Transformational Geometry Lesson Plan

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  • 1. Transformational Geometry Lesson Plan Jeff Shocket
  • 2. Transformational Geometry
    • Grade Level: 7 th or 8 th
    • Subject Area: Geometry
    • Topics addressed: Dilations, Reflections, Rotations, and Transformations
    • Web 2.0 Tools:
      • National Library of Virtual Manipulatives (NLVM): Geometry 6-8
      • Glogster
    • Length of Lesson: 6 days
  • 3. Transformational Geometry
    • Aim: To discover transformational geometry
    • Objectives:
      • Determine what Dilations, Reflections, Rotations, and Transformations are
      • Demonstrate the ability to perform different transformations
  • 4. Description of Project
    • Purpose
      • Provide students with a way of understanding what transformational geometry is
      • Understand the difference between Dilations, Reflections, Rotations, and Translations
      • Have students learn on their own using technology
      • Practice the different math concepts
  • 5. Description of Project
    • Task:
      • Students will be asked to use NVLM Geometry to learn and understand the difference between:
        • Dilatation
        • Reflection
        • Rotation
        • Transformation
      • Students will practice using the rules given specific examples
  • 6. Description of Project
    • Procedures:
      • Day 1 (40 minutes)
        • Students will be instructed to go to the computer lab. The computer lab needs to be equipped with either a blackboard or a Smartboard
        • The instructor will begin the lesson by talking about what transformational geometry is (brief background) and introduce the first transformation: Dilatation
        • Students will be then given a worksheet to complete
        • HW – back of the worksheet has the HW assignment
  • 7. Description of Project
    • Procedures (Continued)
        • The worksheet will instruct them to do the following:
          • Go to the following website: and click on “ Transformations – Dilation ”
          • On the website, there is an activity the students will complete
          • Students will answer the activity questions, come up with a definition, properties, general rules, and a symbol for what a dilation is
          • Students will complete the back of the worksheet for HW
  • 8. Description of Project
    • Procedures:
      • Day 2
        • The lesson will start off with collecting the worksheet from the previous day and introduce the new transformations: Reflection and Rotation
        • Students will be then given a worksheet & HW to complete (similar to day 1) to complete
      • Day 3
        • The lesson will start off with collecting the worksheet from the previous day and introduce the new transformations: Translation
        • Students will be then given a worksheet & HW to complete (similar to day 1) to complete
        • Once finished with translation worksheet, students will either finish any worksheets they have not finished, or the Composition Activity (bonus points)
  • 9. Description of Project
    • Procedures:
      • Days 4 & 5
        • Divide the class up into 4 groups. Each group (assigned or not) will create a poster on 1 of the 4 (assigned) transformations featuring:
          • The rules for the transformation
          • Properties of the transformation
          • Symbol of the transformation
          • Examples of the transformation
        • Each group will get the worksheet for their transformation back graded
        • They will use the following website:
          • (The teacher will sign up for an account and the students will all use the same user)
          • These posters should be very detailed and precise. They should feature organization, color, precision, and uniqueness.
      • Day 6
        • Students will get back all the worksheets graded
        • Presentations of the posters on the Smartboard
        • Students will take/edit notes on all the transformations
        • Teacher will grade the posters & the presentations
  • 10. Timeline
    • Day 1
      • Introduction
      • Dilations
    • Day 2
      • Reflections
      • Rotations
    • Day 3
      • Translation
      • Online Activity
    • Day 4
      • Create a Poster featuring one of the transformations (assigned)
    • Day 5
      • Finish posters
    • Day 6
      • Presentations
  • 11. Resources
    • NVLM
      • Transformations –
        • Dilations
        • Reflections
        • Rotations
        • Translations
        • Compositions
    • Smartboard
    • Poster Website
  • 12. Description of Project
    • Daily Worksheets for Students to Complete
            • Dilations
            • Reflections
            • Rotations
            • Translations
            • Compositions
    • Evaluation: Rubric
      • Students will be evaluated on:
        • The completion of each worksheet
        • The daily HW assignments
        • Daily Check-up
        • Team collaboration
        • Poster Critique
  • 13. NYS Standards – Problem Solving
    • 8.PS.4 - Observe patterns and formulate generalizations
    • 8.PS.5 - Make conjectures from generalizations
    • 8.PS.6 - Represent problem situations verbally, numerically, algebraically, and graphically
    • 8.PS.9 - Work backwards from a solution
    • 8.PS.11 - Work in collaboration with others to solve problems
  • 14. NYS Standards – Representation
    • 8.R.1 - Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
    • 8.R.2 - Explain, describe, and defend mathematical ideas using representations
  • 15. NYS Standards – Geometry
    • 8.G.7 - Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)
    • 8.G.8 - Draw the image of a figure under rotations of 90 and 180 degrees
    • 8.G.9 - Draw the image of a figure under a reflection over a given line
    • 8.G.10 - Draw the image of a figure under a translation
    • 8.G.11 - Draw the image of a figure under a dilation
    • 8.G.12 - Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation
  • 16. Technology Standards (ISTE)
    • 1. Creativity and Innovation : Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
      • create original works as a means of personal or group expression.
      • identify trends and forecast possibilities. (Days 1, 2, 3)
    • 2. Communication and Collaboration : Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. (Days 4,5)
      • interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media.
      • communicate information and ideas effectively to multiple audiences using a variety of media and formats.
      • contribute to project teams to produce original works or solve problems.
  • 17. Technology Standards (ISTE)
    • 3. Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information. (Days 4, 5)
      • locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
      • evaluate and select information sources and digital tools based on the appropriateness to specific tasks.
    • 4. Critical Thinking, Problem Solving, and Decision Making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. (Days 1, 2, 3, 4, 5)
      • identify and define authentic problems and significant questions for investigation.
      • plan and manage activities to develop a solution or complete a project.
      • collect and analyze data to identify solutions and/or make informed decisions.
  • 18. Technology Standards (ISTE)
    • 5. Digital Citizenship : Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. (Days 1, 2, 3, 4, 5, and 6)
      • exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity.
    • 6. Technology Operations and Concepts : Students demonstrate a sound understanding of technology concepts, systems, and operations. (Days 1, 2, 3)
      • understand and use technology systems.
      • select and use applications effectively and productively.
      • transfer current knowledge to learning of new technologies.
  • 19. Technologies Used
    • Student:
      • National Library of Virtual Manipulatives (NLVM)
      • Web 2.0 Tool: Glogster
      • Smartboard
    • Teacher:
      • Smartboard
      • Glogster
  • 20. Learning Activities
    • Teacher Preparation
      • Reserve the computer lab for 5 days
      • Reserve the Smartboard / projector
      • Make sure that Glogster is not blocked by the schools firewall
      • Copies of the worksheets
      • Grades:
        • Have all the worksheets graded by day 6
        • Have each groups worksheet graded by day 4
    • Student-centered Learning Activities
      • Students will learn each of the transformation (how they work) from the NVLM website
      • Students will apply the knowledge from the NVLM website to complete the Homework assignment each night.
      • Students will collaborate with each other to create a poster and present to the class about each transformation (definitions, properties, general rules, symbols and examples)
  • 21. Higher Order Thinking – Bloom’s Taxonomy
    • Knowledge
      • Students will have to master transformational geometry and recall the information when making the poster and presenting to the class.
    • Comprehension
      • Students will have to understand what the different types of transformations are. They will also have to predict what will happen given a specific example.
    • Application
      • Students will have to demonstrate the different transformations and show how to apply each transformation.
  • 22. Higher Order Thinking – Bloom’s Taxonomy
    • Analysis
      • Students will compare the different transformations to find the difference between them. They will also explain the different properties for each transformation.
    • Synthesis
      • Students will need to draw conclusions to find the different rules on the different transformations.
    • Evaluation
      • Students will assess and explain different examples to determine different transformations. Students will have to explain which transformation(s) was used that transformed the image.