MAA PREP WORKSHOP
Laurie Burton and Maria Fung
Western Oregon University
July 8 th 2003

 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

 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

 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 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 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

 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

 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

 Construct a minimal message for seeing a rhombus that is not a square.
 Critique the following message:
1.
Make a right angle.
2.
Bisect the right angle.
3.
Place the mirror perpendicular to the bisector in Step
2 (with the reflecting side facing the vertex of the right angle)
4.
Be sure that the mirror cuts off equal lengths on the sides of the right angle.

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

 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

 Foundational Geometry:
 Concept Pages
 Conceptually Centered Exams
 Problems of the Week (Explorations of
Geometric Relationships)
 Article Reports
 Textbook Homework

 Advanced Geometry:
 Geometry Lab Reports ( √-, √, √+)
 Readings Reports and Reflections
 Final Projects
 Geo-Jeopardy Final
 Vocabulary Lists
 Quizzes & Exams
 Extensive Homework

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