Native American Designs

Lisa Scott

I.  Objective: The learner will be introduced to transformational geometry using Native American Designs. These transformations will include a reflection, rotation, and translation. The learner will be introduced to the mathematical vocabulary for line of symmetry and rotational symmetry. The learner will use transformations and symmetry to create a Native American Design of their own.

II.  Materials: PowerPoint Native American Designs, Computers with Geometer’s Sketchpad for each student or pairs of students, Copies of Native American Designs Rubric.

III.  Lesson: Native American Designs

  1. Day 1: Go through the PowerPoint presentation “Native American Designs”. Discuss the definitions for a reflection, rotation, translation, line of symmetry and rotational symmetry. Look for these transformations and symmetries in the Native American Designs.
  2. Day 2: Review the definitions from Day 1.
  3. Introduce Geometer’s Sketchpad. Do the “Basics” on page 9-14 from the book, Geometer’s Sketchpad Learning Guide.
  4. Encourage Free Play. Have students play with the free hand tools, point, compass, and segment. Use the selection arrow and text tool. Demonstrate how to undo objects.
  5. Demonstrate how to construct a polygon and its interior. Perform a reflection of the polygon over a marked “mirror line”. Show a reflection over a line that contains the side of a figure and a reflection over a line that does not intersect the figure. Demonstrate the “click and drag” and how to change the color of the interior of the image polygon.
  6. Perform a rotation of the constructed polygon around a marked point by a fixed angle. Demonstrate the “click and drag”.
  7. Demonstrate a translation by a marked vector.
  8. Show how to hide objects that the students don’t want seen but are necessary for the construction of the transformation.
  9. Ask students to work on their Native American Designs. Circulate and help as needed.

IV.  Assessment: Students create their own Native American Designs. The design needs to include a reflection, rotation, translation, line of symmetry, and rotational symmetry.

V.  Summary: Native American Designs are rich with transformational geometry. This lesson introduced three transformations. These included a reflection, a rotation, and a translation. This lesson also addressed the definition for a line of symmetry and rotational symmetry using Native American Designs.


Native American Designs

Grade Sheet

Name______

1. Create your design using Geometer’s Sketchpad.

2. Print your design. (5 points)

3. Include a reflection (blue), translation (red) and rotation (yellow) in your design. (5 points each, total 15 points)

4. Your design must have at least one line of symmetry (green). (5 points)

5. Your design must have at least one example of rotational symmetry (purple). (5 points)

6. You will also receive up to 5 points for design originality. (5 points)

Score out of 35 total points possible:

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