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Transformational Geometry Lesson Plan


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Published in: Technology, Education

Transformational Geometry Lesson Plan

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