
5. Projects (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)
6. Written Essays (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)
INSTRUCTIONAL MATERIALS
1. Text: Geometry by McDougal Littell
2. Straightedge, Protractor, Compass
3. Calculators will not be used in this course.
3-26-02