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FractalTetrahedrons
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
1
OverviewInthislesson,studentswillcooperatetocreatealarge,complexfractaltetrahedron.Atetrahedronisathree-dimentionalsolidmadeoffourtriangles.Eachstudentwillcreatetheirownfractaltetrahedronoutoftoothpicksandmini-marshmallows.Studentswillthengrouptogetherinteamsoffourandcombinetheirtetrahedronsintoalargerversionofthesameshape.Tocontinue,fourgroupsoffourwilljointheirtetrahedronsintoanevenlargerversion,andsoon.Appropriatefor:gradesK–12,collegeandadultsObjectives
• Tocreateacomplexpatternbyrepeatingasimpleprocessoverandoveragain
• Toanalyzeandcomposeshapesaccordingtopropertiesoftheirlinesandangles
• Touseoperationstoexplainpatternsinarithmetic
• Toobservemathematicaltrendsandcreatemodelstomakepredictions• Toattendtoprecision• Todraw,constructanddescribegeometricalfiguresanddescribetherelationships
betweenthem• Toexhibitteamworkwhenusingeachstudent’sindividualtetrahedrontomakea
largerproduct
Materials • Toothpicks(500forclassof16to20students)• Mini-marshmallows,setouttodryoutatleast24hoursbeforeactivitytoensure
firmness(1bagforclassof16to20students)• Protractors• Tetrahedronworksheet
BriefthestudentsthattheseareconstructionmaterialsandNOTfoodorcandy!Thesestalemarshmallowsareforaneducationalproject…notasnack!Toothpicksaresharp,andmustbehandledcarefullybychildren.Letstudentsknowthattheresourcesarelimited.Ifstudentsbreaktheirtoothpicksoreatmarshmallows,theymaynotbeabletocompletetheirpartoftheproject.
FractalTetrahedrons
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
2
CommonCoreStandardsforMathematics
CommonCoreStandardsforEnglishLanguageArts
Code Standard Grade Code Standard GradeCC CountingandCardinality K NS NumberSystem 6,7NBT NumberandOperationsin
BaseTenK,1 RP RatiosandProportional
Relationships6,7
OA OperationsandAlgebraicThinking
K–5 SP StatisticsandProbability 6
MD MeasurementandData K–5 EE ExpressionsandEquations
6,7
G Geometry K–7 F Functions 8NF NumberandOperations–
Fractions4
Code Standard GradesK–5 Grades6–8 Grades9–12RL Reading:Literature 1,4,7,10 1,4,7,10 1,4,10RI Reading:
InformationalText1,3,4,7,10 1,3,4,7,10 1,3,4,10
FS FoundationalSkills 1,2,3forgradesK–1;3and4forgrades2–5
Noneavailable Noneavailable
W Writing 2,3,8;4forgrades3–5 2,3,4 2,3,4,9SL Speakingand
Listening1,2,3,4,5,6 1,2,3,4,5,6 1,2,3,4,5,6
L Language 1,4,6;3forgrades2–5 1,3,4,6 1,3,4,6RST Scienceand
TechnicalSubjectsNoneavailable 1,3,4,6,7,10 2,3,4,6,7,10
FractalTetrahedrons
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
3
InstructionsAtetrahedronisasimplethree-dimensionalshapemadeoffourequilateraltriangles.Thebasicbuildingblockofthefractaltetrahedronismadewithfourmarshmallowsandsixtoothpicks.
Tomakeasecond-ordertetrahedron,ratherthanbuildingfourofthebuildingblocksandjoiningthem,itiseasierforstudentstobuildthebaseoftriangles,asshownhere,andthenextendtheouterthreetrianglesintotetrahedrons.Addasinglebuildingblocktothetoptocompletetheirsecond-ordertetrahedron.
Whenagroupofstudentshasfinishedtheirtetrahedrons,theycanassembleallfourofthemintoalargercreationcontaining16ofthebuildingblocks.Studentscandosobyarrangingthreeofthemintoabaseandthenaddingthefinaloneontop.Thiswillrequireteamworkastheymustremoveonemarshmalloweachfromthecorneroftheirindividualtetrahedronsinordertocarefullyjointhemtogether.
buildingblock
FractalTetrahedrons
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
4
Fractalsareneverendingpatterns,thenextstepistotaketheoutputoffourgroupsoffourstudents,andcombinethemintoabiggertetrahedroncomprisedof16by4or64buildingblocks.Ifpossible,mergeafewclassessothatyouhave64participants,whichwillallowthemtoreachthenextlevel,agianttetrahedronmadeof256buildingblocks.Childrenlovetheexpansivepossibilitiesofthissortoffractalengineering.Challengethemtofigureoutthearithmeticoftheircreationsateachlevel.
Elementary-agedstudentsfromAlbuquerque,NMbuildingtetrahedrons