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# 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
• 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: http://nlvm.usu.edu/en/nav/category_g_3_t_3.html 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:
• http://www.glogster.com/ (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
• 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.