2. Geometry (HS)

 
  1. Reasoning About Numbers, Systems and Quantitative Situations (L1)
  2. Calculation, Algorithms, and Estimation (L2)
  3. Mathematical Reasoning, Logic, and Proof (L3)
  4. Figures and Their Properties (G1)
  5. Relationships Between Figures (G2)
  6. Transformations of Figures in the Plane (G3)

 

Additional Links to General Mathematics Sites

 

7. Transformations of Figures in the Plane (G3)

Students will solve problems about distance-preserving transformations and shape-preserving transformations. The transformations will be described synthetically and, in simple cases, by analytic expressions in coordinates.

 

High School

  1. G3.1 Distance-preserving Transformations: Isometries
    1. Rigid Motions in the Plane
      Need Geometer's Sketchpad or TI92. An exhaustive study of a variety of rigid isometrics using the previously named technology. This is a teacher lesson plan.
    2. Rotations and Rotational Symmetry
      A nice 4 part lesson plan to use in 9th grade geometry to teach rotations and rotational symmetry. Interactive applets are included along with questions for reflection and understanding. Students are able to create their own designs.
    3. Symmetries and Their Properties: Glide Reflections
      A five part lesson plan including a student tutorial, interactive applets and questions for understanding. A good lesson for 9th grade geometry to reinforce the properties of glide relflections. Students are able to create their own designs.
    4. Symmetries and Their Properties
      A four part lesson plan with student interaction that helps to reinforce the properties of reflections through tutorials with applets included. Perfect for 9th grade geometry. Questions for understanding are included.
    5. Symmetries and Their Properties- Translations
      A 5 lesson activity on translations for 9th grade geometry. The activities include tutorials, interactive applets and questions for understanding. Student will be actively engaged in this lesson.
    6. Teacher Resources for Inversions
      This site provides several classroom activities based on inversions. Worksheets are appropriate for grades 3-12 for teaching symmetry, art, geometry, language arts, and creative thinking. Teacher lesson plans and printable worksheets are included.
    7. The Geometry Center
      This student interactive site explores symmetry, tiling, wallpaper groups, fractals and isometries. It includes animations of transformations.
  2. G3.2 Shape-preserving Transformations: Dilations and Isometries
    1. Howe-Two Software
      This page demonstrates transformations with interaction of the students. It offers other links to math web sites as well.
    2. Interactive
      Great demonstration on tessellations. You can adjust a regular polygon and then press the "tessellate" button and it will show you what it looks like.
    3. Sketchpad Homework
      Teachers will find detailed instructions for several sketchpad applications. It begins with basic commands and advances to more difficult lessons. Requires the program Geometer's Sketchpad
    4. The Four Types of Symmetry in the Plane
      This site provides teacher notes on transformations of shapes in two dimensions. The site is not interactive but contains diagrams, sample questions and recommended projects.
    5. The Cylinder Problem
      This site poses a problem that involves comparing cylinders. It involves a number of mathematical concepts and problem-solving approaches that can lead to rich discourse in the classroom.
    6. The Moving Sofa Problem
      Outstanding! This "Study Works" site provides a complete set of lessons for upper middle school through high school. Students must determine whether couches, of varying shapes, can fit around a narrow corner. In addition, students calculate areas of different shaped furniture and explore properties of regular and irregular objects. Teacher notes, worksheets, and discussion topics are included.
    7. Totally Tessellated
      Outstanding - This site uses tessellations to explore transformations and symmetry. It includes high school quality animated examples and hands-on activities for students.
    8. Visualizing Topography
      Visualizing Topography is an instructional tour that shows how to visualize topography in 3D. It contains Quick Time movies and questions that help students visualize two-dimensional topography in three dimensions. Student worksheets and teacher guides are included.

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