Name:________________________________

FractalTetrahedrons

FractalsareSMART:Science,Math&Art!www.FractalFoundation.org

Copyright2018FractalFoundation,allrightsreserved

1.Whatisafractal?2.Describethefourtypesoffractalpatterns.a) b) c) d) 3.Createexampleofthreefractalpatternsthatdonotrequireacomputertocreate.a) b) c)4.Makeyourbasictetrahedron.5.Whattypeoffractalpatternisatetrahedron?6.Whatdoes“tetra”standfor?Whyisatetrahedronnamed“tetrahedron”?7.Usingaprotractor,measuretheanglesofallthedifferentsidesofyourtetrahedron.

a)Whatarethey?

b)Areyouranglesaboutthesameorreallydifferent?

c)Whattypeoftriangleisyourtetrahedron?

Name:________________________________

FractalTetrahedrons

FractalsareSMART:Science,Math&Art!www.FractalFoundation.org

Copyright2018FractalFoundation,allrightsreserved

8.Nowlet’sseewhatpatternswecanfindwhenwebuildourtetrahedrons.Howbigcanwebuildone?NOTE:Asyoumovefromfirsttosecondorder,secondtothirdorder,etc,savethemarshmallowsyoutakeoff–theywillhelpyouseethepatterns!

9.a.Howdoyougetfromyourowntetrahedrontothenextstepup?Whatdoyoudotobuildit?b.Whatisthemathematicalexpressionforhowmanytoothpicksyouhaveinyourownversusthenextsizeup?c,Whatisthemathematicalexpressionforhowmanymarshmallowsyouhaveinyourownversusthenextsizeup?Hint–youaredoingtwomathematicalproceduresd.Whatishappeningtothelengtheachtimeyoumakeabiggertetrahedron?10.Usethemathematicalexpressionstopredicthowmanymarshmallowsandtoothpicksyouhaveinthenexttwosizesupandbuildthose!

#Toothpicks #Marshmallows Length(cm)

Firstordertetrahedron

Secondordertetrahedron

Thirdordertetrahedron

Fourthordertetrahedron

Name:________________________________

FractalTetrahedrons

FractalsareSMART:Science,Math&Art!www.FractalFoundation.org

Copyright2018FractalFoundation,allrightsreserved

Adaptationstodifferentgrades

• 3rdandup:measurevolumeandarea• 4thandup:createfractions/ratiosbasedonproportionsanddiscusswhichonesare

bigger/smaller• 5thandup:grapheachstep(first,second,thirdordervs#marshmallowsand#

toothpicks)andseewhatkindoflinedatacreate• 6thandup:createequations(makeanequationthatshowsthatrelationship),ratios

andproportions,graphnumberseachiteration–typeofline,areaandvolume,dostatisticsonmeasurements–discusssamplesandspread;graphdistributionandstandarddeviation,discussaccuracyinanglesandlengthsoftoothpicksinmakingadesignthatistrulysymmetricalandstable

• 7thandup:measuresurfaceareaandvolume• 8thandup:modelrelationshipswithquantities,modelchemicalcompounds,

molecularstructure–engineering(alsobridgebuilding),modeling(NextGenerationScienceStandards)

Wherehaveyouseenothertetrahedronshapesorfractalsaroundyou?Whatideasdoyouhaveofwheretetrahedronscanbeused?Modeltoabiggersizewithstrawsandclay,PVCpipe,metal,etc.