Syllabus 2008-2009
Applied Geometry
Mrs. Sarah M Vincent
Objective: Geometry objectives are designed for students who have completed the objectives for Algebra I. Study includes experiences and activities that foster in students a feeling for the value of geometry in their lives. Emphasis is placed on development of conjectures by inductive processes using manipulatives and computer software. Cooperative learning groups are particularly effective in allowing students to become proficient in analyzing conjectures and in formulating both formal and informal proofs. Emphasis should be placed on connections to other branches of mathematics and other disciplines, and on workplace applications. The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives.
|
Objectives
|
Students will
|
|
|
represent eometric figures, such as points, lines, planes, segments, rays, and angles pictorially with proper identification and distinguish between undefined and defined terms.
|
|
|
|
differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.
|
|
|
|
use the basic concepts of symbolic logic including identifying the converse, inverse, and contrapositive of a conditional statement and test the validity of conclusions with methods that include Venn Diagrams.
|
|
|
|
validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning.
|
|
|
|
construct formal and informal proofs by applying definitions, theorems, and postulates related to such topics as
· complementary, / supplementary, / vertical angles, / angles formed by perpendicular lines, and / justify the steps.
|
|
|
|
compare and contrast the relationships between angles formed by two lines cut by a transversal when lines are parallel and when they are not parallel, and use the results to develop concepts that will justify parallelism.
|
|
|
|
make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.
|
|
|
|
identify general properties of and compare and contrast the properties of convex and concave quadrilaterals
· parallelograms / rectangles / rhombuses / squares / trapezoids
|
|
|
|
draw conclusions in problem solving situations that include two and three dimensions of figures based on the properties of similarity.
|
|
|
|
investigate measures of angles and lengths of segments to determine the existence of a triangle (triangle inequality) and to establish the relationship between the measures of the angles and the length of the sides (with and without technology).
|
|
|
|
verify and justify the basis for the trigonometric ratios by applying properties of similar triangles and use the results to find inaccessible heights and distances. Using the ratios of similar triangles to find unknown side lengths and angle measures, construct a physical model that illustrates the use of a scale drawing in a real-world situation.
|
|
|
|
apply Pythagorean Theorem & its converse to solve real-world problems & derive special right triangle relationships (i.e. 30-60-90, 45-45-90).
|
|
|
|
investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.
|
|
|
|
find angle measures of interior and exterior angles; given a polygon, find the length of sides from given data; and use properties of regular polygons to find any unknown measurements of sides or angles.
|
|
|
|
develop properties of tessellating figures and use those properties to tessellate the plane.
|
|
|
|
derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.
|
|
|
|
apply concepts of analytical geometry such as formulas for distance, slope, and midpoint and apply these to finding dimensions of polygons on the coordinate plane
|
.
|
|
|
construct a triangle’s medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.
|
|
|
|
create and apply concepts using transformational geometry and laws of symmetry, of a
· reflection / translation / rotation / glide reflection / dilation of a figure, &/ develop logical arguments for congruency & similarity.
|
|
|
|
compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports.
|
|
|
|
approximate the area of irregularly shaped regions based on the approximations and the attributes of the related region, develop a formula for finding the area of irregularly shaped regions. Plan, organize and present results by justifying conclusions.
|
|
Geometry students at the mastery level investigate, make conjectures, justify, compare and contrast and apply, as appropriate relationships involving the properties of parallel and perpendicular lines, right triangles, congruent and similar figures, convex and concave quadrilaterals, other polygons, tessellating figures, and circles. They represent geometric figures pictorially with proper identification and distinguish between undefined and defined terms. They investigate measures of angles and draw conclusions for the relationship to its arcs. They draw and justify conclusions in real-world settings as they differentiate and apply inductive and deductive reasoning.
In a problem solving situation, they apply the Pythagorean Theorem and its converse, draw conclusions that include two and three dimensions, and solve formulas using nets. They use symbolic logic to construct logical arguments and test the validity of conclusions. They apply undefined terms, definitions, postulates, and theorems to construct formal and informal proofs. They use the properties of similar triangles to verify and justify the trigonometric ratios by applying the results to construct a physical model that illustrates the use of a scale drawing in a real-world situation and determine the measure of inaccessible heights or distances. They create and apply concepts using transformational geometry to construct transformations and explore congruencies and similarities and develop logical arguments. They apply concepts of analytical geometry to develop and apply formulas, to construct arguments, and to solve practical problems.
They compare and contrast the properties of Euclidean geometry with other geometries. They construct a triangle’s medians, altitudes, angle and perpendicular bisectors and develop logical concepts to be used in solving real-world problems.
Text Book: Geometry, Glencoe Mathematics, ISBN: 0-07-865106-9 This textbook is provided to the students as a resource.
Materials: Geometry tools and paper are provided. Students are required to come to class each day with their pencils, notebook, file folder and scientific calculator.
Grades Scale adopted by the Harrison County Board of Education
93-100 A
85-92 B
75-84 C
65-74 D
0-64 F
Grades will be bases on class work, labs, homework, quizzes and tests.
Absences: It is the student’s responsibility to check the “make-up” box and LiveGrades to make sure all make-up work is completed and turned in on time. (See SHHS handbook)
|
Electronic Curriculum Materials by Janet Benincosa
|
|
GEOMETRY
|
|
Big Ideas / Content
|
Discovering Algebra
|
Objectives
|
Glencoe Geometry
|
WESTEST
|
Activities
|
Selected Technology Resources
|
|
1st Six Weeks
|
|
Introducing Geometry
|
Chapter 1
|
M.O.G.3.1
M.O.G.3.8
|
Sections 1-1, 1-2, 1-4,
|
MA.10.3.1
|
Investigations as listed in Chapter 1
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Reasoning
|
Chapter 2
|
M.O.G.3.2
M.O.G.3.5
M.O.G.3.6
|
Sections 2-1, 2-2, 2-4, 2-8
|
MA.10.3.2**
|
Investigations as listed in Chapter 2
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Tools of Geometry
|
Chapter 3
|
M.O.G.3.18
|
Section 5-1
|
MA.10.3.1
|
Investigations as listed in Chapter 3
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
2nd Six Weeks
|
|
Triangle Properties
|
Chapter 4
|
M.O.G.3.4
M.O.G.3.7
M.O.G.3.10
M.O.G.3.20
|
Chapter 4
|
MA.10.4.3
|
Investigations as listed in Chapter 4
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Polygon Properties
|
Chapter 5
|
M.O.G.3.4
M.O.G.3.8
M.O.G.3.14
|
Chapter 8
|
MA.10.4.3
|
Investigations as listed in Chapter 5
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
3rd Six Weeks
|
|
Circle Properties
|
Chapter 6
|
M.O.G.3.4
M.O.G.3.13
M.O.G.3.17
|
Chapter 10
|
MA.10.3.4*
|
Investigations as listed in Chapter 6
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Transformations and Tessellations
|
Chapter 7
|
M.O.G.3.15
M.O.G.3.19
|
Chapter 9
(Through Section 9.5)
|
N/A
|
Investigations as listed in Chapter 7
|
Graphing Calculators
Geometer’s Sketchpad www.keypress.com
|
|
Area of Polygons
|
Chapter 8
(through 8.5)
|
M.O.G.3.14
|
Chapter 11
(Sections 1-3)
|
MA.10.4.4***
|
Investigations as listed in Chapter 8
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
4th Six Weeks
|
|
Area of Polygons
|
Chapter 8
(Sections 8.6)
|
M.O.G.3.14
M.O.G.3.16
M.O.G.3.21
|
Chapter 11
(Section 11-4)
|
MA.10.4.4***
|
Investigations as listed in Chapter 8
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Pythagorean Theorem
|
Chapter 9
|
M.O.G.3.12
M.O.G.3.13
|
Activity 1-3
Sections 7-2, 7-3
|
MA.10.3.5*
|
Investigations as listed in Chapter 9
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Volume
|
Chapter 10.1 - 10.2
|
M.O.G.3.16
|
Chapter 13
(Sections 13-1 through 13-3)
|
MA.10.4.4***
|
Investigations as listed in Chapter 10
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
5th Six Weeks
|
|
Volume and Surface Area
|
Chapter 10.3 to end Chapter 8 (Section 8.7)
|
M.O.G.3.16
|
Chapter 12
|
MA.10.4.4***
|
Investigations as listed in Chapter 10
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Similarity
|
Chapter 11
|
M.O.G.3.9
M.O.G.3.11
|
Chapter 6,
Chapter 13 (Section 13-4)
|
MA.10.3.3**
|
Investigations as listed in Chapter 11
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Trigonometry
|
Chapter 12 through 12-4
|
M.O.G.3.11
|
Sections 7-4, 7-5
|
N/A
|
Investigations as listed in Chapter 12
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
6th Six Weeks
|
|
Trigonometry
|
Chapter 12
(Sections 12.4 to end)
|
M.O.G.3.11
|
Sections 7-4, 7-5
|
N/A
|
Investigations as listed in Chapter 12
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|
Geometry as a Mathematical System
|
Chapter 13
|
M.O.G.3.4
M.O.G.3.5
M.O.G.3.6
M.O.G.3.8
M.O.G.3.17
|
Sections 2-5, 2-6,
4-7, 5-3
|
N/A
|
Investigations as listed in Chapter 13
|
Graphing Calculators
Geometer’s Sketchpad
www.keypress.com
|
|