By Kim Rakosky, April 29, 2007
- Elementary School
Three or four forty-minute periods
In this lesson, students will study repeating patterns (frieze patterns) found in their surroundings. They will tour their homes, schools, and neighborhoods in search of frieze patterns by examining ornamental architecture, clothing, home, furnishings, etc. They will sketch and/or photograph the patterns, and later describe, compare, and classify them as reflections, translations, or rotations.
MathStandard 5.5 Uses motion geometry (e.g., turns, flips, slides) to understand geometric relationships. Standard 8.1 Recognizes a wide variety of patterns (e.g., basic linear patterns such as [2, 4, 6, 8 . . .], simple repeating and growing patterns) and the rules that explain them. Standard 9.2 Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically.
- understand the concept of a growing pattern, i.e. the concept of simple, repeating patterns such as translations, rotations, and reflections (slides, turns, and flips)
- create "frieze friends" by decorating a "string" of paper outlines of girls, boys, and/or animals in specific frieze patterns (picture paper doll chains)
- recognize and classify frieze patterns in art, jewelry, textiles, and architecture from other cultures
Websites: Multicultural examples of Frieze Patterns
- pencils, colored pencils, crayons, markers, or other drawing materials
- blank paper
- outline templates for simple shapes of boys, girls, and/or animals (outline 6 on a blank page and copy for students to cut out)
- set of directions for creating a rotation, translation, or reflection pattern with specific colors on the cutouts
- handout with examples of the 3 types of motion geometry in a repeating pattern (frieze)
motion geometry=translations, rotations, reflections: translation=Also known as a slide. Linear movement of a design in one repeating direction rotation=Also known as a turn. Movement of a design by a certain degree in repeated steps (i.e. 1/2 turn-180 degrees, 1/4 turn-45 degrees) reflection=Also known as a flip. Movement of a design creating a mirror image with vertical symmetry frieze=repeating pattern found in architecture, jewelry, textiles, art, etc. ornamental=design element meant to add visual appeal architecture=the art and science of building design horizontal=East-West line or design vertical=North-South line or design symmetry=mirror image design; can be vertical, horizontal or both configuration=the manner in which objects or designs are arranged or grouped
1. Define and provide examples of frieze patterns. Stress that they may be found in textiles, jewelry, architecture, and art. (Examples can be found under the “Resources” section above.) 2. Give students oral directions to practice drawing simple reflections, rotations, and translations. (i.e. " Draw a capital L, repeat it in a 1/4 turn rotation 6 times; Draw a letter S, repeat it in a translation pattern 6 times, etc.” (Use for post-assessment also) 3. Take a neighborhood and school tour to search for frieze patterns. Record them by photographing/or sketching. 4. Analyze and classify the frieze patterns found on the walk according to the three types of motion geometry. 5. Demonstrate in front of the class how to complete a frieze friend by following a complete set of directions. Adjust the level of difficulty in directions to suit your class needs. Example: Draw three blue vertical lines on the boy's shirt; repeat them in a translation pattern on all your frieze friends. Next: draw a red horizontal arrow pointing to the left on his left shoulder. Repeat the arrow in a reflection pattern on his right shoulder, repeat for all the frieze friends, etc. 6. Distribute outline handout and directions for creating frieze friends. You may give one set of directions or several, depending on whether you want the students to work individually or in groups. 7. Assist students as they create their frieze friends. Have them cut out each friend after creating the design. 8. Display frieze friends along with the directions used to create them and the original sketches and/or photos from the neighborhood now labeled with the correct classification of characteristics.
9. Extend lesson by visiting Web sites featuring photos of frieze patterns around the world. Have each group research a particular frieze pattern found in a particular part of the world.
1. Students will complete a set of six frieze friends according to given directions and the rubric below: A: Frieze friend shows a complete, neat, correct repeating pattern. B: Frieze friend shows a complete, neat, and mostly correct pattern-allowing for minor errors in amount of turn, symmetry, etc. C: Frieze friend shows an attempt to follow directions for repeating pattern but may have skipped a part or recorded one part of pattern incorrectly. D: Frieze friend is attempted but incomplete and student shows significant misunderstanding or lack of understanding of the three basic types of motion geometry. E: No attempt to follow directions. 2. Give students oral directions to practice drawing simple reflections, rotations, and translations. (i.e. " Draw a capital L, repeat it in a 1/4 turn rotation 6 times; Draw a letter S, repeat it in a translation pattern 6 times, etc. (A post-lesson quiz)
3. Differentiate instruction by altering the difficulty of the directions and/or adding the more complex skill of recognizing the 7 mathematical configurations (see resources) of frieze patterns.
Enrichment Extension Activities
1. Have a contest to design a t-shirt using the three types of motion geometry and fabric paint (or a poster contest). 2. Create posters using stamped out patterns made from a carved block of florist's foam dipped in paint. View Adinkra patterns used in African textiles for ideas and cultural links. (or global tile patterns, etc.). Challenge students to search the Internet for other repeating patterns from around the world. 3. Create a slideshow using PowerPoint of photographs and sketches used in this lesson to present to other classes or audiences.
4. Extend by identifying and creating frieze patterns by teaching about the seven mathematical frieze configurations (see resources for details) and other plane geometry pattern concepts. This is an advanced skill, better suited for middle or high school level.