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Geometry Theme

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

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  1. Geometry Theme MAA PREP WORKSHOP Laurie Burton and Maria Fung Western Oregon University July 8th 2003

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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.

  10. Paper Folding Activity • Another hands-on method of discovering lines of symmetry for various quadrilaterals • Opportunity for sharing different ways of producing required shapes

  11. 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

  12. 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

  13. 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

  14. Geometry Assessment I • Foundational Geometry: • Concept Pages • Conceptually Centered Exams • Problems of the Week (Explorations of Geometric Relationships) • Article Reports • Textbook Homework

  15. Geometry Assessment II • Advanced Geometry: • Geometry Lab Reports (√-, √, √+) • Readings Reports and Reflections • Final Projects • Geo-Jeopardy Final • Vocabulary Lists • Quizzes & Exams • Extensive Homework

  16. 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

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