Tesselations

 

Tesselation DesignStudents start with a small square of paper, and create their own tesselating designs. A great tie-in to a math lesson!

 

Materials

  • 12"x18" white drawing paper
  • 3"x3" square tagboard
  • pencils
  • scissors
  • crayons or markers
  • black permanent markers
  • tape

Directions

  1. Introduce key vocabulary words: tessellation, polygon, angle, plane, vertex and adjacent. Ask students to tell you what they know about the word tessellation. Discuss the three basic attributes of tessellations:
    • Tesselations are repeated patterns. Ask students to find examples of repeated patterns in the room. Generate a list of the words one could use to describe these patterns. Tell students that while those are repeated patterns, only some are tessellations because tessellations are a very specific kind of pattern.
    • Tessellations do not have gaps or overlaps. If students have pointed to a pattern in the room that has a gap or an overlap in it, point out that it does not fit the definition of a tessellation.
    • Tessellations can continue on a plane forever. Define plane (use a concrete example in the room) and show students how the pattern could continue on that plane if it were to go on beyond the confines of the building (e.g., it could continue as a pattern on the ceiling without any gaps or overlaps even if the ceiling were to continue forever, far beyond the walls of your school).

  2. Tesselation Figure 1Give each student the small square. Have them draw a curving line that begins on one side of the square, and ends on an adjacent side. In Figure 1, the line was started on the top side, and ended on the right side.

  3. Cut on the line to make two pieces.

  4. Fit the two pieces back together to make the square. Take one of the pieces, and slide the piece out. Do not flip it over or rotate it.

  5. Tesselation Figure 2Slide the piece to the opposite side and secure it there with tape. Be careful not to overlap the piece or make a gap. Keep the piece at the same height top to bottom as it was on the original square. It should fit perfectly at the seam. This is your tessellating tile.

  6. Start in one corner of the white drawing paper, and trace the tile. Slide the tile down the page until it matches on the other side, without flipping, rotating, leaving gaps, or overlapping. Trace the tile again.

  7. To make the second row, fit the tile into the last shape you traced, and then flip the tile over horizontally. (The example picture above was not lined up correctly on the horizontal rows.)

  8. Repeat tracing the tile until you fill up the page. Do not worry about shapes that are cut off by your paper's edge. Remember a tessellation can go on forever on a continuous plane.

  9. After you have traced the tile across the entire page, choose two colors to use to color your design in a checkerboard pattern. You can choose either two complementary colors, or two contrasting colors. If you use crayons, you can vary the pressure on a crayon by pressing hard or lightly to create a deeper or lighter color. You can add more texture by gently overlaying a light coat of another complementary color. Each tile of the same color must be exactly the same. In the example above, the purple spaces were colored with purple, using heavier pressure at the bottom of the spaces. Then the spaces were lightly colored over with a bluish purple.

  10. Finally, trace the outlines of each tile with a black permanent marker. You can use the marker to add small details to each tile, but remember that each tile must be exactly the same.