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Tech Integration Project
Lesson Accelerator: Project Overview

Terrifying Tessellations
Software Type: Visual Modeling
The example project created in this Lesson Accelerator addresses NETS Performance Indicators for middle grades as used in a(n) Mathematics curriculum. It could also be used with older learners or adapted for lower grades. See the section on Extending and Adapting at the bottom of this page for ideas on how to use this same project for different subjects, grades, and skill levels.
Project Launchers
Lesson Accelerator Project Launcher pages contain video tutorials that show you, step-by-step, how to create this project using specific software applications, as well as a movie showing you what the finished project looks like. They also provide a download of all the example files used in the project, so you can recreate it.
When you've reviewed all the information on this page and would like to go to a Project Launcher, click the application name below that corresponds to the one you'd like to use for the project.
Go to: Geometer's Sketchpad 4 (Mac) - Project Launcher
Go to: Geometer's Sketchpad 4 (PC) - Project Launcher
Description
Students will be using visual modeling software to create an image in the style of M.C. Escher. They will begin by creating a hexagonal background pattern that will act as a grid for their tessellations. They will then create reptilian shapes through the process of rotation and translate the shape in various directions to complete the tessellation. The underlying grid will be hidden and the students will be able to print out their tessellated image. This project is especially suited for cross-disciplinary discussions about concepts that relate to both mathematics and the visual arts.
Goals
To provide students with the opportunity to use visual modeling software to create an interactive tessellation in the style of the late Dutch graphic artist M.C. Escher, using the geometrical transformations of rotation and translation.
Objectives
The student will be able to:
  • Open a new document and identify components of the software interface.
  • Construct segments and regular hexagons.
  • Rotate a hexagon & tessellate to cover the page.
  • Construct a polygon in the shape of a reptile.
  • Identify and modify different properties of a shape.
  • Tessellate the page with reptile shapes, using the process of translation.
  • Hide the underlying hexagonal grid and print the image.
Preparation and Skill Mastery
Students should have mastered basic computer skills, such as the use of input devices (mouse, keyboard, etc.), opening and closing applications, and saving documents to a personal folder or directory.

Students should be familiar with the properties of simple two-dimensional shapes such as a regular hexagon, and be aware of which shapes will tessellate the plane and why this occurs.
Materials
  • A computer with visual modeling software installed.
  • A printer (optional)
  • Access to the Internet (optional)
Task List
The tasks to be completed for this project include:
  • Opening & saving a new document.
  • Setting document preferences.
  • Constructing a segment and regular hexagon.
  • Rotating & tessellating the hexagon.
  • Creating the reptile shape and constructing the interiors.
  • Translating reptile shapes in different directions on the grid.
  • Hiding the underlying grid and printing the final image.
Assessment
Assessment can be based on the following:
  • A rubric for assessing mastery of the project skills is included in the downloadable resource packet. This may be used by the teacher for assessing student mastery, or as a self-assessment tool by the student.
Extending or Adapting
Here are some possible ways that this lesson plan might be extended or adapted for different timeframes, grade levels, and skill/ability levels:
  • This project can provide a technology component to discussions about the interaction and relationships involved between mathematical concepts and artistic rendering of those concepts.
  • This project can be extended to include the use of the Measure Menu to measure the area of the reptiles and the hexagons. Students can be encouraged to compare the results and justify their conclusions about what they find.
  • Students can investigate what other shapes will tessellate and then create a variety of different Escher-style tessellations. Visit http://www.mcescher.com for additional information.
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