Download Honors Geometry Curriculum

Honors Geometry
Curriculum
282 – 01
Northern Berkshire Vocational Regional School District
Charles H. McCann Technical High School
70 Hodges Cross Road
North Adams, MA 01247
Teacher: John Euchler
June 2006
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Course Philosophy
In order to fulfill our mission of graduating “individuals who are technically skilled and
academically prepared to meet the challenges of a global economy” (Charles H. McCann
mission statement), it is important that our graduates have achieved mathematical
competence in many areas. The Honors Geometry course is designed for grade 10
students who have completed the Honors Algebra curriculum as Algebra is integrated
throughout this course. Students will achieve competence in reaching the following
goals:
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•
•
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To express mathematical ideas coherently both verbally and in writing
To explore the connections that exist within mathematics and with other
disciplines
To develop critical thinking and problem solving skills
To demonstrate understanding of more advanced math concepts
Course Description
Honors Geometry is a full year, double period course that meets every other week.
This course includes the basic structure of Euclidean Geometry and the development of
formal proofs. Examples of solid geometry are integrated throughout the course.
Practical applications, including algebraic methods, are applied to problem-solving.
Topics include development of the logical study of Euclidean Geometry through the use
of axioms, postulates, and theorems as they relate to points, lines, planes, polygons,
prisms, angles, circles, and arcs; congruence and properties of polygons, constructions,
congruent triangles, parallel and perpendicular lines, the Pythagorean Theorem, similar
polygons, perimeter, circumference, area, surface area, total area, volume. Students often
research a topic or person and present their findings to the class. These projects expand
the students’ knowledge of mathematics and help prepare them for their senior class
project.
Course Syllabus
Instructional Philosophy
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Honors Geometry will allow students to explore and experience mathematics through a
variety of activities and real world applications. Emphasis will be placed on students’
understanding of key concepts and the ability of students to demonstrate their learned
knowledge through exams, projects, discussions and written work. Students will be
encouraged to inquire, discuss, analyze, and question the various topics presented
throughout the course in order to promote complete mastery of topics.
Major Course Projects and Activities
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Homework
o A variety of homework assignments will be given to students
throughout the course to help reinforce learning objectives.
Homework assignments are worth 15% of a student’s grade each
quarter.
Notebook/Portfolio
o Students will be required to compile a course notebook/portfolio
which will include all class notes, homework assignments, homework
corrections, handouts, classroom activities/projects, quizzes, and
exams.
o The notebook/portfolio will be collected at the end of each marking
quarter. It will be graded on organization and completeness.
o Students are encouraged to organize this notebook/portfolio in order to
have a master resource for the course.
o The notebook is worth 10% of a student’s grade each quarter.
Attendance/Participation
o Daily attendance, preparation, and participation are expected, will be
recorded, and are worth 10% of a student’s grade each quarter. This is
in accordance with McCann’s Attendance Policy which is outlined in
detail in the Student/Parent Handbook.
o When an attendance/participation grade is given, the following items
are being considered: being present and prepared for class, whether
students display cooperation, successful progress towards completing
class work, and participation in daily activities.
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Other
o A variety of projects and activities may be incorporated as deemed
appropriate by the individual course instructors.
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COURSE ASSESSMENT PLAN
For the Honors Geometry students at Charles H. McCann Technical School the following
assessment plan will be followed. This plan is in alignment with the program assessment
plan of the Mathematics Department at Charles H. McCann Technical School which is
stated as follows:
GRADING SYSTEM:
“Report cards are issued quarterly and serve as a guideline for students and their
parents to measure achievement. Parents are encouraged to contact teachers and
counselors to ensure a continuing participation in student progress. Courses are graded
numerically in accordance with the following values.” (2005-2006 Charles H. McCann
Student/Parent Handbook)
90-100
Advanced
I
80-90
Proficient
X
70-80
Satisfactory
T
65-70
Passing
0-64
Failing
Incomplete (make-up
required)
Excused
Below standard (no
credit)
MATH ACADEMIC GRADING POLICY:
65% Tests & Quizzes
Test
Quizzes
Projects
Research reports
25% Homework/Notebook Portfolio
15% Homework
10% Notebook Portfolio
Lecture Notes
Homework
Collection of all
assignments
10% Attendance/Participation
Cooperation
Class Work
Attendance
Participation
Effort and Diligence
Extra Help – Homework Club – Tuesday and Thursday from 3-4 PM and with
teacher by appointment. The Honors Geometry instructor is available after school
for extra help a minimum of six hours per week.
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FINAL EXAMINATIONS
“Final examinations must be taken when scheduled. A grade of “F” will be given for any
examination missed unless previously approved by the Principal. Final examinations will
be by course title for all students. No exemptions will be given.” (2005-2006 Charles H.
McCann Student/Parent Handbook) In the Honors Geometry course, the final
examination will be counted as two test grades in the fourth marking period.
Timeline:
Honors Geometry: Grade 10
• First Quarter
o Patterns and Inductive Reasoning
• Conjectures
o Algebra Review
• Probability
o Points, Lines, and Planes
• Collinear/Noncollinear points
• Coplanar Points and Lines
• Postulates
o Segments, Rays, Parallel Lines and Planes
• Opposite Rays
• Skew Lines
o Algebra Review
• Solving Linear Equations
o Measuring Angels and Segments
• Ruler Postulate
• Congruent Segments
• Segment Addition
• Protractor Postulate
• Classifying Angles
• Congruent Angles
• Angle Addition
• Midpoint
• Perpendicular Lines
o Constructions
• Straightedge
• Compass
• Congruent Segments
• Congruent Angles
• Perpendicular Bisectors
• Angle Bisectors
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o Using Deductive Reasoning
• Properties of Equality and Real Numbers
• Properties of Congruence
• Vertical Angles
• Adjacent Angles
• Complementary Angles
• Supplementary Angles
o The Coordinate Plane
• The Distance Formula
• The Midpoint Formula
o Triangles
• Triangle Angle-Sum Theorem
• Exterior Angle Theorem
• Classifying Triangles
o Polygons
• Convex
• Concave
• Polygon Interior Angle-Sum Theorem
• Polygon Exterior Angle-Sum Theorem
• Regular Polygons
• Second Quarter
o Parallel and Perpendicular Lines in the Coordinate Plane
• Slope Review
• Graphing Lines/Graphing Calculator
• Slopes of Parallel Lines
• Slopes of Perpendicular Lines
o Algebra Review
• Writing Linear Equations
o Classifying Quadrilaterals
• Parallelograms
• Rhombus
• Rectangle
• Square
• Kite
• Trapezoid
• Isosceles Trapezoid
o Circles
• Radius/Diameter
• Central Angles and Arcs
• Arc Addition Postulate
o Congruent and Similar Figures
• Similarity Ratio
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o Transformations
• Reflections
• Translations
• Rotations
• Reflectional Symmetry
• Line Symmetry
• Rotational Symmetry
• Dilations
o Triangle Relationships
• Isosceles Triangle Theorems
• Proofs – Two-Column Form
• Midsegments of triangles
• Triangle Inequalities
• Third Quarter
o Perimeter
o Area
• Rectangles
• Parallelograms
• Triangles
o Algebra Review – Simplifying Radicals
o Pythagorean Theorem
• Pythagorean Triples
• Converse of Pythagorean Theorem
o Special Right Triangles
• 45º - 45º - 90º Triangles
• 30º - 60º - 90º Triangles
o Area of trapezoids
o Area of Regular Polygons
o Circles
• Circumference
• Arc Length
• Area
• Sectors
• Segments of Circles
o Lateral and Surface Area
• Prisms
• Cylinders
• Pyramids
• Cones
o Volume
• Prisms
• Cylinders
• Pyramids
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•
•
Cones
Spheres
• Fourth Quarter
o MCAS Review
o Parallel Lines and Related Angles
• Corresponding Angles
• Alternate Interior Angles
• Same-Side Interior Angles
o Proving Lines Parallel
o Proving Triangles Congruent
• SSS
• SAS
• ASA
• AAS
o Congruent Right Triangles
o Properties of Parallelograms
o Properties of Trapezoids
o Properties of Kites
Standards
Massachusetts Mathematics Curriculum Framework
Learning Standards for Grades 9 -10 (November 2000)
Course Curriculum
Topic
Patterns and Inductive
Reasoning
Triangle/Triangle
Relationships
Standard
10.P.1 Describe, complete, extend, analyze, generalize, and
create a wide variety of patterns, including iterative,
recursive (e.g., Fibonacci Numbers), linear, quadratic, and
exponential functional relationships.
10.G.1 Identify figures using properties of sides, angles, and
diagonals. Identify the figures' type(s) of symmetry.
10.G.5 Solve simple triangle problems using the triangle
angle sum property and/or the Pythagorean theorem.
Classifying
Quadrilaterals/Properties
of Quadrilaterals
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10.G.1 Identify figures using properties of sides, angles, and
diagonals. Identify the figures' type(s) of symmetry.
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Parallel Lines and Related
Angles
10.G.3 Recognize and solve problems involving angles
formed by transversals of coplanar lines. Identify and
determine the measure of central and inscribed angles and
their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on
the same circle.
Circles
10.G.3 Recognize and solve problems involving angles
formed by transversals of coplanar lines. Identify and
determine the measure of central and inscribed angles and
their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on
the same circle.
Pythagorean Theorem
10.G.5 Solve simple triangle problems using the triangle
angle sum property and/or the Pythagorean theorem.
Constructions
10.G.2 Draw congruent and similar figures using a
compass, straightedge, protractor, and other tools such as
computer software. Make conjectures about methods of
construction. Justify the conjectures by logical arguments.
Congruent and Similar
Figures
10.G.4 Apply congruence and similarity correspondences
(e.g., ∆ABC ∆XYZ) and properties of the figures to find
missing parts of geometric figures, and provide logical
justification.
Special Right Triangles
10.G.6 Use the properties of special triangles (e.g.,
isosceles, equilateral, 30°-60°-90º, 45°-45°-90°) to solve
problems.
The Coordinate Plane
10.G.7 Using rectangular coordinates, calculate midpoints
of segments, slopes of lines and segments, and distances
between two points, and apply the results to the solutions of
problems.
Parallel and Perpendicular
Lines in a Coordinate
Plane
10.G.7 Using rectangular coordinates, calculate midpoints
of segments, slopes of lines and segments, and distances
between two points, and apply the results to the solutions of
problems.
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10.G.8 Find linear equations that represent lines either
perpendicular or parallel to a given line and through a point,
e.g., by using the "point-slope" form of the equation.
Transformations
10.G.9 Draw the results, and interpret transformations on
figures in the coordinate plane, e.g., translations, reflections,
rotations, scale factors, and the results of successive
transformations. Apply transformations to the solutions of
problems.
Perimeter and Area
10.M.1 Calculate perimeter, circumference, and area of
common geometric figures such as parallelograms,
trapezoids, circles, and triangles.
Lateral and Surface Area
10.M.2 Given the formula, find the lateral area, surface
area, and volume of prisms, pyramids, spheres, cylinders,
and cones, e.g., find the volume of a sphere with a specified
surface area.
Surface Area and Volume
10.M.3 Relate changes in the measurement of one attribute
of an object to changes in other attributes, e.g., how
changing the radius or height of a cylinder affects its surface
area or volume.
Vocational/Technical Education Curriculum Frameworks
Strands 1, 4, 5, and 6
Strand 4: Employability
4.b Develop employability skills to secure and keep employment in chosen field
4.B.01a
4.B.03a
4.B.06a
4.B.07a
4.B.08a
Apply strategies to enhance effectiveness of all types of communications in
the workplace
Locate information from books, journals, magazines, and the Internet
Explain information presented graphically
Use writing/publishing/presentation applications
Apply basic skills for work-related oral communication
4.c Solve problems using critical thinking
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4.C.01a
4.C.04a
4.C.05a
Demonstrate skills used to define and analyze a given problem
Explain strategies used to formulate ideas, proposals and solutions to
problems
Select potential solutions based on reasoned criteria
Strand 6: Underlying Use of Technology
6.c Demonstrate ability to use technology for research, problem solving, and
communication
6.C.03a Demonstrate the use of appropriate electronic sources to conduct research
(e.g., Web sites, online periodical databases, and online catalogs)
6.C.04a
6.C.05a
6.C.06a
Demonstrate proper style (with correct citations) when integrating electronic
research results into a research project
Collect, organize, analyze, and graphically present data using the most
appropriate tools
Present information, ideas, and results of work using any of a variety of
communications technologies (e.g., multimedia presentations, Web pages,
videotapes, desktop-published documents)
Vocational/Technical Education Curriculum Frameworks
Strand 3:Embedded Academics
Automotive Technology
3.B.01c 10.G.3
Recognize and solve problems involving
angles formed by transversals of coplanar
lines. Identify and determine the measure of
central and inscribed angles and their
associated minor and major arcs. Recognize
and solve problems associated with radii,
chords, and arcs within or on the same circle.
9/10
Geometry
3.B.02c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.03c 10.M.1.
Calculate perimeter, circumference, and area
of common geometric figures such as
parallelograms, trapezoids, circles, and
triangles.
9/10
Measurement
3.B.04c 10.M.2
Given the formula, find the lateral area, surface 9/10
area, and volume of prisms, pyramids,
spheres, cylinders, and cones, e.g., find the
volume of a sphere with a specified surface
Measurement
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area.
Carpentry/Cabinetry
3.B.01c 10.G.3
Recognize and solve problems involving angles
formed by transversals of coplanar lines.
Identify and determine the measure of central
and inscribed angles and their associated minor
and major arcs. Recognize and solve problems
associated with radii, chords, and arcs within or
on the same circle.
9/10 Geometry
3.B.02c 10.G.8
Find linear equations that represent lines either
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
9/10 Geometry
3.B.03c 10.G.10 Demonstrate the ability to visualize solid
objects and recognize their projections and
cross sections.
9/10 Geometry
3.B.04c 10.M.1
Calculate perimeter, circumference, and area of
common geometric figures such as
parallelograms, trapezoids, circles, and
triangles.
9/10 Measurement
3.B.05c 10.G.8
Find linear equations that represent lines either
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
9/10 Geometry
Electricity
3.B.01c 10.M.1
Calculate perimeter, circumference, and area
of common geometric figures such as
parallelograms, trapezoids, circles, and
triangles.
9/10 Measurement
3.B.02c 10.G.5
Solve simple triangle problems using the
triangle angle sum property and/or the
Pythagorean theorem.
9/10 Geometry
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Information Technology
3.B.01c 10.G.3
Recognize and solve problems involving angles 9/10
formed by transversals of coplanar lines.
Identify and determine the measure of central
and inscribed angles and their associated minor
and major arcs. Recognize and solve problems
associated with radii, chords, and arcs within or
on the same circle.
Geometry
3.B.02c 10.G.4
Apply congruence and similarity
9/10
Geometry
correspondences (e.g., ∆ABC ≅ ∆XYZ) and
properties of the figures to find missing parts of
geometric figures, and provide logical
justification.
3.B.03c 10.G.6
Use the properties of special triangles (e.g.,
isosceles, equilateral, 30°-60°-90°, 45°-45°90°) to solve problems.
9/10
Geometry
3.B.04c 10.G.7
Using rectangular coordinates, calculate
midpoints of segments, slopes of lines and
segments, and distances between two points,
and apply the results to the solutions of
problems.
9/10
Geometry
3.B.05c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.06c 10.G.9
Draw the results, and interpret transformations 9/10
on figures in the coordinate plane, e.g.,
translations, reflections, rotations, scale factors,
and the results of successive transformations.
Apply transformations to the solutions of
problems.
Geometry
3.B.07c 10.M.2
Given the formula, find the lateral area, surface 9/10
area, and volume of prisms, pyramids, spheres,
cylinders, and cones, e.g., find the volume of a
sphere with a specified surface area.
Measurement
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3.B.08c 10.G.3
Recognize and solve problems involving angles 9/10
formed by transversals of coplanar lines.
Identify and determine the measure of central
and inscribed angles and their associated minor
and major arcs. Recognize and solve problems
associated with radii, chords, and arcs within or
on the same circle.
Geometry
3.B.09c 10.G.4
Apply congruence and similarity
9/10
Geometry
correspondences (e.g., ∆ABC ≅ ∆XYZ) and
properties of the figures to find missing parts of
geometric figures, and provide logical
justification.
3.B.10c 10.G.6
Use the properties of special triangles (e.g.,
isosceles, equilateral, 30°-60°-90°, 45°-45°90°) to solve problems.
9/10
Geometry
3.B.11c 10.G.7
Using rectangular coordinates, calculate
midpoints of segments, slopes of lines and
segments, and distances between two points,
and apply the results to the solutions of
problems.
9/10
Geometry
3.B.12c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.13c 10.G.9
Draw the results, and interpret transformations 9/10
on figures in the coordinate plane, e.g.,
translations, reflections, rotations, scale factors,
and the results of successive transformations.
Apply transformations to the solutions of
problems.
Geometry
3.B.14c 10.M.2
Given the formula, find the lateral area, surface 9/10
area, and volume of prisms, pyramids, spheres,
cylinders, and cones, e.g., find the volume of a
sphere with a specified surface area.
Measurement
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Machine Technology
3.B.01c 10.G.3
Recognize and solve problems involving angles 9/10
formed by transversals of coplanar lines.
Identify and determine the measure of central
and inscribed angles and their associated minor
and major arcs. Recognize and solve problems
associated with radii, chords, and arcs within or
on the same circle.
Geometry
3.B.02c 10.G.5
Apply properties of angles, parallel lines, arcs, 9/10
radii, chords, tangents, and secants to solve
problems.
Geometry
3.B.03c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.04c 10.G.5
Apply properties of angles, parallel lines, arcs, 9/10
radii, chords, tangents, and secants to solve
problems.
Geometry
3.B.05c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.06c 10.M.1
Calculate perimeter, circumference, and area of 9/10
common geometric figures such as
parallelograms, trapezoids, circles, and
triangles.
Measurement
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Metal Fabrication
3.B.01c 10.G.3
Recognize and solve problems involving angles 9/10
formed by transversals of coplanar lines.
Identify and determine the measure of central
and inscribed angles and their associated minor
and major arcs. Recognize and solve problems
associated with radii, chords, and arcs within or
on the same circle.
Geometry
3.B.02c 10.G.5
Apply properties of angles, parallel lines, arcs, 9/10
radii, chords, tangents, and secants to solve
problems.
Geometry
3.B.01c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.03c 10.M.1
Calculate perimeter, circumference, and area of 9/10
common geometric figures such as
parallelograms, trapezoids, circles, and
triangles.
Measurement
3.B.04
10.G.1
Identify figures using properties of sides,
angles, and diagonals. Identify the figures'
type(s) of symmetry.
9/10
Geometry
3.B.05
10.G.2
Draw congruent and similar figures using a
compass, straightedge, protractor, and other
tools such as computer software. Make
conjectures about methods of construction.
Justify the conjectures by logical arguments.
9/10
Geometry
3.B.06
10.G.4
Apply congruence and similarity
9/10
Geometry
9/10
Geometry
correspondences (e.g., ∆ABC ≅ ∆XYZ) and
properties of the figures to find missing parts of
geometric figures, and provide logical
justification.
3.B.07
10.G.6
Use the properties of special triangles (e.g.,
isosceles, equilateral, 30°-60°-90°, 45°-45°90°) to solve problems
Computer Assisted Drafting
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3.B.01c 10.G.3
Recognize and solve problems involving angles 9/10
formed by transversals of coplanar lines.
Identify and determine the measure of central
and inscribed angles and their associated minor
and major arcs. Recognize and solve problems
associated with radii, chords, and arcs within or
on the same circle.
Geometry
3.B.02c 10.G.5
Apply properties of angles, parallel lines, arcs, 9/10
radii, chords, tangents, and secants to solve
problems.
Geometry
3.B.03c 10.G.8
Find linear equations that represent lines either 9/10
perpendicular or parallel to a given line and
through a point, e.g., by using the "point-slope"
form of the equation.
Geometry
3.B.04c 10.M.1
Calculate perimeter, circumference, and area of 9/10
common geometric figures such as
parallelograms, trapezoids, circles, and
triangles.
Measurement
Performance Standards
In the Mathematics Department at Charles H. McCann Technical School
performance standards focus on inquiry-based learning, which include problem solving,
research papers, and following the steps of the order of operations. Tests and quizzes are
essential. Rubrics are utilized whenever possible to help students understand the goals of
the assignment and to aid in keeping grading consistent. Weekly progress reports are
shown to each student to allow them to keep track of any missed assignments or low test
grades. Students are expected to actively participate in all classroom activities and daily
attendance/performance is an integral part of all students’ grades.
Competency Reporting Systems
Math teachers at McCann will be using the school’s database system, which
includes an electronic rankbook, for tracking student progress. Mid-quarter progress
reports and end of quarter report cards will be issued to students and parents through
utilization of this system. Mathematics teachers may also use the “Easy Grade Pro”
program as an electronic grade book and competency reporting system. This program
allows teachers to provide all students with a weekly assessment of class progress, which
all math teachers will attempt to carry out on a regular basis.
Utilization of the high school web site (http://www.mccanntech.org) will provide
students and parents with the expected course requirements. The web site will be
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updated daily to inform students of their responsibilities. We encourage parents to
frequently visit this site to help students make progress towards their goals.
Instructional Activities
The Math Department at McCann uses the following instructional activities:
• Competency based learning
• Project based learning
• Cooperative learning groups
• Integration with technical areas
• Integration with academic subjects
• Direct instruction
• Open-ended questions
• Interactive questioning
• Cooperative learning
• Whiteboard projects
• Library research
• Demonstrations
• Recitation/Review
• Collins Writing Prompts
• Other topics may be included in the class as deemed appropriate by
the individual course instructors.
Honors Geometry uses these addition instructional activities:
• Hands-on explorations
• Investigations
• Constructions
Resources
Textbook
Bass, Laurie E. et al. Geometry tools for a Changing World. Prentice Hall.
Needham, Massachusetts: 1998.
Instructional Materials and Supplies
Graphing calculators/Scientific calculators
Compasses
Protractors
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