TESSELLATIONS
by Magen Winters

SUBJECT:
Geometry

TOPIC:
Regular Tessellations


Magen Winters
To obtain a downloadable copy of the worksheet that accompanies this bulletin board, click on the button below.

TITLE: Tessellations

INTERACTIVITY: The main activity associated with this bulletin board is learning. Using a worksheet with directions, students will be guided through activities on the bulletin board.

DIRECTIONS:

ACTIVITY A:

  • Read about types of transformations.
  • Slide the square, rotate the rhombus, and flip the arrow.

ACTIVITY B:

  • Using the felted area of the board, arrange the shapes (one set of shapes at a time) to figure out which shapes tessellate.
  • On the worksheet, write the name of the shape that does not tessellate.

ACTIVITY C:

  • View the chart on the board that shows regular polygons, number of angles, and total angle measure.
  • In your worksheet, calculate the measure of each interior angle and see if you can figure out if each shape tessellates.
  • Try to make a conclusion about angle measures and tessellation shapes.
  • Remove the yellow square on the board and check your answers.

ACTIVITY D:

  • Examine the 2 tessellations in Area D and see if you can find what makes them tessellate.

ACTIVITY E:

  • Observe the breakdown of one of M.C. Escher’s tessellations that resembles a Pegasus.

ACTIVITIES F, G, H:

  • Locate tessellations F, G, and H. Complete the chart on the worksheet by identifying the underlying shape and transformations associated with each of the three tessellations.

TIME: Students should complete these activities in approximately ten minutes.

SPECIAL CONSTRUCTION: The background is cloth with a tessellating pattern (other geometric patterns could also work). The translation activity is composed of two laminated squares and one laminated rectangle the length of the two squares. Two rows of thread are sewn along the length of the rectangle, passing through two straws glued to the back of one square. This square has a knob attached so the square can slide left and right. The rhombi are laminated and held together with a fastener. The rear rhombus is stapled to the board. The two reflection arrows are laminated and taped together. One arrow is stapled to the board. The felt is held in place with staples in many places (it would be best to sew the felt to the cloth background). The shapes used for the felt are laminated and have Velcro stickers on the back of them.

OTHER COMMENTS: This bulletin board is the first in a series of three bulletin boards about tessellations. Each requires mastery of the previous one in order to understand the next, more complex, board in the series.

CREDIT: One enrichment activity is required per month and this bulletin board activity will be required as the enrichment activity during the month it is up. Students will receive points for completing the worksheet as part of the enrichment portion of their grade. Specific points for this activity will be built into the rubric. Students who do not complete the worksheet will lose points. There is an extra credit associated with the bulletin board where students can construct their own tessellation. I will strongly encourage them to complete this activity and they will be awarded extra points based on the complexity and accuracy of their design.

Magen Winters
2/6/04