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Photo by John O’NolanStandard Benchmarks and ValuesCluster: Understand congruenceand similarity using physical models,transparencies, or geometry software.8.G.1: Verify experimentally the properties ofrotations, reflections, and translations:a. Lines are taken to lines, and linesegments to line segments of thesame length.b. Angles are taken to angles of thesame measure.c. Parallel lines are taken to parallel lines.8.G.2: Understand that a two dimensionalfigure is congruent to another if the secondcan be obtained from the first by a sequence ofrotations, reflections, and translations, giventwo congruent figures, describe a sequencethat exhibits the congruence between them.8. G.3: Describe the effect of dilations,translations, rotations and reflections on twodimensional figures using coordinates.8.G.4: Understand that a two dimensionalfigure is similar to another if the secondcan be obtained from the first by a sequenceof rotations, reflections, translations, anddilations; given two similar two dimensionalfigures, describe a sequence that exhibits thesimilarity between them.
TRIBAL TATTOOTRANSFORMATIONSLaura Farris8th Grade (Adapted for Special Education Students)1 Week (Three 90 minute periods)Why is it important to learn more about theworld around you? How could knowing about measuring toolsand techniques help people to learn aboutcultural diversity? Are there ways that understanding tribal tattooingmight help us learn and appreciate more aboutthe world around us?Enduring UnderstandingsTribal tattoo designs represent deep cultural andreligious meaning from around the globe. The designsare often drawn in black and involve certain symbolsand characters from different continents. Most tribalCritical Skills and Concepts Are there ways that understanding tribal tattooingmight help students become more introspectiveabout their own heritage and culture?tattoo designs have represented tribal affiliations withspecific meanings and beliefs. An excellent websiteexplaining the significance of Hawaiian Tribal Tattoosis http://www.mythichawaii.com/tribal-tattoos.htm. Flipping a figure into a mirror image createsa reflection. Turning a figure a certain number of degreescreates a rotation. Sliding a figure without turning or flipping createsa translation. Enlarging or shrinking a figure creates dilation.Ethnomathematics2
LESSONAuthentic Performance TaskCreate a personalized tribal tattoo using Hawaiian or Polynesian symbols. Thestudent must be able to show and explain reflection, rotation, translation,symmetry and/or dilation in his/her pattern.Authentic AudienceSchool community including other students, parents, teachers,and administration.Other EvidencePrecursor skills: ArithmeticStudent must be able to: be able to identify basic two-dimensional regular and irregular shapeshave knowledge about the Cartesian coordinate systemhave instruction on transformation movement (slides, turns, flips, andenlarging and reducingLearning PlanBackground:For centuries, various arts of tattooinghave graced the bodies and satisfied thesouls of the aboriginal peoples of Oceania.The vast majority of what we know todayabout these ancient arts has been passeddown through legends, songs, and ritualceremonies. The roles, techniques andmotifs of the arts of tatau, moko, and uhihave continued to exist for over 2,000years. The oldest of these traditions is inSamoa, and the youngest is in Aotearoa/TeWaipounamu. Hawaiian tattoos are colorfuland vibrant, yet they are symbolic and full ofmeaning. Some design elements that werecommon throughout Polynesia were lineargeometric motifs, petroglyphs, and verybasic pictographic representations of men,animals, birds or other man-made objects.Each of the geometric designs, includinglines; triangles; circles and other polygonal3Tribal Tattoo Traditionssymbols had multiple meanings basedon placement on the body, incorporationwith other designs, and the person beingtattooed. It was usually up to the masterto determine what was appropriate foreach person and to then explain the storyto that person. In the olden days, you hadto deserve tattoos of Hawaiian traditionon your body. While they were sported bymost male warriors, some women weregiven the privilege of possessing Hawaiiantattoos because of their pivotal roles inthe community. Apart from tribal designs,environmental and natural styles becamesynonymous with Hawaiian tattoos.Examples of colorful tattoos of Hawaiianimageries include depictions of exoticflowers, turtles, arrows, sharks, lizardsand dolphins.(As referenced by numerous authors atwww.pbs.org/skinstories/culture/)
Preparation2. Have students reflect and fill out “Tribal Tattoos Survey: How Would IRepresent Myself?” worksheet.Plan1. Students design, construct, share, and explain movements of their chosentattoo (uhi) designs using the terms rotation, transformation, reflectionand dilation.2. Have students choose two or three Hawaiian or Polynesian designs tocombine to make a tattoo design. Encourage students to find the meaningof the tattoo designs and relate it to their own life or experiences.LESSON1. Introduce Tribal Tattoo culture with http://www.mythichawaii.com/tribal-tattoos.htm or the above aforementioned website. (There are other goodwebsites also). Have student discussion concerning the information andimportance of symbols in their own culture.3. Give students overhead film sheets. Using black permanent markers havestudents explore how designs may be transformed with above actions andtrace the symbols on the overhead projector sheet. As shapes are movedhave students explain to partner or adult what type of move (rotation,transformation, reflection and dilation) has been performed.(Note: a copier could be used to create dilations).4. When student are pleased with their tattoo creation put on the copier(with white paper behind) to make a permanent black/white product. Havestudents perform for others and explain design and movement of shapesto others.5. Review rubrics for papers and presentations. Draft, revise and finalize tomake more accurate.ExtensionAfter students have created their design have them superimpose the design on an X/Ycoordinate graph and record rotation, transformation, reflection and dilation movementsusing approximate ordered pairs to track a certain point in the design as movementsare made.Examples: See the Power Point slides to reference 8th grade student illustrations.Appendices A, B, and C show Tattoo Patterns, Assessment for Critical Skills and Conceptsand Scoring Rubric.Ethnomathematics4
Name:Date:Tribal Tattoos Survey:How Would I Represent Myself?What are some important places for you? What symbols represent these places?What are your favorite hobbies / activities? What symbols represent these activities?What is an animal that represents you? Why?What else is important to you and should be represented in your personal tattoo?What color best represents you?Ideas for a Personal Motto.5Tribal Tattoo Traditions
APPENDIX ATattoo DesignsEthnomathematics6
APPENDIX A7Tribal Tattoo Traditions
Assessment for Critical Skills and ConceptsSkillsConcepts8.G.1 Geometry -Verifyexperimentally the propertiesof rotations, reflections,and translations:a. Lines are taken to lines,and line segments toline segments of thesame length.b. Angles are taken to angles ofthe same measure.c. Parallel lines are taken toparallel lines. Determiningreasonableaccuracy Attention to detail Understandingof translation,rotation,reflection, anddilation Understandingof history andtattoo culture8.G.2: Geometry - Understand that atwo dimensional figure is congruentto another if the second can beobtained from the first by a sequenceof rotations, reflections, andtranslations, given two congruentfigures, describe a sequencethat exhibits the congruencebetween them. Visual / spatialdevelopment Accuracy ofcalculationsAssessmentFormativefeedback frompeers andteachers duringtransformations Be able to explain Appropriate use oftechnology Attention to detail Neatness Fine motor skills8.G.3 Geometry - Describe the effect Oral presentationof dilations, translations, rotations Listening to othersand reflections on two dimensional Understandingfigures using coordinates.transformations Generalizingresults intosentences Formativefeedback Accuracy ofdrawing Transformationdrawing projectrubric Understandingof geometrictransformations CollaborativediscussionAPPENDIX BStandard Benchmarks Formativefeedback duringdiscussion of allprojects Communicationskills Inferencing resultsand being able tocompare to others’results8.G.4 Geometry - Understand thata two dimensional figure is similarto another if the second can beobtained from the first by a sequenceof rotations, reflections, translations,and dilations; given two similartwo dimensional figures, describe asequence that exhibits the similaritybetween them. Oral presentation Listening to others Understandingtransformations Generalizingresults intosentences Inferencing resultsand being able tocompare to others’results Understandingof geometrictransformations Attention to detail Neatness Formativefeedback duringdiscussion of allprojects Accuracy ofdrawing Transformationdrawing projectrubric Communicationskills Revising tocreate qualityproducts thataccurately displayinformationEthnomathematics8
APPENDIX CRubric for Tattoo Transformations94Demonstratesa thoroughunderstandingof translation,reflection,rotation, anddilation.Well organizedwith authenticdesigns and thereis acute attentionto neatness.Mathematicalterms andsymbols are usedappropriatelyand are oftenelaborated upon.Thorough analysisand creativityof the problemwith accuratesolutions.Tribal Tattoo Traditions3Demonstrates anunderstandingof translation,reflection,rotation, anddilation.2Demonstratesa partialunderstandingof translation,reflection, rotation,and dilation.Organized andmost designs areauthentic andthere is attentionto neatness.Mathematicalterms andsymbols are usedappropriately.Organization andneatness needs toimprove and thereare some authenticdesigns.Some mathematicalterms and symbolsare used correctly.Analysis ofthe problemand creativityis evident,considerableaccuracy.Analyzes theproblem withsome success andcreativity, accuracyneeds to improve.1Demonstrateslittleunderstandingof translation,reflection,rotation, anddilation.Very weakevidence oforganization,authentic designs,and neatness.Mathematicalterms and symboluse are weak, notenough referencesto mathematicalterms are used.Very littleevidence ofanalysis. Someeducated guesses.Accuracy andcreativity is weak.
tattoos because of their pivotal roles in the community. Apart from tribal designs, environmental and natural styles became synonymous with Hawaiian tattoos. Examples of colorful tattoos of Hawaiian imageries include depictions of exotic flowers, turtles, arrows, sharks, lizards and dolphins. (As referenced by numerous authors at
