Download mathematics department curriculum

MATHEMATICS DEPARTMENT CURRICULUM
Honors Geometry
DISTRICT OUTCOMES:
NUMBER SENSE (aka Arithmetic)
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
MEASUREMENT
5.3.1.1
TLW perform computed measurements including special triangles and all types of angles including clock 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, blueprints
5.3.3.2
TLW use formulas such as Pythagorean, area, perimeter, volume, slope, distance. circumference
ALGEBRA
5.4.2.3
5.4.3.2
5.4.3.3
TLW develop and use Coordinate Geometry throughout the course
TLW use and apply linear and quadratic equations, simplify radicals, use inequalities and systems of equations
TLW use and apply the analytic geometry of lines
GEOMETRY
5.5.1.1
TLW understand and apply basic Geometric concepts including points, lines, planes, rays, collinearity, and equidistance
5.5.1.2
TLW construct, analyze and use 2- and 3-D figures, 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: two column, paragraph, indirect, 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 using the Law of Sines and Cosines as well as Rt Triangle Trig.
5.5.3.3
TLW solve real-life problems involving geometry and logical thought processes
DATA
None
WRITTEN:
UPDATED:
UPDATED:
TEXTBOOK:
Summer, 2004
BY: Jennifer Ceh, Bill Pickert
Fall, 2004
BY: Jennifer Ceh, Bill Pickert, Greg Stritar, Pat Banach
Summer, 2008
BY: Lauren Osbourn, Vicki Breneman, Pat Banach, Loretta Gesmond
Geometry for Enjoyment and Challenge, McDougal-Littell, 1991/2000 Impression
SYLLABUS
Honors Geometry
INSTRUCTOR:
______________________
COURSE
DESCRIPTION
This course is designed to prepare talented mathematics students for success in all areas that require a rigorous
development of traditional Geometry topics. Students will relate and apply geometric concepts to algebra, statistics,
Data analysis, probability and discrete mathematics. . This course has a strong emphasis on formal proofs as well as
algebraic, paragraph, flowchart, andcoordinate proofs. Topics include points, lines and planes, the connection
between reasoning and proof, parallel & perpendicular lines, congruent triangles, polygons, proportions and similarity,
right triangle trigonometry,circle geometry, coordinate geometry and transformations. In addition, students will perform
actual measurements using both appropriate measuring instruments and geometric methods. Students will be expected
to bring a TI-30 scientific calculator/graphing calculator to class every day.
EXPECTATIONS
CREDIT:
SCHOOL YEAR: __________
TIME: ________ COURSE NUMBER: 321
After successfully completing this course, the student will understand that
1. points, lines and planes are the essential building blocks for creating the shapes, dimensions and beauty of our world.
2. proportions and ratios, including trigonometric ratios, are used to create maps, artwork, architecture and many
other things in the real world.
3. polygons and circles are the fundamental building blocks for the aesthetic and structural world around us.
4. in order to form logical arguments, complex ideas are developed through the connection of smaller, previously
accepted or proven ideas.
5. measurement is used to describe and analyze the sizes, area and capacities of many things in our world
1 credit
AREAS OF
STUDY:
LEVEL:
First Semester
1
2
3
4
5
6
Introduction to Geometry
Basic Concepts and Proofs
Congruent Triangles
Lines in the Plane
Parallel Lines and Related Figures
Line & Planes in Space
9,10 - Honors
Second Semester
7
8
9
10
11
12
Polygons
Similar Polygons
Pythagorean Theorem/Trig/Law Sines & Cosines
Circles
Area
Surface Area & Volume
TIMELINES
Honors Geometry
First Semester
Suggested Timelines
Chapter 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Introduction to Geometry
3.8
The HL Postulate (1)
14 days
Getting Started (1)
Measurements of Segments, Angles & Clock Angles (2)
Collinearity, Betweenness and Assumptions (1)
Beginning Proofs (2)
Division of Segments and Angles (2)
Paragraph Proofs (1)
Deductive Structure (1)
Statements of Logic (1)
Probability (1)
Suggested Timelines
Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Congruent Triangles
What are Congruent Figures? (1)
Three Ways to Prove Triangles Congruent (2)
CPCTC and Circles (2)
Beyond CPCTC (2)
Overlapping Triangles (2)
Types of Triangles (1)
Angle-Side Theorems (2)
Parallel Lines and Related Figures
12 days
12 days
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Perpendicularity (1)
Complementary and Supplementary Angles (1)
Drawing Conclusions (1)
Congruent Supplements and Complements (1)
Addition and Subtraction Properties (2)
Multiplication and Division Properties (2)
Transitive and Subtraction Properties (1)
Vertical Angles (1)
Chapter 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Basic Concepts and Proofs
10 days
Detours and Midpoints (1)
The Case of the Missing Diagram (1)
A Right-Angle Theorem (1)
The Equidistance Theorems (2)
Introduction to Parallel Lines (1)
Slope (2)
Chapter 5
Chapter 2
Lines in the Plane
16 days
Indirect Proof (1)
Proving that Lines are Parallel (2)
Congruent Angles Associated with Parallel Lines (2)
Four-sided Polygons (2)
Properties of Quadrilaterals (2)
Proving that a Quadrilateral is a Parallelogram (2)
Proving that Figures are Special Quadrilaterals (2)
Number of Teaching Days
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute, Stand. Testing
TOTAL DAYS: (75)
56 days
2 days
12 days
_______
75 days
TIMELINES
Honors Geometry
Second Semester
Suggested Timelines
Chapter 7
7.1
7.2
7.3
7.4
7 days
10.5
10.6
10.7
10.8
10.9
Triangle Application Theorems (1)
Two Proof-oriented triangle Theorems (2)
Formulas Involving Polygons (1))
Regular Polygons (1)
Chapter 8
81
8.2
8.3
8.4
8.5
Polygons
Similar Polygons
12 days
Ratio & Proportion (2))
Similarity (1)
Methods of Proving Triangles Similar (2)
Congruences &Proportions in Similar Triangles (2)
Three Theorems involving proportions (2)
Chapter 9
The Pythagorean Theorem
9.1 Review of Radicals & quadratic equation (1)
9.2
Intro to Circle (1)
9.3
Altitude-on-Hypotenuse (2)
9.4
Geometry’s Most Elegant Theorem (1)
9.5
the distance formula (1)
9.6
OPTIONAL – Families of Right Triangles
9.7
Special Right Triangles (2)
9.8
The Pythagorean Theorem & Space Figures (1)
9.9
Introduction to Trigonometry (1)
9.10
Trig Rations (2)
***
Law of Sines & Cosines (3)
Chapter 10
Circles
10.1
The Circle (1)
10.2
Congruent Chords (2)
10.3
Arcs of a Circle (2)
10.4
OPTIONAL: Secants & Tangents
13 days
Angles Related to a Circle (1)
More Angle-Arc Theorems (2)
Inscribed and Circumscribed Polygons (1)
OPTIONAL
The Power Theorems
Circumference and Arc Length (1)
Chapter 11
Area
11.1
Understanding Area (1)
11.2
Areas of Parallelograms and Triangles (2)
11.3
The Area of a Trapezoid (2)
11.4
Areas of Kites and Related Figures (2)
11.5
Areas of Regular Polygons (2)
11.6
Areas of Circles, Sectors, and Segments (2)
11.7
Ratios of Areas (1)
11 days
Chapter 12
12 days
17days
12.1
12.2
12.2
12.3
12.4
12.5
12.6
Surface Area and Volume
Understanding Area (1)
Surface Area of Prisms (2)
Surface Area of Pyramids (2)
Surface Areas of Circular Solids (2)
Volumes of Prisms and Cylinders (2)
Volumes of Pyramids and Cones (2)
Volumes of Spheres (1)
Number of teaching days
Performance Assessment
63 days
6 days
Review for Semester Exam
Miscellaneous Days
Total Days
2 days
19 days
90 days