Download Geometry

Geometry
Course Syllabus
Fall 2005
Mrs. Kurncz
Room 115
Phone: 668-3115
E-mail: [email protected]
Conference: 1st Block
COURSE DESCRIPTION: The content and questions of this course integrate algebra
and some discrete mathematics with geometry. Pure and applied mathematics is also
integrated throughout this course. The equipment needed for this course is a ruler,
compass, a protractor, graph paper, and a scientific calculator.
PREREQUISITES: A grade of 80% or better in 8th grade Beginning Algebra or a grade
of “C” or higher in High School Beginning Algebra.
TYPE OF COURSE: Intermediate
OBJECTIVES:
Patterns:
● Give justifications for conclusions involving different figures
● Follow the basic laws of reasoning to make conclusions
● Write converse, inverse, or contrapositive of a conditional
Shape and Shape Relationship
● Make and determine the perspective of drawings
● Give the dimensions of figures and objects
● Given a property of points and lines, tell whether it is true for each of the four
descriptions of points: dots, locations, ordered pairs, and nodes
● Apply properties of betweenness
● Determine whether a triangle can be formed with sides of three given lengths
● Apply the Triangle Inequality in real situations
● Distinguish between convex and nonconvex regions
● Draw and identify polygons
● Identify polygons used for real objects
● Draw hierarchies of triangles and polygons
● Perform the following construction with a straightedge and a compass:
perpendicular bisector, perpendicular from point to line, perpendicular to line at point
● Apply angle measure to describe real situations
● Apply constructions and drawings in real situations
● Perform drawing and constructions applying the definition of reflection image
● Apply the Trapezoid Angle Theorem and the theorems about alternate interior angles
● Find unknown measure of angles using the Isosceles Triangle, Triangle Sum,
Quadrilateral Sum, and Polygon Sum Theorems
● Classify special polygons by their properties
Geometry
Cont . . .
● Identify properties of triangles and quadrilaterals
● Determine properties of congruent figures
● Given appropriate information, write proofs, using theorems, postulates of definitions
studied
● Draw triangles satisfying given conditions and determine whether all such triangles are
congruent
● Determine whether figures are congruent from information given in drawings
● Write proofs that triangles are congruent
● Apply the triangle congruence and corresponding parts of congruent figures theorems
to prove that segments of angles are congruent
● Determine whether conditions are properties of or sufficient conditions for
parallelograms
● Use theorems about triangles and parallelograms to explain real situations
● Draw a tessellation using a given figure as a fundamental region
● Describe or apply a method for determining the area of an irregular-shaped region
● From 2-dimensional views of a figure, determine properties of the 3-dimensional figure
● Identify parts of common 3-dimensional figures
● Distinguish 3-dimensional figures by their defining properties
● Recognize 3-dimensional figures in the real world
● Know the conditions under which Calalieri’s Principle can be applied
● Using coordinates in individual figures, prove that segments in them are congruent,
perpendicular, or parallel
● Using coordinates, prove theorems involving parallel of perpendicular sides, congruent
segments, midpoints or combinations of these in triangles and quadrilaterals
● Draw size transformation images of figures
Position:
● Apply distance to real situations
● Determine distance on a number line
● Graph points and lines in the coordinate plane
● Draw reflection images of segments, angles, and polygons over a given line
● Draw all symmetry lines of segments and angles
● Apply properties of reflections to make conclusions, using properties of reflections and
reflection theorem
● Apply properties of symmetry to make conclusions about symmetric figures
● Locate and make symmetry lines in designs
● Find coordinates of reflection images of points over the coordinate axis
● Draw or identify images of figures under composites of reflections
● Apply properties of reflections to obtain properties of translations and rotations
● Apply reflection theorems for translations and for rotations
● Determine the isometry which maps one figure onto another
● Use reflections to find a path from an object to a particular point
● Describe or apply a method for determining the area of an irregular-shaped region
● Draw common 3-dimensional shapes and plane sections of those shapes
● Give views of a figure from top, sides, or bottom
Geometry
Cont . . .
● Determine and draw symmetry planes in 3-dimensional figures
● Apply coordinate geometry in three dimensions
● Find the point of intersection of two lines in the coordinate plane
Measurement:
● Draw and analyze drawings of angles
● Draw angles with a given measure and measure drawn angles
● Determine measures of angles formed by parallel lines and transversals
● Determine measures of angles in figures and their reflection images
● From a net, make a surface and vice versa
● Determine what happens to the surface area and volume of a figure when its
dimensions are multiplied by some number
Inference and Prediction:
● Write the converse of a conditional
● Use logical (p=>Q) rotation
● Apply properties of if-then statements in real situations
Concepts and Properties of Numbers:
● Apply the properties of a good definition
Number Relationships:
● Calculate cube roots
Operations and Properties:
● Recognize the use of undefined terms and postulates
Algebraic and Analytical Thinking:
● Write and interpret statements in “if-then” form
● Use algebra to represent and find measures of angles
● Determine the slope of a line from its equation or given two points on it
● Determine the slope of a line parallel or perpendicular to a given line
● Calculate perimeters of parallelograms, kites, and equilateral polygons from lengths of
sides
● Calculate areas of squares, rectangles, parallelograms, trapezoids, and triangles from
relevant lengths
● Given areas of figures, determine relevant lengths
● Calculate lengths and measures of arcs, the circumference, and the area of a circle from
relevant lengths and vice versa
● Apply Pythagorean Theorem to calculate lengths of sides in right triangles and other
figures
● Apply the Pythagorean Converse
● Tell how to derive formulas for area
● Apply perimeter formulas for parallelograms, kites, and regular polygons to real
situations
● Apply the Pythagorean Theorem in real situations
● Apply formulas for the area and circumference of a circle to real situations
● Determine the areas of polygons on a coordinate plane
● Given appropriate lengths, calculate area and lengths in 3-dimensional figures
Geometry
Cont . . .
● Calculate surface areas and volumes of cylinders, prisms, and spheres from appropriate
lengths and vice versa
● Calculate surface areas and volumes of pyramids and cones from appropriate lengths
and vice versa
● Develop formulas for specific figures from more general formulas
● Apply formulas for surface area and volume to real situations
● Apply the Distance formulas and Diagonal of a Box formulas in real situations
● Determine the distance between two points in the coordinate plane
● Determine the coordinates of the midpoint of a segment in the coordinate plane
Discrete Mathematics:
● Analyze networks
● Determine the union and intersection of sets
GRADING SCALE:
93% - 100%
A
90% - 92%
A87% - 89%
B+
83% - 86%
B
80% - 82%
B77% - 79%
C+
73% - 76%
70% - 72%
67% - 69%
63% - 66%
60% - 62%
59% and below
C
CD+
D
DE
CLASSROOM POLICIES AND PROCEDURES:
Students will be expected to use their time wisely in class to start on their homework.
Homework is always due at the beginning of class and will not be accepted late. Grades
will be based on notes, homework, quizzes, projects, tests, and exams. I will try and
provide a monthly calendar so students can plan ahead if they know they will be busy
with other activities. Students are expected to come to class prepared. They will need to
bring their book, paper, pencil, calculator, and other measuring tools every day! Notes
will be taken daily and are expected to be put in the three-ring binder. These will be
collected on test days and graded for content. Students are expected to be in their seats
when the bell rings. In order for every student to be successful, it is important that
students are respectful and polite to everyone. Disruptive behavior will not be tolerated.
If you ever have any concerns or questions, please feel free to call or email me. Working
together, we can have a fun and successful semester!
Thanks!
Mrs. Kurncz