Tessellations!!!

Objectives:

·  Develop and use spatial sense through the use of Internet based technology.

·  Create individual tessellations using one, two, and three regular polygons in the patterns.

·  Deepen understanding of properties of regular polygons.

·  Deepen understanding of rotations of regular polygons.

Materials:

·  Reserve computer lab for 2-3 days

·  Grading rubric

·  Lab worksheet

·  16 ft. reproduction of Escher’s Changing of Seasons

·  Fully functioning website… http://matti.usu.edu/nlvm/

Prerequisite Knowledge:

·  Working knowledge of angles (including interior angles of a regular polygon), sums of angles, properties of a regular polygon

·  Familiarity with computers and the Internet

NCTM Standards:

·  Geometry

·  Problem Solving

·  Connections

·  Reasoning and Proof

Activity:

Day 1

  1. Have a student help you unroll the Escher sketch.

o  Could we extend the design up further? Is it possible to extend it out?

Escher created special pieces that fit back in themselves or with other pieces. This allowed for no open spaces between any of the pieces.

o  Can this design go on forever? (Tiling a plane)

o  What are some examples of tiling a plane (tessellating) that you have seen before?

Not all shapes or combinations of shapes will successfully tessellate a plane. You will be given specific shapes (regular polygons) to work with when you are expected to create a tessellation.

  1. Overview of tessellation project. Hand out the lab worksheet and discuss what the students will be expected to do in the computer lab.
  1. Review of computer lab rules:

o  No food/drinks in the lab

o  Must sit in assigned seats

o  No checking e-mail, using IM, surfing the web, etc.

o  You can only be on the project site, otherwise you will receive a 0 for the project

  1. Go to the computer lab. Get the class started by demonstrating a basic tiling using squares.
  1. Students must work on creating a different tiling using only 1 type of regular polygon. Remember to be creative and to use different colors/color patterns. Print the screen and answer the related questions on the lab worksheet.
  1. Repeat step 5, only now tessellate using 2 regular polygons. Don’t forget to be creative.

Day 2

  1. Finish questions concerning the first two tessellations created.
  1. Students continue the previous day’s activities, but this time they must create a tessellation using 3 regular polygons. Remember to be creative and to use different colors/color patterns. Print the screen and answer the related questions on the lab worksheet.
  1. If any students finish early, they can create a tessellation using 4 regular polygons for extra credit.

Formative Assessment:

·  Collect and grade 3 tessellations from each student with an accompanying lab worksheet.

Summative Assessment:

·  Walk around and observe student progress.

Assessing the Lesson:

·  Students will write 7 sentences discussing what they felt, learned, and accomplished over the past two days.

·  The teacher will read these statements and use that information to fill out the rubric for the assessment of internet resources.