Design Explorations: Frieze Patterns

By Cooper-Hewitt National Design Museum, October 18, 2006

Grade Level

  • Middle School

Category

  • Graphic Design

Subject Area

  • Arts
  • Language Arts
  • Mathematics

Lesson Time

Two fifty-minute class periods

Introduction

In this activity, students will explore frieze patterns. A frieze pattern is a mathematical concept to classify designs on two-dimensional surfaces, which are repetitive in one direction, based on the symmetries in the pattern. Students will explore examples of frieze patterns in architecture and art, and create an original design using a frieze pattern.

National Standards

Mathematics
Standard 5. Level III. Understands and applies basic and advanced properties of the concepts of geometry Benchmark 4. Understands geometric transformations of figures (e.g., rotations, translations, dilations)
Standard 9. Understands the general nature and uses of mathematics
Writing
Standard 1. Level III. Uses the general skills and strategies of the writing process 5. Uses content, style, and structure (e.g., formal or informal language, genre, organization) appropriate for specific audiences (e.g., public, private) and purposes (e.g., to entertain, to influence, to inform)
Reading
Standard 7. Level III. Uses reading skills and strategies to understand and interpret a variety of informational texts
1. Uses reading skills and strategies to understand a variety of informational texts (e.g., electronic texts; textbooks; biographical sketches; directions; essays; primary source historical documents, including letters and diaries; print media, including editorials, news stories, periodicals, and magazines; consumer, workplace, and public documents, including catalogs, technical directions, procedures, and bus routes)
4. Uses new information to adjust and extend personal knowledge base
Standard 4. Level III. Gathers and uses information for research purposes
3. Uses a variety of resource materials to gather information for research topics (e.g., magazines, newspapers, dictionaries, schedules, journals, phone directories, globes, atlases, almanacs, technological sources)
Listening & Speaking
Standard 8. Level III. Uses listening and speaking strategies for different purposes
6. Makes oral presentations to the class (e.g., uses notes and outlines; uses organizational pattern that includes preview, introduction, body, transitions, conclusion; uses a clear point of view; uses evidence and arguments to support opinions; uses visual media)
Visual Arts
Artistic Expression & Communication Standard 2. Level III. Knows how to use structures (e.g., sensory qualities, organizational principles, expressive features) and functions of art 3. Knows how the qualities of structures and functions of art are used to improve communication of one's ideas
Working With Others
Standard 1. Contributes to the overall effort of a group
Thinking & Reasoning
Standard 5. Applies basic trouble-shooting and problem-solving techniques

Common Core State Standards

English Language Arts Standards: Speaking and Listening

Grade 6-8

Comprehension and Collaboration:

  • CCSS.ELA-LITERACY.SL.6-8.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade level topics, texts, and issues, building on others' ideas and expressing their own clearly.
  • CCSS.ELA-LITERACY.SL.6-8.1.A Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
  • CCSS.ELA-LITERACY.SL.6-8.2 Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation.
  • CCSS.ELA-LITERACY.SL.8.3 Delineate a speaker's argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced.

Presentation of Knowledge and Ideas:

  • CCSS.ELA-LITERACY.SL.6-8.4 Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation.
  • CCSS.ELA-LITERACY.SL.6-8.5 Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest.
  • CCSS.ELA-LITERACY.SL.6-8.6 Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grade 8 Language standards 1 and 3 here for specific expectations.)

English Language Arts Standards: Science & Technical Subjects 

Grade 6-8     

Integration of Knowledge and Ideas:

  • CCSS.ELA-LITERACY.RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
  • CCSS.ELA-LITERACY.RST.6-8.8 Distinguish among facts, reasoned judgment based on research findings, and speculation in a text.
  • CCSS.ELA-LITERACY.RST.6-8.9 Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

Objectives

Students will do the following:
  • explore frieze patterns
  • summarize information
  • conduct Internet research
  • design a frieze pattern
  • create a presentation

Resources

Materials

  • computer with Internet access
  • drawing or construction paper
  • markers, crayons, pencils
  • stapler, scissors, glue

Procedures

Building Background
What is a Frieze Pattern?
1. Tell the students that they are going to learn about frieze patterns, which are designs made from horizontal or vertical repetitions of the same shape. As a class, read about frieze patterns at the following website: http://www.nexuslearning.net/books/ml-geometry/Chapter7/ML%20Geometry%207-6%20Frieze%20Patterns.pdf 2. Discuss how the patterns are created and review each of the seven patterns listed below:
  • Translation
  • Glide reflection
  • Two parallel reflections
  • Two half turns
  • A reflection and a half turn
  • Horizontal reflection
  • Three reflections
  Show the students the patterns at the following website: http://www.nexuslearning.net/books/ml-geometry/Chapter7/ML%20Geometry%207-6%20Frieze%20Patterns.pdf   3. As a class, explore additional examples of frieze patterns from the following websites:         4. Ask the students to look for examples of frieze patterns in their everyday life observations.
Steps for Learning
Designing a Frieze Pattern
The purpose of this activity is for students to create an original design for a frieze pattern. 1. Tell the students that they are going to create a design for a frieze pattern. Divide the class into small groups and provide each group with the "Frieze Pattern Design" handout. 2. Provide time for each small group to present its work to the class.
3. Discuss the different elements of each group presentation, and how each group addressed this task.

Assessment

Reflection
Create a class rubric with your students that will help them understand the effectiveness of their design process. Use the following guidelines to help create the rubric.
-How effective was your brainstorming in generating ideas? Excellent        Good            Adequate           Poor
-Rate how effectively you analyzed the information you used to identify your problem.
Excellent        Good            Adequate           Poor
-Rate the effectiveness of your presentation.
Excellent        Good            Adequate           Poor
-Rate how clearly you communicated your ideas.
Excellent         Good            Adequate           Poor
-Rate how clearly you communicated your solution.
Excellent         Good            Adequate           Poor
-Rate your effectiveness as problem solvers.
Excellent         Good            Adequate           Poor
-Rate your creativity.
Excellent         Good            Adequate           Poor

Enrichment Extension Activities

Activity One: Identifying Patterns
Ask your students to identify frieze patterns at the following website http://www.math.uic.edu/~burgiel/Mtht420/4/activity.html
Activity Two: Exploring Frieze Patterns in Art
Ask your students to create a collection of images of frieze patterns in art objects. Tell them to begin by exploring Ming porcelains and Victorian wallpaper.

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