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Geometry Syllabus


1. PROGRAM TITLE: InterMath - Geometry                           

2. GOALS ADDRESSED

    Participants will:

  • Expand and strengthen their mathematical knowledge and capabilities, specifically in the domain of geometry by investigating challenging geometry problems
  • Engage in problem solving by identifying patterns, forming conjectures, and developing proofs through the use of technology
  • Use mathematics-specific technologies such as dynamic geometry software, graphing programs, spreadsheets, and the Internet to explore geometry investigations
  • Write and post online solution processes to the investigations using web page development software
  • Develop middle school mathematics instructional activities and strategies that incorporate technology-enhanced mathematical investigations
  • Develop a network of peer educators available for continued support during and following the workshop

3. IMPROVEMENT PRACTICES

Participants will gain knowledge and practice in developing instructional activities and strategies for teaching geometry in the middle school classroom in order to positively affect student achievement. Participants will also improve their own mathematical competencies in the area of geometry.

4. COMPETENCIES

    Participants will be able to:

  • Select and use appropriate technological software to explore, analyze, and represent geometry problems
  • Communicate their mathematical thinking by expressing their reasoning, analysis, and extensions of the mathematical concepts associated with an investigation in written, verbal, and visual forms
  • Modify geometric investigations for appropriate use in the middle school classroom
  • Make connections between InterMath experiences and standards-based reform documents, such as the NCTM standards

5. PERFORMANCE INDICATORS

    As a result of this course, participants will demonstrate their ability to:

  • Incorporate technology into the learning and teaching of geometric concepts
  • Communicate mathematical understanding of a variety of geometric concepts in the form of an online portfolio of investigation solutions
  • Plan middle school instructional activities based on InterMath experiences

6. PREPARATION PHASE

Dates: Fall 2002
Instructor: Dr. Wilson/Dr. Gootman
Location: UGA campus
Strategies: Internet exploration, electronic and classroom discussions, lectures, exploration of mathematical investigations, investigation write-ups, collaborative brainstorming, lesson planning, presentations

 

7. ASSESSMENT

Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of write-ups will be provided throughout the workshop. Assessment will be based on use of representation, analysis, appropriate selection and use of technological tools, creation of extensions, and accuracy of mathematics. In addition to the investigation write-ups, the participants will also create a mathematics lesson that integrates technology and geometry for use in their own classroom.

8. COURSE OUTLINE

I. Class 1

A. Introduction to InterMath
B. Introduction to Technology
C. Work through a geometry investigation as a whole class using technology
D. Discuss the components and structure of a write-up (including extensions)

II. Class 2

A. Participants engage in investigations in Points, Lines and Planes
B. Participants begin their first web page write-ups to include in their online portfolios
C. Continued technological teaching and support (especially with GSP and the structure of a write-up)

III. Class 3

A. Participants engage in the Circles investigations
B. Participants add write-ups to include in their online portfolios
C. Continued technological teaching and support (especially with GSP and the structure of a write-up)

IV. Classes 4-5

A. Participants engage in the Triangle Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of spreadsheet program

V. Classes 6-7

A. Participants engage in the Quadrilateral Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of graphing program

VI. Class 8

A. Participants engage in the Polygon Investigations
B. Participants add write-ups to their online portfolios

C. Discuss and brainstorm ideas about modifying the InterMath experience for a middle school mathematics classroom

VII. Classes 9-10

A. Participants engage in the 3-D Object Investigations
B. Participants add write-ups to their online portfolios

VIII. Class 11

A. Participants explore systems of measurement and Logic investigations
B. Participants add middle school lesson plan to their online portfolios

IX. Class 12

A. Participants engage in Coordinate Geometry Investigations
B. Each participant creates a technology-enhanced mathematical investigation for their own classroom
C. Participants add middle school lesson plan to their online portfolios

X. Class 13

A. Participants engage in Transformational Geometry Investigations
B. Participants add write-ups to their online portfolios
C. Participants should work on a lesson plan consistent with InterMath for their students

XI. Class 14

A. Each participant will take a Geometry exam

B. presents their entire instructional activity to the entire class
C. Class will provide feedback on the lesson plan

 

9.  MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS
(Click Here to see a list of selected InterMath investigations clustered for Geometry )

Points, Lines and Planes

  • Solve problems involving properties and concepts of points, lines and planes in a two-dimensional setting
  • Classify lines as parallel, perpendicular, intersecting and skewed

Circles

  • Solve problems involving properties and concepts of circles such as area, circumference, diameter, sector, angles, arcs, radius, equation of a circle and Pi

Quadrilaterals

  • Classify quadrilaterals as squares, rectangles, parallelograms, trapezoids, or rhombi
  • Solve problems involving properties of quadrilaterals such as parallel lines, diagonals, midpoints, length, width, area, perimeter
  • Explore what happens to the area and perimeter of a quadrilateral as the dimensions are modified
Triangles
  • Classify triangles as acute, obtuse, right, equilateral, equiangular, isosceles, and scalene
  • Explore triangle properties and triangle centers such as medians, altitudes, angle bisectors, centroid, orthocenter, circumcenter, incenter, etc.
  • Solve triangle problems involving change of dimensions, perimeter, area, and the Pythagorean Theorem

Polygons

  • Classify polygons as regular, convex, and congruent
  • Construct polygons in GSP; determine which can create tessellations
  • Explore problems involving properties of polygons such as vertex angles, interior angles, exterior angles, area, perimeter, apothem, lines of symmetry, diagonals

3-D Objects

  • Solve problems involving volume and surface area of cubes, cylinders, rectangular solids, spheres, cones, and pyramids
  • Explore the properties of vertices, edges, faces, and dimensions of solids