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 Author: MARY BETH ATWELL
 Date Created: 6/22/2006 5:13:00 PM EDT
 
Volume of Cones
VITAL INFORMATION
Subject(s):
 Mathematics, Technology
Grade/Level:
 8
Time Required:
 Four 45 minute class periods
Objective(s):
  • discover the formula for the volume of a cone
  • discover how the volume of a cone relates to the volume of a cylinder with the same radius and height
  • discover how changes in the height and radius affect the volume of cones
Summary:
 Students will discover how the volume of a cone relates to the volume of a cylinder with the same radius and height.  The students will use this information to discover the formula for the volume of a cone.  The students will explore the volume of cones through manipulatives to hypothesize and discover how changes in the radius and height affect its volume.
IMPLEMENTATION
Learning Activities:
1. Volume of cones/Instructional
 
 
2. Volume of cones/Exploration
 
Resources and Unit Handouts:
  • Technology resources:
    PowerPoint, Cortona and notepad/textpad
  • The number of computers required is 1 per student.
  • Cortona and notepad should be loaded on each computer
  • Drawing of the first cone to be used. I recommend it be made on card stock for durability. This cone will be used in both lessons.


    • Attachments:
     1. VRML cone/cylinder demo
    This is the file to show the comparison of a cone and cylinder with the same radius and height.
     2. background of cone demo
    This needs to be downloaded in the same folder as the VRML cone/cylinder demo.
     3. VRML student exploration
    This is the file the students will manipulate to see a visual representation of different size cones and cylinders.
     4.  VRML student cone exploration
    This is the file the students will manipulate to see a visual representation of different size cones.
    Links:
     1. Explorelearning
    This site contains a large amount of useful 3-D creative math animations and visulaizations.
STANDARDS
Standards compiled from learning activities:
WV- West Virginia Content Standards and Objectives
• Subject : Math
• Grade or Course : Eighth Grade
• Standard : Standard 4: Measurement (MA.S.4)
Students will:
 Detail : demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurement; and
 Detail : apply appropriate techniques, tools and formulas to determine measurements through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics.
 Objective MA.8.4.2 : use the concept of volume for cone and pyramids as one-third the product of the area of the base and the height.
• Subject : Technology
• Grade or Course : Eighth Grade
• Standard : Standard 6: Technology Problem-solving and Decision-making Tools (TEC.S.6)
Students will:
 Detail : use technology resources for solving problems and making informed decisions; and
 Detail : employ technology in the development of strategies for solving problems in the real world.
 Objective TEC.8.6.1:  select and use technology tools to solve problems and make decisions related to content areas.

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 4: Use 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 5: Apply productivity/multimedia tools and peripherals to support personal productivity, group collaboration, and learning throughout the curriculum. (3, 6)
 Performance Objective 8: Select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems. (5, 6)

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
• Area : Interpersonal and self-direction skills
 Skill : Interpersonal and collaborative skills
 Skill : Self-direction
 Skill : Accountability and adaptability
 Skill : Social responsibility