NEWPORT-MESA UNIFIED SCHOOL DISTRICT Course Description ESSENTIALS

							Math: Essentials of Geometry                                                                    1



                               NEWPORT-MESA UNIFIED SCHOOL DISTRICT
                                         Course Description

                                     ESSENTIALS OF GEOMETRY

Content covered in this course is described in the Course of Study. Based upon student needs, teachers
select appropriate materials from the Instructional Materials List. Classroom presentations of course
content are determined by the instructor and described under Teacher Activities. A more detailed outline
of this course can be obtained from the instructor.

OVERVIEW:
“Essentials of Geometry” is a two-semester course designed to make geometry concepts accessible to
students at all levels. The course focuses on key topics in order to provide a sound foundation in the
fundamental principles of geometry. This course does not satisfy the prerequisites needed to continue
on to Algebra 2.

COURSE OF STUDY OBJECTIVES:
  1. The student will demonstrate understanding by identifying and giving examples of the
     undefined terms such as axiom, theorems inductive and deductive reasoning.
     1.1 SUGGESTED STUDENT ACTIVITY:
         • Creating a geometry reference file that will include definitions and theorems
         • Create vocabulary note cards with illustrations of undefined terms for their reference file
         • Work in small cooperative learning groups
         • Sorting and charting illustrations of axioms and undefined terms
     1.2 INSTRUCTIONAL MATERIALS USED:
         • Graph paper, lined paper, Index cards, markers, poster board
         • Compass, straight edge, protractor
         • Charts, diagrams
     1.3 TEACHER ACTIVITIES:
         • Oversee sorting activities
         • Projects illustrating intersections of lines and planes
         • Coaching investigations
         • Demonstrations

    2. The student will write geometric proofs, including proof by contradiction.
       2.1 SUGGESTED STUDENT ACTIVITY:
           • Sort data appropriately in two column proofs, paragraph proofs and indirect proofs
           • Work in cooperative learning groups to create completed proofs
           • Explaining justification to the class and group members
           • Continue adding theorems and definitions to reference card file
           • Investigations with various proofs
       2.2 INSTRUCTIONAL MATERIALS USED:
           • Teacher made materials
           • Graph paper; lined paper, index cards, poster board
       2.3 TEACHER ACTIVITIES:
           • Supervise small cooperative learning groups
           • Coaching investigations
           • Demonstrations




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Math: Essentials of Geometry                                                               2



    3. The student will construct and judge the validity of a logical argument, including giving
       counter examples.
       3.1 SUGGESTED STUDENT ACTIVITY:
           • Students will categorize statements by hypothesis, conclusion, converse, inverse and
              contrapositive and judge the truth of those statements
           • Work in small cooperative learning groups
           • Demonstrate their results by producing charts of statements
           • Continue reference card file
       3.2 INSTRUCTIONAL MATERIALS USED:
           • Poster board
           • Graph paper; lined paper, index cards
       3.3 TEACHER ACTIVITIES:
           •   Supervise and assist cooperative learning groups
           • Asking questions
           • Coaching investigations
           • Demonstrations

    4. The student will prove basic theorems involving congruence and similarity.
       4.1 SUGGESTED STUDENT ACTIVITY:
           • Organize steps of proof and match with appropriate reasons
           • Work in small cooperative learning groups
           • Conduct investigations using constructions to determine congruence
           • Create additional theorem cards for reference file
       4.2 INSTRUCTIONAL MATERIALS USED:
           • Graph paper; lined paper; index cards, poster board
           • Compass, straight edge, protractor
       4.3 TEACHER ACTIVITIES:
           • Supervise and assist learning groups
           • Coaching investigations
           • Demonstrate constructions for congruence

    5. The student will prove triangles are congruent or similar and will be able to use the
       concept of corresponding parts of congruent triangles.
       5.1 SUGGESTED STUDENT ACTIVITY:
           • Work in small cooperative learning groups
           • Use manipulative materials to illustrate corresponding parts
           • Investigations
       5.2 INSTRUCTIONAL MATERIALS USED:
           • Manipulative materials that create congruent triangles
           • Graph paper; lined paper, index cards, poster board
           • Compass, straight edge, protractor
       5.3 TEACHER ACTIVITES:
           • Supervise and assist small groups
           • Asking questions
           • Coaching investigations
           • Demonstration use of manipulative materials

    6. The student will know and be able to use the Triangle Inequality Theorem.
       6.1 SUGGESTED STUDENT ACTIVITY:
           • Work in small cooperative groups using manipulative materials to demonstrate the
              changes in the side opposite and angle as the size of the angle changes
           • Create posters representing the concepts of the Triangle Inequality theorem
           • Explaining their understanding orally or in written form



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Math: Essentials of Geometry                                                                      3



          6.2 INSTRUCTIONAL MATERIALS USED:
              • Manipulative materials that represent the sides of triangle; linguini or udon for example
              • Graph paper; lined paper, index cards, poster board, construction paper
              • Compass, straight edge, protractor
          6.3 TEACHER ACTIVITIES:
              • Supervise and assist small groups
              • Asking questions
              • Coaching investigations
              • Demonstration concepts of Triangle Inequality theorem

    7. The student will prove and use theorems involving properties of parallel lines cut by a
       transversal, the properties of quadrilaterals and the properties of circles.
       7.1 SUGGESTED STUDENT ACTIVITY:
           • Work in small cooperative learning groups
           • Create parallel lines using constructions and manipulative materials
           • Investigate relationships of angles formed by parallel lines cut by a transversal
           • Continue adding cards illustrating theorems to reference file
       7.2 INSTRUCTIONAL MATERIALS USED:
           • Manipulative materials that represent parallel lines such as linguini, udon or other
              materials
           • Graph paper; lined paper, index cards, construction paper
           • Compass, straight edge, protractor
       7.3 TEACHER ACTIVITIES:
           • Supervise and assist small groups
           • Asking questions
           • Coaching investigations
           • Demonstrate angle relationships and constructions

    8. The student will know, derive and solve problems involving perimeter, circumference,
       area, volume, laterals area and surface area of common geometric figures.
       8.1 SUGGESTED STUDENT ACTIVITY:
           • Use templates to cut two and three dimensional geometric figures and determine area
           • Work in small cooperative learning groups
           • Explaining their understanding orally or in written form
           • Investigate general equations for computing area and surface area
           • Create cards illustrating formulas for reference file
       8.2 INSTRUCTIONAL MATERIALS USED:
           • Templates for geometric figures
           • Graph paper; lined paper, index cards, construction paper, tape, scissors
           • Compass, straight edge, protractor
       8.3 TEACHER ACTIVITIES:
           • Supervise group work
           • Asking questions
           • Coaching investigations
           • Demonstrations

    9. The student will compute the volumes and surface area of prisms, cylinders, cones and
       spheres.
       9.1 SUGGESTED STUDENT ACTIVITY:
           • Use models created in objective 8 or manipulative materials to compute volume
           • Work in small cooperative learning groups
           • Investigations
           • Continue adding to reference card file



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Math: Essentials of Geometry                                                                   4



          9.2 INSTRUCTIONAL MATERIALS USED:
              • Manipulative materials of geometric solids
              • Graph paper; lined paper; index cards, construction paper, sand, unit cubes
              • Compass, straight edge, protractor
          9.3 TEACHER ACTIVITIES:
              • Supervise small groups
              • Asking questions
              • Coaching investigations
              • Demonstrate volume relationships of cones/cylinders and pyramids/prisms using sand to
                 fill geometric solids and compare

    10. The students will compute the areas of polygons including rectangles, scalene triangles,
        equilateral triangles, rhombi, parallelograms and trapezoids.
        10.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups to construct and cut polygons in order to
                determine, demonstrate and discover the formulas for determining area of these
                polygons
            • Create posters and charts illustrating the formulas for area of various polygons
        10.2 INSTRUCTIONAL MATERIALS USED:
            • Marking pens, scissors, poster board or construction paper
            • Graph paper; lined paper; index cards
            • Compass, straight edge, protractor
        10.3 TEACHER ACTIVITIES:
            • Supervise group activities
            • Asking questions
            • Coaching investigations

    11. The students will determine how changes in dimensions affect the perimeter, area and
        volume of common geometric solids.
        11.1 SUGGESTED STUDENT ACTIVITY:
            • Create geometric solids as before, but this time doubling, tripling or halving the on or
                more of the dimensions
            • Use manipulative solids and sand and graph paper to compute new areas and volumes
        11.2 INSTRUCTIONAL MATERIALS USED:
            • Marking pens, poster paper, construction paper
            • Graph paper; lined paper; index cards
            • Compass, straight edge, protractor
        11.3 TEACHER ACTIVITIES:
            • Supervise learning groups
            • Coaching investigations
            • Demonstrate constructions

    12. The students will find and use the measures of sides, interior and exterior angles of
        triangles and polygons to classify figures and solve problems.
        12.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Conduct investigations to determine the measures of interior and exterior angles of
                triangles and other polygons
            • Create charts, posters and reference cards displaying and organizing the data discovered
                and their formulas
        12.2 INSTRUCTIONAL MATERIALS USED:
            • Construction paper, markers, poster board
            • Graph paper; lined paper; index cards
            • Compass, straight edge, protractor



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Math: Essentials of Geometry                                                                   5



          12.3 TEACHER ACTIVITIES:
              • Supervise group activities
              • Asking questions
              • Coaching investigations

    13. The students will prove relationships between angles in polygons using properties of
        complementary, supplementary, vertical and exterior angles.
        13.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Measure interior, exterior, vertical and opposite angles of polygons and generalize the
                relationship between them
            • Make posters and reference cards illustrating these generalizations
        13.2 INSTRUCTIONAL MATERIALS USED:
            • Poster board, markers, construction paper
            • Graph paper; lined paper; index cards
            • Compass, straight edge, protractor
        13.3 TEACHER ACTIVITIES:
            • Supervise and assist group activities
            • Asking questions
            • Coaching investigations

    14. The students will use the Pythagorean Theorem to determine distance and find the
        missing lengths of sides of right triangles.
        14.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Using graph paper, create various right triangles to illustrate and prove the Pythagorean
                Theorem
            • Using graph paper apply Pythagorean theorem to developing the distance formula and
                using that to find missing lengths of sides of triangles
            • Continue adding to reference card file
        14.2 INSTRUCTIONAL MATERIALS USED:
            • Graph paper; lined paper; index cards
            • Compass, straight edge, protractor
        14.3 TEACHER ACTIVITIES:
            • Assist group work
            • Asking questions
            • Coaching investigations

    15. The students perform basic constructions including angle bisectors, perpendicular
        bisectors and parallel lines.
        15.1 SUGGESTED STUDENT ACTIVITY:
            • Perform constructions using compass and straight edge
            • Work in small cooperative learning groups to use multiple constructions to create various
                angles and triangles as well as parallel lines and geometric figures
            • Create reference cards illustrating constructions for reference file
        15.2 INSTRUCTIONAL MATERIALS USED:
            • Graph paper; lined paper; index cards, poster board, construction paper, markers
            • Compass, straight edge, protractor
        15.3 TEACHER ACTIVITIES:
            • Supervise small group activities
            • Asking questions
            • Coaching investigations
            • Demonstrate constructions and combinations of constructions



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Math: Essentials of Geometry                                                                    6




    16. The students will prove theorems using coordinate geometry, including midpoint of a
        segment, distance and various equations of lines and circles.
        16.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Create posters and reference cards illustrating the concepts of midpoint and distance
                formulas
            • Investigate changes in circles and the impact those changes have on the corresponding
                equation of those circles.
        16.2 INSTRUCTIONAL MATERIALS USED:
            • Graph paper; lined paper; index cards
            • Compass, straight edge, protractor
        16.3 TEACHER ACTIVITIES:
            • Guide and assist group activities
            • Asking questions
            • Coaching investigations
            • Demonstrations

    17. The students will know the definitions of basic trigonometry functions defined by the
        angles of a right triangle.
        17.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Using graph paper students will create various right triangles and discover trig function
                relationships
            • Students will create reference cards illustrating these relationships
        17.2 INSTRUCTIONAL MATERIALS USED:
            • Graph paper; lined paper; index cards, markers, scissors
            • Compass, straight edge, protractor
        17.3 TEACHER ACTIVITIES:
            • Guide and assist group activities
            • Asking questions
            • Coaching investigations
            • Demonstrations

    18. The students will use the trigonometry functions to solve for unknown lengths and angles
        of right triangles.
        18.1 SUGGESTED STUDENT ACTIVITY:
             • Work in small cooperative learning groups
             • Using trig functions, students will estimate and them compute unknown lengths and
                 angles
        18.2 INSTRUCTIONAL MATERIALS USED:
             • Scientific calculators
             • Graph paper; lined paper; index cards, markers
             • Straight edge, protractor
        18.3 TEACHER ACTIVITIES:
             • Supervise group activities
             • Asking questions
             • Coaching investigations
             • Demonstrate use of scientific calculators




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Math: Essentials of Geometry                                                                        7



    19. The students will solve for unknown sides of right triangles using the relationships of 30-
        60-90 and 45-45-90 triangles.
        19.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Using Pythagorean Theorem, create various special right triangles (above) and discover
                the relationships of the lengths of the sides
            • Make posters and reference cards illustrating these relationships
        19.2 INSTRUCTIONAL MATERIALS USED:
            • Graph paper; lined paper; index cards, markers, construction paper
            • Straight edge, protractor
        19.3 TEACHER ACTIVITIES:
            • Oversee and assist group activities
            • Asking questions
            • Coaching investigations
            • Demonstrations

    20. The students will solve problems regarding relationships of chords, secants, tangents,
        inscribed angles, inscribed and circumscribed polygons of circles.
        20.1 SUGGESTED STUDENT ACTIVITY:
            • Work in small cooperative learning groups
            • Given carefully selected examples students will discover the relationships between
                angles and lengths of chords, secants and tangents
            • Students will create posters and reference cards illustrating these relationships
        20.2 INSTRUCTIONAL MATERIALS USED:
            • Poster board, markers
            • Graph paper; lined paper; index cards
            • Straight edge, protractor, rulers
        20.3 TEACHER ACTIVITIES:
            • Supervise group activities
            • Asking questions
            • Coaching investigations
            • Demonstrations

    21. The students will know the effect of rigid motion on figures in the plane and space
        including translation, rotation, and reflections.
        21.1 SUGGESTED STUDENT ACTIVITY:
            • Using graph paper and reflective manipulative materials as well as cut our geometric
                shapes, students will discover the effects of translations, rotations, and reflections and
                plot their new locations on the coordinate plane
            • Investigations
        21.2 INSTRUCTIONAL MATERIALS USED:
            • Various manipulative geometric figures
            • Reflective manipulative materials
            • Graph paper; lined paper; index cards
            • Straight edge
        21.3 TEACHER ACTIVITIES:
            • Supervise and assist group activities
            • Asking questions
            • Coaching investigations
            • Demonstrations




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Math: Essentials of Geometry                                                                     8




Instructional Materials

          Textbooks
                 District Adopted Textbook:
                 Larson, Ron; Boswell, Laurie and Stiff Lee 2003. Geometry Concepts and Skills. Illinois:
          McDougal Littell

          Supplementary Materials
                Various manipulative materials
                Teacher-generated materials

Submitted by Debbie Pipes, Newport Harbor High School, March 2004




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