Geometrical Transformations


KNPB PBS LearningMedia

Overview:
Understand geometrical transformations to create tessellations.

Objectives:

  • Students understand the elementary transformations in geometry (translate, reflect, rotate, dilation). Examine how transformations of points on the coordinate plane affect their placement. Find the coordinates of images that have been rotated, reflected, translated, or dilated.
  • Students relate transformations to art and create a tessellation. *Possible extension lesson: MC Escher documentary.


planar-image.jpgCurriculum Topics:
Math | Geometry | Transformations

Grade Level:
9-10

Suggested Time:
50-55 minute class (3 days, or 4 if using MC Escher extension or in class time to draw)

Lesson Outline:

Day One:

  1. Open the interactive, Planar Figures - Transformations on the interactive whiteboard (or on their personal iPad/laptop). Guide the students through this interactive lesson or let them explore independently. This will give the students a good overview of planar transformations. (30 min)
  2. Begin notes on transformations in the coordinate plane (attached flipcharts/PDF). (20 min)


Day Two:

  1. Finish notes if necessary.
  2. Open the interactive, Determine Coordinates of Transformations - Shooting Pool on the interactive whiteboard (or on their personal iPad/laptop). Guide the students through this interactive lesson or let them explore independently. This interactive lesson does a great job of solidifying coordinate transformations while relating it to shooting pool.


Day Three:

  1. Explore “tessellations” on the web (again, teacher led, or individual/group with laptops/iPads). Show the tessellations.org as one example on the web. Have them explore and find different examples of tessellations. (30min)
  2. Introduce tessellation project (art) they are to complete in ____ days. Pass out rubric and explain expectations. (20min)
  3. Other Options
        • Make one for them, and show how to trace and re-trace to fill the paper.
        • Have them create their stencil in class and monitor the cutting and make sure the shape will tessellate.
        • Have them start project in class.


Day Four (Optional):

  1. Show MC Escher video. This is a documentary on YouTube that is great for a MC Escher introduction. It is a lengthy video, and would take an entire period. So plan accordingly if using this video.
  2. Allow class time to create tessellations and be able to assist students with their work.


LearningMedia Resources:


Supplemental Materials:

Source: Geometry: Concepts and Applications, Glencoe McGraw-Hill www.geomconcepts.com


Additional Media Resources:


Standards:

  • (CS 4.0): Students will identify, represent, verify, and apply spatial relationships and geometric properties to solve problems, communicate, and make connections within and beyond the field of mathematics.
  • (C.CO. 6): Use geometric descriptions of rigid motion to transform figures and to predict the effect of a given rigid motion on a given figure.

 

Lesson contributed by Jason Mattick

 
For a demonstration or more details, contact Karen Karst-Hoskins
at karenh@knpb.org or call 775.682.7805 or 775.544.9061.


Funding provided by NV Energy and the Walmart State Giving Program.
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