The Math Forum

Activity 1

Navajo Burntwater Designs

An exercise in using translations and reflections to create symmetrical designs.

by Kim Sweeney

Table of Contents || Versión español


  1. One 18" X 24" sheet of construction paper per group
  2. Four rulers
  3. Four sets of "stair-step" templates [4 pieces per set = 16 total pieces]

  4. Colored pencils
  5. One pair of scissors


  1. The Reader reads these directions aloud.
  2. The Materials Manager checks materials.
  3. The Listener reports missing materials to the teacher (if necessary).
  4. The Scribe folds the paper in half horizontally and vertically, then opens it flat:

    and draws a two-inch border all the way around the inside:

  5. The Materials Manager cuts the paper into four pieces on the folds and gives one of the smaller pieces of paper to each group member.
  6. The Group Members discuss a plan for creating the pattern.
  7. Group members work individually on their fourth of the design using the "stair-step" templates to trace around, creating a design by flipping (reflecting) or sliding (translating) the templates.
  8. Group members color the design, coordinating the colors with other group members.


The product for this center is one Burntwater design for each individual. The Scribe checks off the station on the recording sheet.


  1. Place the Burntwater designs in the group folder.
  2. Count the templates and return them to the materials basket.
  3. Place the rulers, colored pencils, and scissors in the materials basket.

versión español

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