Intermath

 

Geometry Course Syllabus

Richmond County

Summer 2004

 

     Instructor: Susan E. Craig

secddc@aol.com

SCraig@davidsonfinearts.org


Office Address: 615 12th Street

Augusta, GA 30901

Telephone: (706) 823-6924 ext.223

 

Important Information: InterMath Website

http://www.intermath-uga.gatech.edu

 

 

Click Here to get detailed instructions to access and modify your homepage and publish write-ups.

  

Click Here to go to participants list

 

Course Policies:

This course will concentrate on using various software applications to solve mathematics problems, to organize pedagogical demonstrations, and to set up problem explorations. All materials for the course are maintained by an Internet Web page site and students will create and use web documents in the course.

The emphasis is on exploration of various mathematics contexts to learn mathematics, to pose problems and problem extensions, to solve problems, and to communicate mathematical demonstrations.

The following technologies will be used:

Geometers Sketchpad 4.04 (from http://www.keypress.com)

Graphing Calculator 3.2 (from http://www.pacifict.com)
Spreadsheets (recommend Microsoft Excel)
Hand Held Calculators such as TI-81, TI-82, or TI-83 (TI: Texas Instruments)

Web Page Browser (recommend Netscape 7.0 or Internet Explorer)
Web Page Authoring Tool (recommend Microsoft Front Page or Microsoft Word)

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 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 geometry investigations for appropriate use in classroom

Make connections between InterMath Institute 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 geometry concepts

Communicate mathematical understanding of a variety of geometry concepts in the form of an online portfolio of investigation solutions

Plan instructional activities based on InterMath experiences

6. COURSE REQUIREMENTS & 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 two independent mathematics lessons and one group lesson that integrate technology and geometry for use in their own classroom. Students will also maintain a reflective journal starting with the initial class meeting.

Electronic Journal: As a part of this course, you are expected to maintain a reflective journal. This journal is a log of your experiences within the course. It should include thoughts about new skills and accomplishments that you acquire; critical incidents that occur; and your thoughts and feelings about content (mathematics/geometry investigations) and technology. If you are experiencing difficulty keeping a journal, discuss it with your instructor who can provide you with additional suggestions and assistance.

 

Electronic Portfolio of Write-ups: Each person will develop a personal Web Page for the course. There will be a set of "Write-up" projects. These are the "homework" for the course. Participants are required to create at least eight write-ups, two from each of the areas, Triangles, Circles, Polygons, and 3-D Geometry. Each Write-up will be prepared as a Microsoft Word document and linked to your personal web page.

 

What is a write-up?

The "write-ups" represent your synthesis and presentation of a mathematics investigation you have done --usually under the direction of one of the assignments. The major point is that it convincingly communicates what you have found to be important from the investigation. A write-up should communicate the essential material you have synthesized from your investigation. The format could be entirely in a word-processing document. Write-ups should be posted to your personal Web Page. If you work as a team on a write-up, post the write-up into each team member's Web Page but label collaborative effort. Criteria should include correct mathematics, use of technology, and how well you communicate. "Solution" might be another word for "Write-up."

 

Click here to see a template for write-ups.

 

Electronic Portfolio of Lesson Plans: Participants are required to create two mathematics lessons independently and one mathematics lesson in a group that integrate technology and geometry for use in their own classroom. The "lessons" are to be your creations of material to incorporate technology into classroom lessons. The material can be individual lessons or a unit of material. Your criteria should be on its usability in your classroom or in other peoples classroom and something you feel good enough about to share with colleagues over the web.

 

Click here to see a template for lesson plans.

8. COURSE OUTLINE

I. Class 1 June 29

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

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

II. Class 2 July 1

III. Class 3 July 8

IV. Class 4

V. Class 5

VI. Class 6

VII. Class 7

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

Each participant will take a Geometry exam

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
  •  

Richmond County Middle School Mathematics Curriculum Objectives which will be addressed

M.6.12 Uses characteristics and properties of lines and line segments to determine relationships between lines. E

M.6.13 Identifies the component parts of an angle, its vertex, and sides or rays; and classifies angles as acute, right,

obtuse, or straight. E

M.6.14 Identifies lines of symmetry. I

M.6.15 Identifies face, edge, and vertex of a geometric solid. E

M.6.16 Identifies congruent and similar geometric figures. E

M.6.17 Identifies effects of basic transformations on geometric shapes. E

M.6.18 Contrasts and classifies simple plane and solid geometric figures by their properties. E

M.6.20 Identifies terms associated with a circle and finds the circumference using pi. I

M.7.17 Classifies angles as acute, right, obtuse, or straight; and names angles using points, numbers, and letters. C

M.7.18 Classifies quadrilaterals and triangles based on their properties. I

M.7.19 Contrasts and classifies plane and solid geometric figures (polygons, cones, cylinders, prisms, pyramids). I

M.7.20 Compares and contrasts geometric figures with respect to congruency and similarity (scaling, dilations). I

M.7.21 Analyzes effects of basic transformations on geometric shapes. I

M.7.23 Finds volume and surface area of prisms and cylinders. E

M.7.24 Finds the perimeter (or circumference) and area of polygons and circles, and the volume and surface area of

geometric solids, using formulas. (Uses student development of formulas when possible). E

M.8.16 Applies formulas (e.g., area, perimeter, circumference, volume, surface area), including investigating and using

the Pythagorean Theorem. E

M.8.19 Classifies plane and solid geometric figures based on their properties/characteristics (number or length of

sides, angle measures, edges, faces, or vertices). This includes quadrilaterals (trapezoid, parallelogram,

square, rectangle, rhombus); triangles (acute, obtuse, right equilateral, isosceles, scalene); solids (prism,

pyramid, cone, cylinder, sphere), and n-gons (pentagon, hexagon, octagon). E

M.8.20 Identifies physical and symbolic representations using appropriate labeling of geometric figures, such as points,

lines, line segments, rays polygons, vertices, angles, and diagonals. I

M.8.21 Uses properties to determine similarity and congruency of geometric figures. I

M.8.22 Solves problems by using the property that the sum of the angles in a triangle is 180 degrees. E

M.8.23 Uses geometric figures, properties, and relations to solve problems. E

M.8.25 Analyzes effects of basic transformations on geometric shapes. I

 

Strand Measurement

M.6.21 Selects and uses appropriate customary and metric units of measure for length (including perimeter), area, volume, capacity, time, temperature, and weight/mass. E

 

M.6.22 Measures angles using a protractor. I

 

M.6.23 Converts from one metric unit to another metric unit, and from one customary unit to another customary unit (length, capacity, weight/mass). I

M.6.24 Estimates measures using strategies such as walking off or pacing, rough comparison, and reference point for length or capacity, and evaluates reasonableness of results. I

M.6.25 Develop and apply formulas for area, perimeter, and volume. E

M.7.25 Selects and uses appropriate customary and metric units of measure for length (including perimeter and circumference), area, volume, capacity, weight/mass, time, temperature, and angle measure. I

M.7.26 Measures angles using a protractor. C

M.7.27 Converts from one metric unit to another metric unit and from one customary unit to another customary unit (length, capacity, weight/mass, time and money). I

Richmond County Geometry Participants

Al Sutton

McNeil Zellars

Shahid Abdul-Jabbar