From Pythagoras to Johnny Depp

Author: Brian Cerullo, Morgan Kent based on unit by: Brian Cerullo 6/22/2007 2:26:00 PM EDT

VITAL INFORMATION

Art, History, Mathematics, Technology
 
8-10
 
1 day
3:30

(In mins)
part one:(15-30)
part two:(30-45)
part three:(45-75)
part four:(45-75)
 

Students will:

  • discover and analyze Pythagorean triples. 
  • apply the Pythagorean Theorem to real- world situations. 
  • create basic three-dimensional shapes utilizing VRML.
 

From Pythagoras to Johnny Depp:

  1. Motivating history on the background of Pythagoras and the Pythagorean theorem using a PowerPoint presentation with audio and video clips 
  2. Introduction to the Pythagorean theorem utilizing a VRML visual (for a proof of the theorem), supporting the lesson with an inquiry based exercise using a Java application, and recognizing Pythagorean triples, including 45, 45, 90 
  3. Constructing an origami model through a series of folds.  After each fold, lengths will be determined to discover the dimensions of the final model 
  4. VRML assessment of students by applying the Pythagorean Theorem to a real-world problem 
  5. VRML exploration designing boxes to stack on one another
 
IMPLEMENTATION

 
 
STANDARDS

Standards addressed by unit:
International- Intl. Technology Education Association: Standards for Technology Literacy
• Category The Nature of Technology
• Standard 3Students will develop an understanding of the relationships among technologies an dthe connections between technology and other fields of study.
• Grade Range 9-12
 Benchmark JTechnological progress promotes the advancement of science and mathematics.
Likewise, progress in science and mathematics leads to advances in technology. the development of binary language, a digital language made up solely of ones an dzeros; the invention of the the transistor, a device designed to replace the vacuum tube; an other use of integrated circuits, a collection of millions of minature transistors, helped spawn a new generation of machines, from laptom computers and compact disc players to digital televison. The mathematical and scientific ideas applied in the development of these digital devices promoted further developments that resulted in new toolsm such as computer modeling. These tools, inturn, are used to explore new scientific and mathematical ideas, thereby spawning additional discoveries

WV- West Virginia Content Standards and Objectives
• Subject Math
• Grade or Course Geometry and Applied Geometry
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 Objective G.3.11 apply the Pythagorean Theorem and its converse in solving practical problems and in deriving the special right triangle relationships.
 Objective G.3.13 given a polygon, find angle measures of interior and exterior angles; find length of sides from given data; and use properties of regular polygons to find missing data.

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 3Analyze advantages and disadvantages of widespread use and reliance on technology in the workplace and in society as a whole. (2)

USA- NCTM (Nat. Council of Teachers of Mathematics): Principles & Standards for School Mathematics
• Area Standards
• Level Grades 9–12
• Topic Geometry
• 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;
 Expectation visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections;
 Expectation use vertex-edge graphs to model and solve problems;
 Expectation use geometric models to gain insights into, and answer questions in, other areas of mathematics;
 Expectation use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.

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
Standards compiled from learning activities:
International- Intl. Technology Education Association: Standards for Technology Literacy
• Category The Designed World
• Standard 17Students will develop an understanding of and be able to select and use information and communication technologies.
• Grade Range 9-8
 Benchmark NInformation an communication systems can be used to inform, persuade, entertain, control, manage, and educate.
Examples of such systems include the Internet, telephones, televisons, radios, computers, and fax machines. Information and communication systems are widely used in commercial endeavors to assist in decision-making and problem solving. Entertainment, which has been enhanced through technology, provides pleasure and enjoyment for people in their free time. The overall usefulness of information is dependent upon such factors as its relevance, timeliness, truth, completness, and cultural value. These factors help shape the meaning of the information, which has become a valued commodity in today’s society.

WV- West Virginia Content Standards and Objectives
• Subject Math
• Grade or Course Geometry and Applied Geometry
• Standard Standard 3: Geometry (MA.S.3)
Students will:
 Objective G.3.1 represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays and angles.
 Objective G.3.4 construct logical arguments in formal and informal methods with direct and indirect reasoning.
 Objective G.3.5 apply definitions, theorems, and postulates related to such topics as complementary, supplementary, and vertical angles and angles formed by perpendicular lines.
 Objective G.3.11 apply the Pythagorean Theorem and its converse in solving practical problems and in deriving the special right triangle relationships.
 Objective G.3.16 develop and apply concepts of analytical geometry such as formulas for distance, slope, and midpoint and apply these to finding dimensions of polygons on the coordinate plane.
• Subject Technology
• Grade or Course Ninth - Twelfth Grade
• Standard Standard 1: Basic Operations and Concepts (TEC.S.1)
Students will:
 Detail demonstrate a sound understanding of the nature and operation of technology systems; and
 Objective TEC.9-12.1.1 use data input skills appropriate to the task.

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 2Demonstrate knowledge of current changes in information technologies and the effect those changes have on the workplace and society. (2)
 Performance Objective 5Apply productivity/multimedia tools and peripherals to support personal productivity, group collaboration, and learning throughout the curriculum. (3, 6)
 Performance Objective 7Collaborate with peers, experts, and others using telecommunications and collaborative tools to investigate curriculum-related problems, issues, and information, and to develop solutions or products for audiences inside and outside the classroom. (4, 5)
• 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 2Make informed choices among technology systems, resources, and services. (1, 2)
 Performance Objective 3Analyze advantages and disadvantages of widespread use and reliance on technology in the workplace and in society as a whole. (2)
 Performance Objective 7Routinely and efficiently use online information resources to meet needs for collaboration, research, publications, communications, and productivity. (4, 5, 6)
 Performance Objective 8Select and apply technology tools for research, information analysis, problem-solving, and decision-making in content learning. (4, 5)
 Performance Objective 9Investigate and apply expert systems, intelligent agents, and simulations in real-world situations. (3, 5, 6)
 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 Algebra
• Instructional program descriptor Understand patterns, relations, and functions
 Expectation relate and compare different forms of representation for a relationship;
• Instructional program descriptor Represent and analyze mathematical situations and structures using algebraic symbols
 Expectation develop an initial conceptual understanding of different uses of variables;
 Expectation use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;
 Expectation recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.
• 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;
 Expectation understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
 Expectation create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Topic Reasoning and Proof
 Instructional program descriptor recognize reasoning and proof as fundamental aspects of mathematics;
 Instructional program descriptor make and investigate mathematical conjectures;
 Instructional program descriptor develop and evaluate mathematical arguments and proofs;
 Instructional program descriptor select and use various types of reasoning and methods of proof.

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 Creativity and intellectual curiosity
• Area Information and communication skills
 Skill Communication skills
• Area Interpersonal and self-direction skills
 Skill Interpersonal and collaborative skills
 Skill Self-direction

USA- 21st Century Skills Guidelines
• Content and Skill Area INFORMATION AND COMMUNICATION TECHNOLOGY (ICT) LITERACY: Technology has become an essential tool for the realization of learning and thinking skills in today’s knowledge economy. Key elements of ICT Literacy include use of ICT in service of:
 Skill Interpersonal and self-direction skills. Becoming more productive in accomplishing tasks and developing interest in improving own skills.