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Geometry Theme MAA PREP WORKSHOP Laurie Burton and Maria Fung Western Oregon University July 8 th 2003 Overview Overview of WOU Geometry Courses Foundations Geometry for Elementary Teachers Geometry for Middle School Teachers Geometry Activities

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geometry theme

Geometry Theme

MAA PREP WORKSHOP

Laurie Burton and Maria Fung

Western Oregon University

July 8th 2003

overview
Overview
  • Overview of WOU Geometry Courses
    • Foundations
    • Geometry for Elementary Teachers
    • Geometry for Middle School Teachers
  • Geometry Activities
    • Explorations on symmetry and reflections
    • Visual approach to the Pythagorean Theorem
    • Geometer’s Sketchpad Lab Explorations
  • Assessment
geometry nctm standards highlights
Geometry NCTM Standards Highlights
  • Analyze properties and characteristics of two- and three-dimensional geometric shapes
  • Describe spatial relationships using coordinate geometry and other representational systems
  • Apply transformations and use symmetry to analyze mathematical situations
geometry for k 8 teachers
Geometry for K-8 Teachers
  • Foundations of Elementary Mathematics sequence includes a one-quarter course on geometry
  • Main topics covered:
    • Geometric figures
      • Geometric Figures; Plane Figures
      • Polygons and Tessellation; Space Figures; Symmetric Figures
    • Measurement
      • Systems of Measurement
      • Area and Perimeter; Volume and Surface Area
    • Motions in geometry
      • Congruence and Constructions
      • Congruence Mappings; Similarity Mappings
  • Introduction to the Geometer’s Sketchpad Package
geometry for k 8 teachers5
Geometry for K-8 Teachers
  • Geometry For Elementary School Teachers is a one-quarter course for mathematics focus students
  • Main topics covered:
    • Geometric Shapes and Measurement
    • Polygons & Circles
    • Perimeter & Circumference, Area, Angles
    • The Pythagorean Theorem
    • Polyhedra
    • Surface Area & Volume
    • Triangle Congruence & Similarity
    • Basic Geometric Constructions
geometry for k 8 teachers6
Geometry for K-8 Teachers
  • Geometry for Middle School Teachers is a mixed advance undergraduate and graduate course
  • Topics covered:
    • Reflections and Symmetry
    • Tessellations
    • Isometries and their Relations
    • Perimeter, Area and the Pythagorean Theorem
    • Similarity
    • Measurement and Similarity Mappings
comments on mirrors and symmetry activity
Comments on Mirrors and Symmetry Activity
  • Introductory activity for the Geometry for Middle School Teachers Course
  • Students use trial and error at first
  • Hands-on experience typically leading to informal proofs
  • Excellent conceptual understanding of reflections and lines of symmetry
  • Good review of quadrilaterals and their properties
more comments on mirrors and symmetry activity
More Comments on Mirrors and Symmetry Activity
  • This activity encourages students to “reflect on reflections”
  • Students have fun exploring and improving their geometric intuition
  • Increases awareness of geometric concepts (e.g. parallel, angle)
  • Follow up: construct and critique minimal “message” for obtaining a specific shape
examples of follow up activities
Examples of Follow-up Activities
  • Construct a minimal message for seeing a rhombus that is not a square.
  • Critique the following message:
      • Make a right angle.
      • Bisect the right angle.
      • Place the mirror perpendicular to the bisector in Step 2 (with the reflecting side facing the vertex of the right angle)
      • Be sure that the mirror cuts off equal lengths on the sides of the right angle.
paper folding activity
Paper Folding Activity
  • Another hands-on method of discovering lines of symmetry for various quadrilaterals
  • Opportunity for sharing different ways of producing required shapes
pythagorean theorem activity
Pythagorean Theorem Activity
  • Find the areas of the squares by using visual methods with the distance between two dots as a unit (and not by measuring the sides and applying the formula for the area of a square)
  • Address the case of an obtuse triangle for part 2 of this activity
  • Show the construction for the proof to students
design your own
Design Your Own
  • Work on creating an activity or lesson plans centered around the topic of tessellations
  • Use the provided materials in your Resource Notebooks
  • Make a poster or a presentation of your work to be shared with the group
activities with the geometer s sketchpad
Activities with the Geometer’s Sketchpad

Work on the following lab activities:

  • Glide Reflections (first part to start)
  • One tessellation activity to start (and finish them all, time permitting)
    • A Tumbling Block Design
    • Tessellations Using Only Translations
    • Tessellations That Use Rotations
  • Dissection Demonstration of the Pythagorean Theorem
  • The Golden Rectangle
  • One activity of More Ideas for Transformation Projects
geometry assessment i
Geometry Assessment I
  • Foundational Geometry:
    • Concept Pages
    • Conceptually Centered Exams
    • Problems of the Week (Explorations of Geometric Relationships)
    • Article Reports
    • Textbook Homework
geometry assessment ii
Geometry Assessment II
  • Advanced Geometry:
    • Geometry Lab Reports (√-, √, √+)
    • Readings Reports and Reflections
    • Final Projects
    • Geo-Jeopardy Final
    • Vocabulary Lists
    • Quizzes & Exams
    • Extensive Homework
assessment continued
Assessment Continued

Example of a grading rubric from Geometry for Middle School Teachers Course:

  • Interpretation (0-2 pts.)
  • Execution (0-2 pts.)
  • Completeness (0-2 pts.)
  • Reflection (0-2 pts.)
  • 0: sketchy, incomplete, incorrect, or missing
  • 1: adequate
  • 2: thoroughly developed, excellent