InterMath Workshop Support

Program:	InterMath ≠ Geometry
Location:	Washington/Wilkes County
Date:	Fall 2006
Instructors and Contact Info:	Al LaPointe ≠ lapointe@uga.edu Susan Sexton ≠ sextons@uga.edu

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

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.

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

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

Assessments:

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.

Course Outline:

August 10, 2006: 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)

August 24, 2006: 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)

September 7, 2006: 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)

September 21, 2006: Class 4

A. Participants engage in the Triangle (part 1) Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of spreadsheet program

September 29, 2006: Class 5-6

A. Participants engage in the Triangle (part 2) and Quadrilateral (part 1) Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of graphing program

October 5, 2006: Class 7

A. Participants engage in the Quadrilateral (part 2) Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of graphing program

October 19, 2006: 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

October 27, 2006: Class 9-10

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

November 2, 2006: Class 11

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

November 16, 2006: 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

December 7, 2006: Class 13

A. Each participant will present their entire instructional activity to the entire class
B. Class will provide feedback on the lesson plan

C. Each participant will take a Geometry exam

MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS

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