Teacher Information Page

Area of Study: Geometry

 Concept for the Lessons: Geometrical Patterns

 The Essential Questions:

• What patterns are found in nature?
• Why are patterns copied by people in art and architecture?
• How do patterns help us describe and understand our world?

 The Project Description:

This unit will incorporate technology into the study of patterns in nature and manmade patterns and how they relate to geometry. During the unit, students will research and report on chosen topics. They will investigate transformations through the study of quilts and artwork and through the creation of tessellations. The project will be appropriate for both pre-algebra, basic geometry, and college preparatory geometry students. Students will use the Internet, Geometer’s Sketchpad, Inspiration, a word processing program, and HyperStudio during the course of the unit.

Kent County's Essential Curriculum:

Standard	Objective	Indicator
Pre-Algebra 7/8 &emdash; II	G H	Draw & construct basic geometric figures using tools and technology. Draw & describe results of transformations such as reflections, etc.
Geometry K	A.1 A.2	Recognize & use basic transformations. Identify & create tessellations using transformations.

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Teacher Learning

• Teaching students to search effectively.
• Helping students determine essential questions
• Managing cooperative groups.
• Develop sufficient skill with Inspiration to help students complete webs.
• Knowledge of presentation skills
• Knowledge of before, during, and after reading skills
• Knowledge of writing process

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Student Learning Goal:

The overall goal is to increase the percentage of eighth grade students who score at the satisfactory and excellent levels in reading to be informed and reading to perform a task as measured by the Maryland School Performance Assessment Program through the content area of mathematics.

Student Learning

• Determine essential questions to be answered through research on their chosen topics.
• Recognize and relate patterns found in nature and manmade to the study of geometry.
• Use Inspiration to organize the major sub-topics for their chosen topics and to brainstorm connections between various topics
• Work cooperatively to find information on their topics and to prepare a presentation for the class.
• Use before, during and after reading to be informed skills to collect and organize information
• Effectively and efficiently navigate websites and search the Internet to collect information.
• Use a word processor of choice
• Select and prepare a creative element relating to their topics.
• Use effective presentation skills.
• Use Inspiration to show comparisons/contrasts between quilters' work and M.C. Escher's work
• Recognize and relate patterns created by artists to study of Geometry
• Use writing process appropriately
• Use Geometer's Sketchpad to manipulate shapes through transformations .
• Use before, during, and after reading to perform a task skills to learn how to create tessellations
• Use HyperStudio to create tessellations

 Resources

• Geometer’s Sketchpad
• Inspiration
• HyperStudio or AppleWorks
• Color printer
• Trade Books
  • Penrose, the Mathematical Cat by Theoni Pappas
  • The Number Devil by Hans Enzensberger
  • M.C. Escher, Visions of Symmetry by Doris Schattschneider
  • Tessellations by Dale Seymour & Jim Britton
  • The Geometry of Art & Nature by Matila Ghyla
• Student Projects
  • Tessellations
  • Geometry -
    • Student Houses 2000
    • Student Houses 2001
  • Algebra Projects
• Internet sites
  • Cool Math Sites
  • Research Websites
  • Rubrics and Checklists
  • Transformation Organizer (complete)
  • Glencoe Math Links (textbook)

     

Lesson Overview

There are three activities that can stand individually or can be used (preferred) to enhance and support each other. If all three are used, the transformation activity should be done last, when an overview of patterns and artistic use has been achieved.

• The patterns activity will take three class days for explanation and research time (including generating a list of subtopics in pairs, using Inspiration software. It will take two-three days for the presentations of the final products. Students will prepare the written reports on their own time.
• The artists activity will take two class periods for investigation of the two internet sites. It will then require a part of a period to compare/contrast as small groups, using Inspiration software. Students will need the rest of the period to complete their conversations, using a word processor. Another period will be required for peer and self-assessments and to allow time for revisions to be made. The final period will be used for reading the conversations.
• The transformations activity will take four and a half class periods. One class period will be needed to use Geometer's Sketchpad to practice basic transformations on regular polygons. Then three more class periods will be needed to find and print the appropriate tessellation directions and to create the two tessellations. Students will then complete the tessellation write-up on their own. A part of a class period will also be necessary to display the finished tessellations and to discuss them

Purpose

• The purpose of these three activities is to help students answer the following essential questions:
  • What patterns are found in nature?
  • Why are nature's patterns copied in art and architecture?
  • How do patterns help us describe and understand our world?

  Patterns

• To focus attention and establish personal connections, the patterns activity will open with a whole class brainstorming activity in which students will name any kind of pattern. All answers will be included in an Inspiration web. The class will then attempt to group the results into areas of similarity. For example, the class might separate manmade and naturally occurring patterns. Then the students will be given the list of topic choices. Prior knowledge of pattern occurrences will be assessed informally at this time. Sharing of ideas during the webbing will correct deficiencies in prior knowledge.

  Artists

• To focus attention and establish personal connections, the artists activity will begin with a class discussion about the relationship between art and geometry. The students will be asked if they believe such a relationship exists and why or why not.

  Transformations

• To focus attention and establish personal connections, the transformations activity will begin with a discussion of the various types of transformations the students will have just finished studying. Each student will be asked to stand up and physically demonstrate a different transformation.

Patterns

• Choose research topic from teacher determined list
• Choose partner
• Lesson on effective internet searching
• Research topic using internet, textbooks, and tradebooks
• Each pair will use Inspiration software to generate subtopic web
• Each student will prepare a two page report presenting topic and relating to study of geometry &endash; rubric provided in advance
• Prepare creative element to enhance topic&endash; rubric provided in advance
• Partners present topic to class & answer questions on topic

  Artists

• Students work in teacher-selected pairs (heterogeneous )to investigate quilt and M.C. Escher websites
• Each student completes questions about website information
• Class brainstorms compare/contrast using Inspiration
• Each student writes a one-page conversation between M.C. Escher and a quilter discussing similarities and differences and relating work to geometry &endash; rubric provided in advance

  Transformations

• Students use Geometer's Sketchpad to investigate transformations in teacher selected pairs (heterogeneous) according to direction sheet. Results to be printed and handed in
• Students in same pairs investigate tessellation site, find appropriate (HyperStudio) directions, and print them out
• Each student completes and prints out two HyperStudio color tessellations &endash; rubric provided in advance

• Patterns closing: brainstorm connections between patterns reported upon.
• Artists closing: read and discuss students' conversations
• Transformations: class display and discussion of tessellations

Patterns

• Class web on kinds of patterns (prior knowledge)
• Subtopic web
• Report (rubric)
• Self and peer (PQP) assessment of report
• Creative element (rubric)
• Presentation

  Artists

• Answers to website questions (2)
• Compare/contrast web
• Written conversation (rubric)
• Peer and self (PQP) assessment of conversation

  Tessellations

• Geometer's sketchpad exercise printout
• Two tessellations (rubric)
• Peer and self-assessment of tessellations
• Written description of tessellations (rubric)

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