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 Author: Mellissa Toothman & Courtney Shafer
 Based on unit by: MELLISSA TOOTHMAN
 Date Created: 6/20/2006 9:07:00 PM EDT
 
Go Fly A Kite
VITAL INFORMATION
Subject(s):
Art, History, Mathematics, Science, Technology

Grade/Level:
7-9

Time Required:

1 week, 5 class periods, 45 Min. per class



Objective(s):
The objective of this unit is for students to be able to identify the characteristics that define a tetrahedron's structure and utilize this knowledge when measuring surface area, constructing their own kites and when exploring other various geometric figures in future units.

Summary:
The tetrahedron lesson will focus on the unique four-sided polygon used by Alexander Graham Bell to disprove scientists’ theory that to increase the surface area of a flying machine the weight would also have to be increased. Students will learn the history of the tetrahedron’s evolution along with the computation of its surface area. The true Bell’s Challenge will be for students to construct and actually fly a tetrahedron kite.


IMPLEMENTATION
Learning Activities:
1. Bell 's Challenge
 
 
2. Tetrahedrons: What are they and how do we use them?
 


Resources and Unit Handouts:
  • Materials and resources:
    Lesson Materials:
    envelopes
    rulers
    tape
    glue sticks
    scissors
    calculators
    colored pencil
    straws
    cotton twine
    tissue paper

    Lesson Resources:
    Surface Area Worksheet
    Tetrahedron Cover Template
    Tetrahedrons: What Are They & How to Use Them-Handout (Power Point)

  • Technology resources:
    Internet Explorer, PowerPoint, Word, VRML (Virtual Reality Modeling Language), Cortona, Text Pad, Projector

  • The number of computers required is 1 per student.
  • Students Familiarity with Software Tool:
    1.) Internet Explorer- Basic internet browser that students typically use on a daily basis.

    2.) Power Point- A program used to create presentations that most students have utilized in the classroom in some form whether it be viewing or creating.

    3.) Microsoft Word- A basic document creation program utilized by most students through home use and in the academic realm.

    4.) VRML- A virtual reality modeling language that can be used to create 3-dimensional images that may be manipulated via the various coding process. Although the students may be familiar with the programs possible outcomes from television animation and the various type of electronic/computer games, students will typically be an uninformed group that do not possess a background in this programming language.

  • Implementation:
    1.) Internet Explorer- Internet browser utilized to research information in regards to the module topic and will be available as a hyperlink in power point presentation as a reference.

    2.) Power Point- Used to direct students to pertinent information regarding the topic & instructions during the demonstration of how to construct a tetrahedron kite.

    3.) Microsoft Word- A word processing program that will be used to create student handouts.

    4.) VRML- Program will be implemented by creating a VRML code that will show students how to construct tetrahedron kites by looping a ste-by-step process of a tetrahedronal kites construction.


  • Attachments:
     1. Tetrahedron Kite Challenge
    Test your ability to transform this VRML code to construct a 4-tetrahedra kite.
     2. The Bell Tetrahedron
    See how much information you can remember from the tetrahedron lesson and unscramble the words to find the hidden quote.
     3. Tetrahedron Puzzle
    Test your ability to transform this VRML code to construct a 4-tetrahedron kite.
     4. Surface Area Worksheet
    Worksheet containing examples to compute surface area.
     5. Tetrahedron Kite Directions
    Step-by-step instructions to construct a tetrahedron kite.
     6. Striped Tetrahedron
     7. Stripes
    Striped texture for tetrahedron.
     8. VRML Tetrahedron Kite Directions
    Illustrated tetrahedron kite directions using VRML.
     9. Straws
    A texture map used for the VRML Tetrahedron Kite Directions.
     10. Tetrahedrons: What Are They & How to Use Them (PowerPoint)
    A Powerpoint presentation providing information on the tetrahedron, its properties, uses and evolution. The presentation also provides instructions on how to construct a tetrahedron using envelopes and how to create a tetrahedron kite. You must also download Attachment 1 and 8-11.
    Links:
     1. Tetrahedron
    Math World includes various features of the tetrahedron alonq with objects that may be rotated to explore the tetrahedron's structure using Mathematica technology. This site is also inclusive of the primary formulas needed to solve such things as surface area.
     2. Tetrahedron Defined
    Internet encyclopedia including various types of information about the tetrahedron. (e.g. history, uses, trivia and geometric relationships)
     3. Bell Tetrahedral Kite
    The history and evolution of the Bell Tetrahedral Kite in regards to Alexander Graham Bell's determination to disprove scientists' theory that to increase double the surface area of an object the weight would have to be increased by 4 times.
     4. How to Construct a Tetrahedron Kite
    One of various web sites with step-by-step directions that guide you through creating a kite with tetrahedra.
     5. The Tetra-harp
    The three sided Tetra-harp (tetrahedron) by its unique shape becomes a transmitting musical instrument, quite different from its four-sided pyramid cousin. A musical instrument of the Tetra-harpšs design may help awaken awareness to the cosmic plan.
     6. The Inventor
    Background information on the inventions of Alexander Graham Bell.
     7. Mysteries of Tetrahedrons
    The tetrahedron shape used as a force field in the construction of a silicate model.
     8. What Is Crystal Habit?
    How tetrahedra shapes are utilized in the constructions of crystals.
     9. Tetrahedron Dice
    Tetrahedron dice are often marked or numbered in each corner of each triangular face and it is the 3 numbers in the upright position on 3 faces that determines the outcome of a throw.
     10. What Shapes Do Dice Have?
    The various shapes of dice and their utilization.
     11. Fair Dice
    Description of how the number of faces a dice possess affect the probability of rolling a certain set.
     12. Tetrahedron Envelope Directions
    The method by which a tetrahedron may be constructed using a small envelope.
     13. Project CITERA
    The CITERA website contains all resources utilized by the CITERA staff and teachers including lessons. From the teachers lessons links to activity and VRML files may be accessed for student use.

STANDARDS
Standards compiled from learning activities:
WV- West Virginia Content Standards and Objectives
• Subject Math
• Grade or Course Seventh Grade
• Standard Standard 1: Number and Operations (MA.S.1)
Students will:
 Objective MA.7.1.7 solve application problems with whole numbers, decimals, fractions and percents.
 Objective MA.7.1.8 use appropriate estimation strategies in problem situations including evaluating the reasonableness of a solution.
• Standard Standard 2: Algebra (MA.S.2)
Students will:
 Objective MA.7.2.2 simplify and evaluate numerical and algebraic expressions with whole numbers, integers, absolute value and exponents using the order of operations and exponential rules.
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 Objective MA.7.3.3 use 2-dimensional representations of 3-dimensional objects to visualize and solve problems.
• Grade or Course Eighth Grade
• Standard Standard 1: Number and Operations (MA.S.1)
Students will:
 Objective MA.8.1.4 use powers, squares, and square roots to solve problems.
 Objective MA.8.1.5 use estimation techniques with whole numbers, decimals, percent, fractions and mixed numbers to solve and verify solutions in application problems.
• Standard Standard 2: Algebra (MA.S.2)
Students will:
 Objective MA.8.2.1 use order-of-operations and exponents rules to solve problems with numerical and algebraic expressions containing whole numbers, integers, absolute value, fractions and exponents.
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 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).
 Objective MA.8.3.6 create scale models including ratio, proportion and similar figures using pencil/paper and dynamic geometry software.
• Grade or Course Algebra/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;
 Objective AGP.3.4 estimate and find the surface area and the volume of three-dimensional figures.
• Grade or Course Algebra I
• Standard Standard 2: Algebra (MA.S.2)
Students will:
 Detail use mathematical models to represent and understand quantitative relationships; and
 Objective A1.2.15 estimate and simplify square roots into both exact and approximate forms.
• 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.
• Subject Science
• Grade or Course Seventh Grade
• Standard Standard 1: History and the Nature of Science (SC.S.1)
Students will:
 Objective SC.7.1.1 realize that scientists formulate and test their explanations of nature using observation, experiments and theoretical models.
 Objective SC.7.1.2 recognize and appreciate that scientific knowledge is subject to modification as new scientific information challenges current theories.
 Objective SC.7.1.4 articulate the historical significance of scientific discoveries as influenced by technological demands, competition, controversy, world events, personalities and societal issues.
• Standard Standard 2: Science as Inquiry (SC.S.2)
Students will:
 Objective SC.7.2.1 cooperate and collaborate to ask questions, find answers, solve problems, conduct investigations to further an appreciation of scientific discovery.
• Standard Standard 5: Scientific Design and Application (SC.S.5)
Students will:
 Detail demonstrate abilities of technological design; and
 Objective SC.7.5.2 test and evaluate different types of materials and/or design approaches in building objects or completing tasks.
• Grade or Course Eighth Grade
• Standard Standard 1: History and the Nature of Science (SC.S.1)
Students will:
 Objective SC.8.1.4 articulate the historical significance of scientific discoveries as influenced by technological demands, competition, controversy, world events, personalities and societal issues.
• Standard Standard 2: Science as Inquiry (SC.S.2)
Students will:
 Objective SC.8.2.1 cooperate and collaborate to ask questions, find answers, solve problems, conduct investigations to further an appreciation of scientific discovery.
 Objective SC.8.2.2 formulate conclusions through close observations, logical reasoning, objectivity, perseverance and integrity in data collection.
• Standard Standard 5: Scientific Design and Application (SC.S.5)
Students will:
 Objective SC.8.5.2 compare scientific inquiry and technological design processes.
• Grade or Course Ninth Grade
• Standard Standard 1: History and the Nature of Science (SC.S.1)
Students will:
 Objective SC.9.1.1 formulate scientific explanations based on the student's observational and experimental evidence, accounting for variability in experimental results.
 Objective SC.9.1.2 recognize that science has practical and theoretical limitations.
 Objective SC.9.1.4 conclude that science is a blend of creativity, logic and mathematics.
 Objective SC.9.1.5 trace the development of key historical concepts and principles describing their impact on modern thought and life by identifying the scientist?s contributions.
• Subject Social Studies
• Grade or Course Seventh Grade
• Standard Standard 5: History (SS.S.5)
Students will:
 Objective SS.7.5.9 use a variety of credible sources to construct and interpret the past.
• Subject Art
• Grade or Course Grade 7 ? General Art
• Standard Standard 2: Elements of Art and Principles of Design (VA.S.2)
Students will:
 Objective VA.7.2.1 compare and contrast the characteristics of elements of art, e.g., line, shape, color, texture, form, space, and value.
 Objective VA.7.2.3 create a non-objective artwork using geometric and/or biomorphic (organic) shapes or forms.
• Grade or Course Grade 8 ? General Art
• Standard Standard 2: Elements of Art and Principles of Design (VA.S.2)
Students will:
 Objective VA.8.2.1 identify and use the elements of art, e.g., line, shape, color, texture, value, form, and space.
• Grade or Course General Art I
• Standard Standard 2: Elements of Art and Principles of Design (VA.S.2)
Students will:
 Objective VAI.2.1 identify similarities and differences in two- and three-dimensional visual art based on the elements of art and principles of design.
 Objective VAI.2.2 analyze structures and functions of two-and three- dimensional artworks.
 Objective VAI.2.3 create two- and three-dimensional artworks based on elements of art and principles of design using appropriate media, processes, and techniques to solve assigned problems.
• Subject Technology
• Grade or Course Seventh Grade
• Standard Standard 6: Technology Problem-solving and Decision-making Tools (TEC.S.6)
Students will
 Objective TEC.7.6.1 use appropriate computer-based productivity tools to create and modify solutions to problems.

USA- ISTE: National Educational Technology Standards (NETS) for All Teachers
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.
• Standard ITechnology Operations and Concepts
Teachers demonstrate a sound understanding of technology operations and concepts.
 Performance Indicator Ademonstrate introductory knowledge, skills, and understanding of concepts related to technology (as described in the ISTE National Education Technology Standards for Students).
 Performance Indicator BDemonstrate continual growth in technology knowledge and skills to stay abreast of current and emerging technologies.
• Standard IVAssessment and Evaluation.
Teachers apply technology to facilitate a variety of effective assessment and evaluation strategies.
 Performance Indicator AApply technology in assessing student learning of subject matter using a variety of assessment techniques.
 Performance Indicator BUse technology resources to collect and analyze data, interpret results, and communicate findings to improve instructional practice and maximize student learning.
 Performance Indicator CApply multiple methods of evaluation to determine students? appropriate use of technology resources for learning,communication,and productivity.

USA- ISTE: Profiles for Technology Literate Students (includes NETS for Students)
• Grade Grades 6-8

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 3Exhibit legal and ethical behaviors when using information and technology, and discuss consequences of misuse. (2)
 Performance Objective 4Use content-specific tools, software, and simulations (e.g., environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research. (3, 5)
 Performance Objective 5Apply productivity/multimedia tools and peripherals to support personal productivity, group collaboration, and learning throughout the curriculum. (3, 6)
 Performance Objective 8Select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems. (5, 6)
 Performance Objective 9Demonstrate an understanding of concepts underlying hardware, software, and connectivity, and of practical applications to learning and problem solving. (1, 6)
• 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 1Identify capabilities and limitations of contemporary and emerging technology resources and assess the potential of these systems and services to address personal, lifelong learning, and workplace needs. (2)
 Performance Objective 4Demonstrate and advocate for legal and ethical behaviors among peers, family, and community regarding the use of technology and information. (2)
 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 Number and Operations
• Instructional program descriptor Compute fluently and make reasonable estimates
 Expectation select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods;
• 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 Number and Operations
• Instructional program descriptor Compute fluently and make reasonable estimates
 Expectation develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
• Topic Geometry
• Instructional program descriptor Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
 Expectation analyze properties and determine attributes of two- and three-dimensional objects;
 Expectation establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;

USA- National Science Education Standards
• Chapter Chapter 6 Science Content Standards
• Grade Level 5-8
• Content Standard AScience as Inquiry: As a result of activities in grades 5-8, all students should develop
• Ability/ Concept Understandings about scientific inquiry
 Detail Different kinds of questions suggest different kinds of scientific investigations. Some investigations involve observing and describing objects, organisms, or events; some involve collecting specimens; some involve experiments; some involve seeking more information; some involve discovery of new objects and phenomena; and some involve making models.
 Detail Current scientific knowledge and understanding guide scientific investigations. Different scientific domains employ different methods, core theories, and standards to advance scientific knowledge and understanding
 Detail Mathematics is important in all aspects of scientific inquiry.
 Detail Technology used to gather data enhances accuracy and allows scientists to analyze and quantify results of investigations.
 Detail Scientific explanations emphasize evidence, have logically consistent arguments, and use scientific principles, models, and theories. The scientific community accepts and uses such explanations until displaced by better scientific ones. When such displacement occurs, science advances.
 Detail Science advances through legitimate skepticism. Asking questions and querying other scientists' explanations is part of scientific inquiry. Scientists evaluate the explanations proposed by other scientists by examining evidence, comparing evidence, identifying faulty reasoning, pointing out statements that go beyond the evidence, and suggesting alternative explanations for the same observations.
 Detail Scientific investigations sometimes result in new ideas and phenomena for study, generate new methods or procedures for an investigation, or develop new technologies to improve the collection of data. All of these results can lead to new investigations.
• Content Standard GHistory and Nature of Science: As a result of activities in grades 5-8, all students should develop understanding of
• Ability/ Concept History of science
 Detail Many individuals have contributed to the traditions of science. Studying some of these individuals provides further understanding of scientific inquiry, science as a human endeavor, the nature of science, and the relationships between science and society.
 Detail In historical perspective, science has been practiced by different individuals in different cultures. In looking at the history of many peoples, one finds that scientists and engineers of high achievement are considered to be among the most valued contributors to their culture.
 Detail Tracing the history of science can show how difficult it was for scientific innovators to break through the accepted ideas of their time to reach the conclusions that we currently take for granted.

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