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Exploring Pure Tessellations

Activity Description Activity GuideHandout


Part 1: Exploring Pure Tessellations

  • In the command center use pd, ht and fd 10 to instruct the turtle to move forward ten steps.
Replaying code in the command center:
Each time you type code in the command center you may replay those commands by moving the cursor to the end of the previous line of code and striking enter. For example if you type rt 60 to instruct the turtle to turn to the right 60 degrees but realize upon the turtle's move that the command should have been rt 120, you have two options. First you could up arrow to rt 60 and strike enter or you could retype rt 60, so the total turn by the turtle is 120 degrees.

Observe how small ten turtle steps are. Use this as a reference when constructing polygons that are large enough and not too large so as to wrap around the screen.
  • In the command center type in MW commands to construct a square.

  • Change the turtle’s orientation and continue to draw squares so that the screen is tessellated. Discuss your approach.

Changing the turtle’s orientation:
To change the turtle’s orientation right click the mouse while the pointer is on the turtle. A command screen will appear (see below) and you may enter desired commands in the instruction line.

  • In the command center type in MW commands to construct an equilateral triangle.

  • Change the turtle’s orientation and continue to draw equilateral triangles so that the screen is tessellated. Discuss your approach.

  • Conjecture as to what other regular polygons will tessellate the screen.

  • Test your conjecture with at least two other shapes.

  • Explain why some polygons tessellate and others do not.

Part 2: Using MW Procedures to Create Tessellations

  • Create a procedure to tessellate the screen with squares. Discuss your procedure.

To save MW procedures:
Two options exist for saving procedures. You may choose to keep all of your procedures for a given project on one procedures page or you may save each procedure as a separate project (see below).

For option one, enter each procedure and separate it by a line to distinguish it from other existing procedures. You may change the font, bold the code, or also incorporate indentation.

For option two, you may enter each procedure on its own page and name the page. For example if you were to save the square procedure above you can pull down the Pages menu and choosing Name Page…(see below).

  • Create a procedure to tessellate the screen with equilateral triangles. Discuss your procedure.

  • Create a procedure to tessellate the screen with hexagons. Discuss your procedure.

Part 3: Coloring a Tessellation

Return to the page of your equilateral triangle tessellation.

  • Open the coloring palette in the command center by clicking on the paintbrush (see the illustration below).

  • Experiment with each of the icons within the color palette and write a working definition for each buttons function. (See attached handout)

  • Conjecture as to the least number of colors needed to color your tessellation so that same colored triangles do not share a boundary. Discuss your conjecture.

  • Color your tessellation to test your conjecture.

  • Color your triangle tessellation so that it appears three-dimensional.

Extensions:

  • Create a tessellation that utilizes at least two different shapes.

  • Create a procedure to tessellate the screen with two different shapes.




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Last modified on August 19, 2001.