Author: Paula Vilone and Kevin Wright
 Based on unit by: Paula Vilone
 Date Created: 6/20/2005 3:09:46 PM EST
 
Platonic Solids
VITAL INFORMATION
Subject(s):
Mathematics

Grade/Level:
8-10

Time Required:
2 hours

Objective(s):
Students will 1. analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2. solve problems using visualization, spatial reasoning, and geometric modeling through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics; 3.classify polyhedrons according to the number and shape of faces; determine the relationship between vertices, faces and edges; and 4.Collaborate with peers, experts, and others to contribute to a content-related knowledge base by using technology to compile, synthesize, produce, and disseminate information, models, and other creative works

Summary:
Students will become familiar with VRML Programming and some 3-D Solids.

IMPLEMENTATION
Learning Activities:
1. VRML and Geometric Solids
 
 
2. Prisms and Polyhedra
 


Resources and Unit Handouts:
  • Teachers need to have Cortona installed on all computers
  • The number of computers required is 1 per 2 students.
  • Technology resources:
    PowerPoint, Cortona, Textpad or Wordpad, Internet Explorer
  • Materials and resources:
    Worksheet handouts (4),Platonics Patterns, Introductory Geometry VRML programs,Sample VRML Program with Animation
  • Students Familiarity with Software Tool:
    Students should be able to edit and save text.


  • Attachments:
     1. Platonics/Geometric Solids PowerPoint

STANDARDS
Standards compiled from learning activities:
International- Intl. Technology Education Association: Standards for Technology Literacy
• Category The Nature of Technology
• Standard 1Students will develop an understanding of the characteristics and scope of technology.
• Grade Range 3-5
 Benchmark DTools, materials, and skills are used to make things and carry out tasks.
People make tools to help themselves or others do their work: a cook uses knives to cut vegetables; a gardener uses a hoe to remove weeds; an accountant uses a computer to store inforamtion. People also use materials, such as paper, wood, cloth and stone to make things they use every day. Most people develop the ablility to do common task,such as cutting paper with scissors,and some develop special abilities, like flying an airplane

WV- West Virginia Content Standards and Objectives
• Subject Math
• Grade or Course Seventh Grade
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 Detail apply transformations and use symmetry to analyze mathematical situations; and
 Detail solve problems using visualization, spatial reasoning, and geometric modeling through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics.
• Grade or Course Eighth Grade
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 Detail analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;
 Detail solve problems using visualization, spatial reasoning, and geometric modeling through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics.
 Objective MA.8.3.2 classify polyhedrons according to the number and shape of faces; determine the relationship between vertices, faces and edges.
 Objective MA.8.3.4 create geometric patterns including tiling, art design, tessellations and scaling using transformations (rotations, reflections, translations).
• Grade or Course Geometry and Applied Geometry
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 Detail analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;
 Detail solve problems using visualization, spatial reasoning, and geometric modeling through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics.
 Objective G.3.15 develop and apply formulas for area, perimeter, surface area, and volume and apply them in the modeling of practical problems.

USA- ISTE: Profiles for Technology Literate Students (includes NETS for Students)
• Grade Grades 9-12

Numbers in parentheses following each performance indicator refer to the standards category to which the performance is linked. The categories are:
1. Basic operations and concepts
2. Social, ethical, and human issues
3. Technology productivity tools
4. Technology communications tools
5. Technology research tools
6. Technology problem-solving and decision-making tools

Reprinted from National Educational Technology Standards for Students - Connecting Curriculum and Technology, copyright © 2000, ISTE (International Society for Technology in Education), 800.336.5191 (U.S. & Canada) or 541.302.3777 (Int’l), iste@iste.org, www.iste.org. All rights reserved. For more information about the NETS Project, contact Lajeane Thomas, Director, NETS Project, 318.257.3923, lthomas@latech.edu. Reprint permission does not constitute an endorsement by ISTE or the NETS Project.

 Performance Objective 5Use technology tools and resources for managing and communicating personal/professional information (e.g., finances, schedules, addresses, purchases, correspondence). (3, 4)
 Performance Objective 8Select and apply technology tools for research, information analysis, problem-solving, and decision-making in content learning. (4, 5)
 Performance Objective 10Collaborate with peers, experts, and others to contribute to a content-related knowledge base by using technology to compile, synthesize, produce, and disseminate information, models, and other creative works. (4, 5, 6)

USA- NCTM (Nat. Council of Teachers of Mathematics): Principles & Standards for School Mathematics
• Area Standards
• Level Grades 6–8
• Topic Geometry
• Instructional program descriptor Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
 Expectation precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
• Level Grades 9–12
• Topic Geometry
• Instructional program descriptor Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
 Expectation explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;
• Instructional program descriptor Use visualization, spatial reasoning, and geometric modeling to solve problems
 Expectation draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;

USA- ITEA/CTTE/NCATE Curriculum Standards for Initial Programs in Technology Teacher Education
• Standard 8LEARNING ENVIRONMENTS
Technology teacher education program candidates design, create, and manage learning environments that promote technological literacy.
• Area Knowledge Indicators:
 Indicator Recognize rich learning environments that provide for varied educational experiences in the technology classroom and laboratory.
 Indicator Identify learning environments that encourage, motivate, and support student learning, innovation, design, and risk taking.

USA- 21st Century Learning Skills & ICT Literacy
• Area Information and communication technology literacy
 Skill Thinking and problem-solving skills
 Skill Critical thinking and systems thinking
 Skill Problem identification, formulation, and solution
 Skill Creativity and intellectual curiosity