MATHEMATICS DEPARTMENT CURRICULUM
Syllabus – Geometry
INSTRUCTOR: __________________________ SCHOOL YEAR: __________ PERIOD: _____ COURSE NUMBER: 317
COURSE DESCRIPTION
This is the second course in the college preparatory mathematics sequence. Units of study include the fundamentals of Geometry, logic and proof,
parallel and perpendicular lines, triangles, polygons, ratio, proportion and similarity (change the name of the unit??), right triangle trigonometry, area,
surface area and volume, circles and transformations. Technological tools, such as the TI graphing calculator, Geometers Sketchpad and Cabri
Junior, will be used for both discovery and problem solving. Classroom sets of graphing calculators will be provided. Students will be expected to
bring a TI-30X IIS scientific calculator to class on a daily basis.
ENDURING UNDERSTANDINGS - After successfully completing this course, the student will understand that:
1.
2.
3.
4.
5.
Points, lines and planes are the essential building blocks for creating the shapes and dimensions of our world.
Proportions and ratios, including trigonometric ratios, are used to create maps, artwork, architecture and many other things in the real world.
Polygons and circles are the fundamental building blocks for the aesthetic and structural world around us.
In order to form logical arguments, complex ideas are developed through the connection of smaller, previously accepted or proven ideas.
Measurement is used to describe and analyze the sizes, area and capacities of many things in our world.
CREDIT:
1 credit
LEVEL:
10 – Regular
PREREQUISITES
This course is open to juniors and seniors, who have passed both semesters of Algebra 1 with a C or better, and have passed both semesters of
Topics in Geometry with a “C” or higher.
AREAS OF STUDY
First Semester
1 Tools of Geometry
2 Reasoning and Proof
3 Parallel and Perpendicular Lines
4 Congruent Triangles
5 Relationships Within Triangles
Second Semester
6 Quadrilaterals
7 Area
8 Similarity
9 Right Triangle Trigonometry
10 Surface Area and Volume
11 Circles
12 Transformations
TIMELINES
Geometry – First Semester
Suggested Timelines
Chapter 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
2.2
2.3
2.4
2.5
3.5
3.6
Reasoning and Proof
Parallel and Perpendicular Lines
Properties of Parallel Lines (3)
Proving Lines Parallel (2)
Parallel Lines and the Triangle Angle-Sum Theorem (2)
The Polygon Angle-Sum Theorems (2)
Algebra 1 Review (pg 151) (1)
Lines in the Coordinate Plane (1)
Slopes of Parallel and Perpendicular Lines (1)
Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
10 days
Conditional Statements (1)
Inverses, Contrapositives, and Indirect Reasoning (1)
(skip Indirect Reasoning until Chapter 5)
Biconditionals and Definitions (1)
Deductive Reasoning (1)
Reasoning in Algebra (2)
Proving Angles Congruent (2)
Chapter 3
3.1
3.2
3.3
3.4
13 days
Patterns and Inductive Reasoning (1)
Points, Lines and Planes (2)
Segments, Rays, Parallel Lines and Planes (1)
Measuring Segments and Angles (2)
Basic Constructions (2)
The Coordinate Plane (1)
Perimeter, Circumference and Area (2)
Chapter 2
2.1
5.4
Tools of Geometry
Suggested Timelines
5.4
15 days
16 days
Congruent Figures (2)
Triangle Congruence by SSS and SAS (2)
Triangle Congruence by ASA and AAS (2)
Using Congruent Triangles: CPCTC (3)
Isosceles and Equilateral Triangles (2)
Congruence in Right Triangles (1)
Using Corresponding Parts of Congruent Triangles (2)
Chapter 5
5.1
5.2
5.3
Congruent Triangles
Relationships Within Triangles
9 days
Midsegments of Triangles (2)
Bisectors in Triangles (1)
Concurrent Lines, Medians and Altitudes (1)
(skip Circle property)
Inequalities in Triangles (3)
Number of Teaching Days
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute, Stand. Testing
63 days
4 days
7 days
_______
TOTAL DAYS: (75)
74 days
TIMELINES
Geometry – Second Semester
Suggested Timelines
Chapter 6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
12 days
Classifying Quadrilaterals (2)
Properties of Parallelograms (2)
Proving that a Quadrilateral is a Parallelogram (2)
Special Parallelograms (2)
Trapezoids and Kites (1)
OPTIONAL - Placing Figures in the Coordinate Plane
OPTIONAL - Proofs Using Coordinate Geometry
Chapter 7
7.1
n/a
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Quadrilaterals
Area
9.3
9.4
9.5
8.1
8.2
8.3
8.4
8.5
8.6
Ratios and Proportions (1)
Similar Polygons (2)
Proving Triangles Similar (2)
Similarity in Right Triangles (2)
Proportions in Triangles (2)
COVER THE BASICS Perimeters and Areas of Similar Figures (1)
Right Triangle Trigonometry
8 days
The Tangent Ratio &
Sine and Cosine Ratios (2)
Angles of Elevation and Depression (2)
OPTIONAL - Vectors
OPTIONAL - Trigonometry and Area
Chapter 10
18 days
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
12 days
Surface Area and Volume
14 days
Space Figures and Nets (1)
OPTIONAL - Space Figures and Drawings
Surface Areas of Prisms and Cylinders (2)
Surface Areas of Pyramids and Cones (2)
Volume of Prisms and Cylinders (2)
Volumes of Pyramids and Cones (2)
Surface Areas and Volume of Spheres (1)
OPTIONAL - Areas and Volumes of Similar Solids
Chapter 11
OPTION – Teach Chapter 11 - Circles, immediately after Chapter 7 rather
than after Chapter 10.
Similarity
Chapter 9
9.1 & 9.2
Area of Parallelograms and Triangles (2)
Review of Square Roots (1)
The Pythagorean Theorem and Its Converse (2)
Special Right Triangles (2)
Areas of Trapezoids, Rhombuses and Kites (2)
Areas of Regular Polygons (2)
Circles and Arcs (2)
Areas of Circles and Sectors (2)
OPTIONAL - Geometric Probability
Chapter 8
Suggested Timelines
Circles
7 days
11.1
Tangent Lines (1)
11.2
Chords and Arcs (2)
11.3
Inscribed Angles (1)
11.4
OPTIONAL – Angle Measures & Segment Lengths
11.5 & 11.6
Circles in the Coordinate Plane & Locus: A Set of Points
Cover the vocabulary with other sections from Chapter 11.
Suggested Timelines
Chapter 12
Transformations
4 days
Use the purple mirrors to cover the basics of the following sections.
12.1
12.2
12.3
12.4
12.5
12.6
12.7
Reflections (1)
Translations (1)
Rotations (1)
OPTIONAL - Composition of Reflections
Symmetry (1)
OPTIONAL - Tessellations
OPTIONAL - Dilations
Number of Teaching Days
Performance Assessment
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute,
Stand. Testing Review, Stand. Testing
75 days
3 days
5 days
TOTAL DAYS: (92)
93 days
10 days
______
STATE GOALS & DISTRICT OUTCOMES
Geometry
STATE GOAL 6 - NUMBER SENSE - Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition,
subtraction, multiplication, division), patterns, ratios and proportions.
5.2.3.2
TLW understand and use arithmetic operations, ratios and/or proportions and multiple methods to obtain exact and/or estimated
results when solving theoretical and/or real life problems
STATE GOAL 7 - ESTIMATION and MEASUREMENT - Estimate, make and use measurements of objects, quantities and relationships and determine
acceptable levels of accuracy.
5.3.1.1
TLW perform computed measurements including special triangles, angles, complementary, supplementary and vertical angles
5.3.2.1
TLW estimate and find measurements using various measuring instruments and determine acceptable levels of accuracy
5.3.2.2
TLW understand, make, and use scale drawings, maps, globes, blueprints, latitude and longitude
5.3.3.2
TLW use formulas such as Pythagoras, area, perimeter, volume & conversions within a measurement system
STATE GOAL 8 - ALGEBRA and ANALYTICAL METHODS - Use algebraic and analytical methods to identify and describe patterns and
relationships in data, solve problems and predict results.
5.4.2.3
TLW develop and use Coordinate Geometry (Ordered Pairs)
5.4.3.2
TLW use and apply linear and quadratic equations, inequalities and systems of equations
5.4.3.3
TLW use and apply the analytic geometry of lines and parabolas
STATE GOAL 9 - GEOMETRY - Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.
5.4.1.1
TLW understand and apply basic Geometric concepts including points, lines, planes, rays, collinearity, and adjacent angles
5.4.1.2
TLW construct, analyze and use 2- and 3-D figures, perspective drawings, tessellations, symmetry, and transformations
5.5.2.1
TLW apply Euclidean relationships including parallel and perpendicular lines, bisectors, medians and altitudes
5.5.2.2
TLW solve congruence, similarity and triangle problems (Non Proof)
5.5.2.3
TLW solve quadrilateral and polygon problems
5.5.2.4
TLW use various types of proof, symbolic logic and reasoned arguments
5.5.2.5
TLW solve problems involving arcs, chords, inscribed angles and radii of a circle
5.5.3.2
TLW understand and use the basic concepts of right triangle trigonometry, including indirect measurement for finding height
and distance
5.5.3.3
TLW solve real-life problems involving geometry and logical thought processes
STATE GOAL 10 - DATA ANALYSIS and PROBABILITY - Collect, organize and analyze data using statistical methods; predict results; and interpret
uncertainty using concepts of probability.
None
WRITTEN:
UPDATED:
Summer, 2004
January 2005, Summer 2005
BY: P. Banach, L. Gesmond, M. Laciak, K. Lukareski, R. Cracco
TEXTBOOK: Geometry, Prentice Hall, 2004