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PLEASANT VALLEY SCHOOL DISTRICT
PLANNED COURSE CURRICULUM GUIDE
GEOMETRY HONORS
Grade 10
I.
COURSE DESCRIPTION AND INTENT:
Honors Geometry (332) is a course, which emphasizes logical reasoning, spatial
visualization skills, and their application to problem solving. Students are expected
to write two columns deductive formal proofs, paragraph type proofs, and use
algebraic skills to set up and solve problems based on geometric representation.
Additionally, students will solve problems related to plane, solid, and coordinate
geometry.
II.
INSTRUCTIONAL TIME:
Class Periods: 6 per 6-day cycle
Length of Class Periods (minutes): 56
Length of Course: One (1) Year
Unit of Credit: 1.00
Updated: May 2012
COURSE: Geometry Honors
STRAND: 2.3.A Part 1
GRADE(S): 10
TIME FRAME: One (1) Year
PA CORE STANDARDS
CC.2.3.HS.A.3
KEYSTONE ASSESSMENT ANCHORS
G.1.3.2.1
RESOURCES
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Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and apply basic geometric concepts to represent and solve
problems, and use either inductive or deductive reasoning to test conjectures and prove
specific facts.
ESSENTIAL CONTENT
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect
proofs/proofs by contradiction).
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INSTRUCTIONAL STRATEGIES
Draw and label a variety of geometric figures.
Use the definitions, theorems and postulates to find the measures of missing angles,
lengths of segments, or coordinates of a midpoint.
Write the hypothesis, conclusion, converse, inverse, contrapositive, and biconditional
of conditional statements and assess the validity of each statement through
cooperative group work and individual reinforcement.
Write and present two column deductive proofs to the class either using the board or
overhead projector.
Discuss common reoccurring proofs and compile a sampling of such proofs for use
with more involved proofs.
Through practice worksheets and a variety of group activities determine the measures
of angles related to parallel lines and polygons.
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Student generated problems used to reinforce various types of angle problems and
proofs.
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Establish within the portfolio sections on:
1. Basic concepts (postulates, theorems, definitions).
2. Common proofs used repeated throughout the course.
3. Algebraic review section to provide examples and rules for the algebra
necessary for this class.
4. A special problems section which includes a weekly SAT problem sheet.
5. A math log to assess student problems and perception of the course etc. this log
provides both teacher and student a place for feedback.
Discuss alternate forms of proof, such as: constructions, visual manipulation of
figures to justify a given fact, and indirect proofs.
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ASSESSMENTS
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Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Utilize crossword puzzles to reinforce or reteach basic terminology.
 Student created index cards of basic facts.
 Students work in pairs to review content.
 Bingo used as a review game for tests or quizzes.
 Tutoring (teacher or peer)
 Cooperative groups (jigsaw, inner circle)
 Utilize reteaching activities and worksheets.
Extensions:
 Create 3-D model to represent the basic geometric shapes.
 Student generated test on the unit lesson.
 Line art projects.
 Student research projects on applications of the concepts presented in the unit to real
life examples.
 Fractals.
 Collages depicting and identifying geometric shape and application.
 Research of Non-Euclidean Geometries (Lobachevsky, Gauss, Reimann).
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Video projects
SAT application problems.
Math journal
Class projects, ex: display cases, magazines and posters.
COURSE: Geometry Honors
STRAND: 2.3.A Part 2
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.3.HS.A.2
CC.2.3.HS.A.3
ASSESSMENT ANCHORS
G.2.2.1.1
G.2.2.1.2
RESOURCES
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




Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and apply properties of parallel lines.
ESSENTIAL CONTENT
G.2.2.1.1. Use properties of angles formed by intersecting lines to find the measures of
missing angles.
G.2.2.1.2 Use properties of angles formed when two parallel lines are cut by a transversal
to find the measures of missing angles.
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INSTRUCTIONAL STRATEGIES
Use the definitions, theorems and postulates to find the measures of missing angles.
Write and present two column deductive proofs to the class either using the board or
overhead projector.
Discuss common reoccurring proofs and compile a sampling of such proofs for use
with more involved proofs.
Through practice worksheets and a variety of group activities determine the measures
of angles related to parallel lines and polygons.
Student generated problems used to reinforce various types of angle problems and
proofs.
ASSESSMENTS








Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Utilize crossword puzzles to reinforce or reteach basic terminology.
 Student created index cards of basic facts.
 Students work in pairs to review content.
 Bingo used as a review game for tests or quizzes.
 Tutoring (teacher or peer)
 Cooperative groups (jigsaw, inner circle)
 Utilize reteaching activities and worksheets.
Extensions:
 Create 3-D model to represent the basic geometric shapes.
 Student generated test on the unit lesson.
 Line art projects.
 Student research projects on applications of the concepts presented in the unit to real
life examples.
 Video projects
 SAT application problems.
 Math journal
 Class projects, ex: display cases, magazines and posters.
COURSE: Geometry Honors
STRAND: 2.3.A Part 3
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.3.HS.A.3
ASSESSMENT ANCHORS
G.1.2.1.1
G.1.2.1.3
G.1.3.1.1
RESOURCES
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



Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and use basic properties of a triangle to solve numeric problems
and write triangular congruence proofs.
ESSENTIAL CONTENT
G.1.2.1.1 Identify and/or use properties of triangles.
G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles.
G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
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INSTRUCTIONAL STRATEGIES
Student will list the corresponding parts for congruent figures and write a proper
congruence relationship.
Use guided discovery, group and individual work, along with physical models to
develop an understanding of and ability to do basic triangular congruence proofs.
A key step approach to each proof will be developed that will guide each student
though the major steps needed for each proof.
Demonstrate correct proofs on the board and provide students with a variety of ways
to think through and develop their own methods to do basic geometric proofs.
Define the median, altitude, and angle bisector of a triangle and talk about the
properties of their respective points of concurrence.
ASSESSMENTS
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Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Utilize matching games to relate statements and reasons in piecing together the
proofs.
 Cooperative group work.
 Group presentation of concepts on the overhead projector for class discussion.
 Tutoring (teacher or peer)
 Utilize reteaching activities and worksheets.
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Extensions:
 Student generated proofs used to supplement book proofs.
 Indirect and coordinate geometry proofs.
 Research project on the many different methods to prove the Pythagorean Theorem.
 Students create a collection of basic “mini” proofs to be displayed throughout the
classroom and included in their portfolios.
 Teacher provided proofs to challenge the skills of the students.
 Point of concurrence concepts and their verification by basic geometric
constructions.
COURSE: Geometry Honors
STRAND: 2.3.A Part 4
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.3.HS.A.3
ASSESSMENT ANCHORS
G.1.2.1.2
RESOURCES
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




Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and use the basic properties of a parallelogram and special
quadrilaterals in numeric problems and proofs.
ESSENTIAL CONTENT
G.1.2.1.2 Identify and/or use properties of quadrilaterals.
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INSTRUCTIONAL STRATEGIES
Develop a flowchart that identifies each quadrilateral and its properties.
Demonstrate proofs using the properties of a parallelogram, and proofs that a
quadrilateral is a parallelogram on the board and overhead projector.
Utilize cooperative group activities to reinforce student understand of the special
quadrilaterals and related problems and proofs.
Use manipulative to help students visualize the shapes and their unique properties.
Create a project in which each cooperative group must select a special quadrilateral
and make a visual and oral presentation to the class on the shapes special properties.
ASSESSMENTS
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Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
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Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Cooperative group work.
 Tutoring (teacher or peer)
 Utilize reteaching activities and worksheets.
 Student created index cards of each special quadrilateral and it’s properties.
 Mind maps showing same and different relationships of the special quadrilaterals.
Extensions:
 Oral presentation of specific quadrilaterals.
 Mind maps
 Teacher provided proofs to challenge the skills of the students.
 Project to illustrate the practical usage of these shapes in everyday life. (Ex.
architecture, design, nature, etc.)
 Student created proofs.
 Center of gravity explorations
COURSE: Geometry Honors
STRAND: 2.3.A Part 5
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.3.HS.A.3
CC.2.3.HS.A.6
ASSESSMENT ANCHORS
G.1.3.1.1
G.1.3.1.2
G.1.3.2.1
RESOURCES
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


Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and use ratios and properties of proportions to prove polygons
similar and solve numeric problems.
ESSENTIAL CONTENT
G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
G.1.3.2.1 Identify and/or use properties of congruent and similar polygons or solids.
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INSTRUCTIONAL STRATEGIES
Demonstrate how to set up and solve various types of proportion problems.
Identify the parts of a proportion and utilize their properties to solve problems in
reinforcement worksheets.
Use the “I have… who has” flashcard game to reinforce student understand of
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proportions and related problems.
Use cooperative groups to work through the proofs of similar triangles.
Demonstrate the set up and solution to problems involving similarity and its related
theorems.
Student will do a mock test to reinforce their understanding of ratio proportion, and
similar polygons.
ASSESSMENTS
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Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Cooperative group work.
 Tutoring (teacher or peer)
 Utilize reteaching activities and worksheets.
 Student created index cards illustrating the properties of proportions
 Mind maps
Extensions:
 Mind maps
 Use of SAT problems related to ratio, proportion, and similar polygons.
 Application of similarity and scale factor to model building, hypotheses testing,
blueprints, photography, etc.
 Use of the properties of proportions in similar triangle proofs.
 Algebraic problems related to ratio and proportion.
 Exploration of the Golden Rectangle.
COURSE: Geometry Honors
STRAND: 2.3.A Part 6
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.2.HS.C.9
ASSESSMENT ANCHORS
G.2.1.1.1
RESOURCES
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


Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and use the Pythagorean Theorem and special right triangle
relationships to solve numeric problems.
ESSENTIAL CONTENT
G.2.1.1.1 Use the Pythagorean theorem to write and/or solve problems involving right
triangles.
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INSTRUCTIONAL STRATEGIES
Prove the Pythagorean Theorem.
Demonstrate through board work how to solve for the missing side of a right triangle
using the Pythagorean Theorem or when appropriate, Pythagorean Triples.
Use a bingo game to reinforce student understanding of the Pythagorean Theorem.
Use the SAT reference section, which precedes each section of an SAT exam to
demonstrate the importance of the 30-60-90 and 45-45-90 special triangle
relationships.
Provide students with visuals as well as written rules for the 30-60-90 and 45-45-90
special triangle relationships and demonstrate how to apply thee rules.
Complete teacher designed worksheets to review the special right triangles.
Utilize group activities to reinforce student understanding of the special right
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triangles.
Ask students to write the converse of the Pythagorean Theorem and use their
statements to develop the converse of the Pythagorean Theorem and its implications.
Students will create sample problems for this chapter to use in a teaching-learning
group activity.
Teacher created mock test will be used to reinforce student understanding of right
triangles.
ASSESSMENTS
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Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Cooperative group work
 Tutoring (teacher or peer)
 Utilize reteaching activities and worksheets.
 Flashcards
 Student created quizzes for reinforcement.
Extensions:
 Use of related SAT problems.
 Use geometric constructions to construct values of square roots.
 Student created problems related to right triangles.
 Solve right triangle problems by correct selection and use of the sine, cosine, and
tangent functions.
 Explore applications of the arithmetic, geometric, and harmonic means.
COURSE: Geometry Honors
STRAND: 2.3.A Part 7
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.2.HS.C.1
CC.2.3.HS.A.3
CC.2.3.HS.A.14
ASSESSMENT ANCHORS
G.2.2.2.1
G.2.2.2.2
G.2.2.2.4
G.2.2.3.1
G.2.2.4.1
RESOURCES
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




Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and use the basic concepts and formulas for area and volume of
two and three-dimensional geometric shapes.
ESSENTIAL CONTENT
G.2.2.2.1 Estimate area, perimeter, or circumference of an irregular figure.
G.2.2.2.2 Find the measurement of a missing length, given the perimeter, circumference,
or area.
G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite
figure.
G.2.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter,
circumference, and area (e.g., How does changing the length of the radius of a
circle affect the circumference of the circle?).
G.2.2.4.1 Use area models to find probabilities.
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INSTRUCTIONAL STRATEGIES
Develop a formula list that will assist the student in identification and application of
the appropriate formula to solve an area calculation problem.
Research practical area applications and present findings to the group in both oral and
written form.
Complete teacher created review packets to reinforce area calculation skills.
Utilize 3-D models of the prism, pyramid, cylinder, cone, and sphere to help visualize
and identify the parts of these shapes.
Teacher directed practice on drawing 3-D shapes to assist in problem solving.
Complete a variety of application problems to practice skills with the volume and
surface area formulas.
ASSESSMENTS
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Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Cooperative group work.
 Tutoring (teacher or peer)
 Utilize reteaching activities and worksheets.
 Use of actual models or constructed areas for the visual learner.
 Flashcards
 Use of geoboards and rubber bands to help visually count the number of square units
in a given region.
 Student generated problems.
Extensions:
 Use of SAT related problems.
 Consumer costing problems related to area and volume.
 Use of distance formula, etc…and coordinate geometry to calculate area or volume.
 Examine property deeds and use dimensions to calculate the area of the property.
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Derive or verify area and volume formulas by experimentation or other means.
Calculate the area or volume of more complex composite two and three-dimensional
shapes.
Use of fractals to construct geometric designs.
COURSE: Geometry Honors
STRAND: 2.3.A Part 8
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.3.HS.A.8
CC.2.3.HS.A.9
ASSESSMENT ANCHORS
G.1.1.1.1
G.1.1.1.2
G.1.1.1.3
G.2.2.2.5
RESOURCES
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





Geometry for Enjoyment and Challenge
Supplementary tests, quizzes and enrichment workbooks for the above text.
3-D models
Compasses rulers and protractors.
Teacher designed activities
Access database for SAT problems and algebraic review.
Geometry- Houghton Mifflin (Book and supplementary materials)
OBJECTIVES
The learner will identify and use the basic parts of a circle and properties involving arcs,
angles, and segments in numeric problems and proofs.
ESSENTIAL CONTENT
G.1.1.1.1 Identify, determine, and/or use the radius, diameter, segment, and/or tangent of
a circle.
G.1.1.1.2 Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a
circle.
G.1.1.1.3Use chords, tangents, and secants to find missing arc measures or missing
segment measures.
G.2.2.2.5 Find the area of the sector of a circle.
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INSTRUCTIONAL STRATEGIES
Prove the theorems and demonstrate the solutions to problems involving the angles
and arcs of a circle.
Students complete teacher made problems packet.
Use collaborative group to review problems related to the circle.
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Create a study guide of formulas to calculate the circumference, arc length, area,
segment area, and composite areas.
ASSESSMENTS
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
Teacher made test and quizzes.
Worksheets and study guides.
Cooperative learning group work.
Homework
Class participation
Projects and extra credit
Portfolio assessment
Teacher observation
CORRECTIVES/EXTENSIONS
Correctives:
 Cooperative group work.
 Tutoring (teacher or peer)
 Utilize reteaching activities and worksheets.
 Flashcards
 Student generated problems.
Extensions:
 Use of SAT related problems.
 Student created problems.
 Use of the unit circle to define the basic trigonometric functions.
 Pulley problems involving common tangents and arc lengths with pulley wheels of
different radii.
COURSE: Geometry Honors
STRAND: 2.3.A Part 9
GRADE(S): 10
TIME FRAME: One (1) Year
PA ACADEMIC STANDARDS
CC.2.3.HS.A.7
ASSESSMENT ANCHORS
G.2.1.1.2
RESOURCES
 Trigonometry - Sullivan
 Resource packets
 Teacher designed materials
OBJECTIVES
The learner will use the definitions of the six trigonometric functions to solve right
triangle problems.
ESSENTIAL CONTENT
G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right
triangles.
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INSTRUCTIONAL STRATEGIES
Jigsaw learning activity to establish the six trigonometric ratios.
Use mnemonic devices such as SOH-CAH-TOA and all students take calculus to help
students to remember basic trigonometry facts.
Use string, pencil, and ruler to mark off radians on a circle.
Inner-outer circle activity to practice calculating trigonometric ratios.
ASSESSMENTS
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Teacher designed tests and quizzes
Activities which demonstrate knowledge of the concepts taught
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Worksheets designed to demonstrate knowledge of the concepts taught
Portfolio assessment
Written or oral presentation of projects
Homework assessment
Cooperative group assessment
CORRECTIVES/EXTENSIONS
Correctives:
 Utilize reteaching activities.
 Individualized instruction via the classroom teacher or math tutoring lab.
Extensions:
 Outdoor, sunny day activity: measure shadows to find the angle of elevation of the
sun.