Geometry Theme

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# Geometry Theme - PowerPoint PPT Presentation

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

MAA PREP WORKSHOP

Laurie Burton and Maria Fung

Western Oregon University

July 8th 2003

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
• Assessment
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
• 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 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 Teachers
• 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
• 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
• 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
• 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
• Another hands-on method of discovering lines of symmetry for various quadrilaterals
• Opportunity for sharing different ways of producing required shapes
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
• 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

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
• Foundational Geometry:
• Concept Pages
• Conceptually Centered Exams
• Problems of the Week (Explorations of Geometric Relationships)
• Article Reports
• Textbook Homework
Geometry Assessment II
• Geometry Lab Reports (√-, √, √+)
• Final Projects
• Geo-Jeopardy Final
• Vocabulary Lists
• Quizzes & Exams
• Extensive Homework
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