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SYLLABUS
Topics in Geometry
INSTRUCTOR:
_____________________________ SCHOOL YEAR: __________
PERIOD: ________ COURSE NUMBER: 321
COURSE DESCRIPTION
This course will cover many of the same topics as traditional Geometry, but will be less rigorous, placing more emphasis on general concepts and
their applications. Units of study include fundamentals of geometry, logic and proof, polygons, perpendicular and parallel lines, applying right
triangles and trigonometry, circles, ratios and proportion, area, surface area and volume, transformations and triangles. Students will be expected to
support their conclusions with substantiated reasoning and logical arguments. Throughout the course, students will be expected to maintain
previously learned algebra skills. Students will be expected to bring a TI-30XIIS 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, 11, 12 - Regular
AREAS OF STUDY
First Semester
Second Semester
1
2
3
4
5
6
7
8
9
10
11
Basics of Geometry
Segments and Angles
Parallel and Perpendicular Lines
Triangle Relationships
Congruent Triangles
Quadrilaterals
Similarity
Polygons and Area
Surface Area and Volume
Right Triangles and Trigonometry
Circles
TIMELINES
Topics in Geometry
First Semester
Suggested Timelines
Chapter 1
1.1
1.2
1.3
1.4
1.5
1.6
Basics of Geometry
11 days
Finding and Describing Patterns (1)
Inductive Reasoning (2)
Points, Lines and Planes (1)
Sketching Intersections (1)
Segments and their measures (2)
Angles and their measures (2)
Chapter 2
Segments and Angles
Suggested Timelines
Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
12 days
Segment Bisectors (1)
Angle Bisectors (2)
Complementary and Supplementary Angles (1)
Vertical Angles (2)
If-Then Statements and Deductive Reasoning (2)
Properties of Equality & Congruence (2)
Chapter 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Parallel and Perpendicular Lines
Relationships Between Lines (1)
Theorems About Perpendicular Lines (1)
Angles Formed by Transversals (2)
Parallel Lines and Transversals (2)
Showing Lines are Parallel (1)
Using Perpendicular and Parallel Lines (2)
Translations (2)
13 days
Classifying Triangles (1)
Angle Measures of Triangles (2)
Isosceles and Equilateral Triangles (1)
The Pythagorean Theorem and Distance Formula (3)
The Converse of the Pythagorean Theorem (2)
Medians of a Triangle (1)
Triangle Inequalities (1)
Chapter 5
2.1
2.2
2.3
2.4
2.5
2.6
Triangle Relationships
13 days
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Congruent Triangles
14 days
Congruence and Triangles (1)
Proving Triangles Congruent – SSS & SAS (2)
Proving Triangles Congruent – ASA & AAS (2)
Hypotenuse-Leg Congruence – HL (2)
Using Congruent Triangles (2)
Angle Bisectors and Perpendicular Bisectors (1)
Reflections and Symmetry (2)
Number of Teaching Days
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute, Stand. Testing
TOTAL DAYS: (75)
63 days
4 days
7 days
_______
74 days
TIMELINES
Topics in Geometry
Second Semester
Suggested Timelines
Suggested Timelines
Chapter 6
Quadrilaterals
10 days
Chapter 9 (con’t)
6.1
6.2
6.3
6.4
6.5
6.6
Polygons (1)
Properties of Parallelograms (2)
Showing quadrilaterals are parallelograms (1)
Rhombuses, rectangles and squares (2)
Trapezoids (1)
Reasoning about Special Quadrilaterals (1)
Chapter 7
7.1
7.2
7.3
7.4
7.5
7.6
11 days
Surface Area and Volume
Solid Figures (1)
Surface Area of Prisms and Cylinders (2)
Surface Area of Pyramids and Cones (2)
Volume of Prisms and Cones (1)
10.1
10.2
10.3
10.4
10.5
10.6
13 days
11 days
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
Right Triangles and Trigonometry
11 days
Simplifying Square Roots (2)
45-45-90 Triangles (1)
30-60-90 Triangles (2)
Tangent Ratio (1)
Sine and Cosine Ratios (1)
Solving Right Triangles (2)
Chapter 11
Classifying Polygons (1)
Angles in Polygons (2)
Area of Squares and Rectangles (1)
Area of Triangles (2)
Area of Parallelograms (2)
Area of Trapezoids (1)
Circumference and Area of Circles (2)
Chapter 9
9.1
9.2
9.3
9.4
Polygons and Area
Volume of Pyramids and Cones (1)
Surface Area and Volume of Spheres (2)
Chapter 10
Ratio and Proportion (2)
Similar Polygons (2)
Showing Triangles are Similar – AA (1)
Showing Triangles are Similar – SSS & SAS (1)
Proportions and Similar Triangles (2)
Dilations (1)
Chapter 8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Similarity
9.5
9.6
Circles
14 days
Parts of a Circle (1)
Properties of Tangents (2)
Arcs and Central Angles (2)
Arcs and Chords (2)
Inscribed Angles and Polygons (1)
Properties of Chords (1)
Equations of Circles (1)
Rotations (2)
Number of Teaching Days
Performance Assessment
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute,
Stand. Testing Review, Stand. Testing
70 days
3 days
5 days
TOTAL DAYS: (92)
88 days
10 days
______
MATHEMATICS DEPARTMENT CURRICULUM
Topics in Geometry
DISTRICT OUTCOMES:
NUMBER SENSE
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
5.3.1.2
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
5.3.3.2
TLW use formulas such as Pythagoras, area, perimeter, volume & conversions within a measurement system
ALGEBRA
5.4.2.3
5.4.3.2
5.4.3.4
TLW develop and use Coordinate Geometry
TLW use and apply linear and quadratic equations, inequalities and systems of equations
TLW review algebraic concepts including operations on polynomials and factoring
GEOMETRY
5.5.1.1
TLW understand and apply basic Geometric concepts including points, lines, planes, rays, collinearity, and adjacent angles
5.5.1.2
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
DATA
5.6.1.1
5.6.3.1
TLW construct, analyze and/or draw conclusions from charts, tables, and/or data graphs
TLW apply the concepts of probability to solve theoretical and/or real-life problems
WRITTEN:
TEXTBOOK:
Summer, 2004
BY:
Geometry Concepts and Skills, McDougal-Littell, 2003
Judy Canning, Kelly Lukareski