Download - Fractal Cutout Card - fractalfoundation.org · Students will make a 3-dimensional fractal cutout card by repeating a simple process of cutting and folding. They can turn their cutout

$: Fractal Cutout Card - fractalfoundation.org · Students will make a 3-dimensional fractal cutout card by repeating a simple process of cutting and folding. They can turn their cutout$
FractalCutoutCard

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

Copyright2015FractalFoundation,allrightsreserved

1

OverviewStudentswillmakea3-dimensionalfractalcutoutcardbyrepeatingasimpleprocessofcuttingandfolding.Theycanturntheircutoutintoafractalpopupgreetingcard,decorateitartistically,andsharethelessonsoffractalswithothers.Althoughitisformedbyaverydifferentprocess,theresultingfractalsharesmuchincommonwiththeSierpinskitrianglefractal.Appropriatefor:gradesK–12,collegeandadultsObjectives

• Togainskillsinmeasuring,cuttingandprecision• Togainexperienceinunderstandingthatrepeating

asimpleprocessesoverandovercancreateacomplexobject

• Todrawandidentifylinesandanglesandclassifyshapesbypropertiesoftheirlinesandangles

• Toexperienceratioandportioninaction• Tocreateandunderstandcomplexpatternsinmath• Toexpresscreativityinconnectionwithmath• Tomodelwithmathandclassifyshapesbypropertiesoftheirlinesandangles• Tolookforandmakeuseofstructure

Materials • 8.5”x11”whitepaper• 8.5”x11”cardstockincontrastingcolor• Scissors• Gluestick• Rulersincentimeters(cm)• CutoutCardworksheet

FractalCutoutCard



2

CommonCoreStandardsforMathematics

CommonCoreStandardsforEnglishLanguageArts

Code Standard Grade Code Standard GradeCC CountingandCardinality K NF NumberandOperations

–Fractions4

NBT NumberandOperationsinBaseTen

K,1 NS NumberSystem 6

OA OperationsandAlgebraicThinking

K–5 RP RatiosandProportionalRelationships

6,7

MD MeasurementandData K–5 SP StatisticsandProbability 6–8G Geometry K–8

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

FractalCutoutCard



3

InstructionsTherearethreeelementstomakingthefractalcutout.Theyarerepeatedoverandoverusingasmallerscale.Thesethreeelementsare1)cutting,2)foldingand3)inverting.

Takeonepieceofpaper,holdithorizontalandthenfolditinhalf,soitlookslikeabook.

1) Cutthroughthefoldededgealongthedottedlineabove.Thecutshouldstarthalfwayupanddownthefoldandgohalfwaytotherightalongthefoldedpaper.

2) Nowfoldoveronehalfandcrease,asshownabove.3) Openupthefolded-overcreasedflap,andfolditinsideitself.Invertingisalittle

tricky,butcritical.Youhavenowcompletedthebasicsteptocreatethefractalcutout,andnowallyouhavetodoiskeeprepeatingthisprocessoverandover.Note:Youdonotneedtobeexact,butestimatethehalfwaypointsascloselyasyoucan.Olderstudentswillgenerallybemoreaccurate,andtheresultingfractalstheymakewillendupmoreuniform.

4) Next,maketwocutshalfwaythrougheachofthefoldededges,atthedottedlines.Thecutswillbehalfaslong,andagainthecutsshouldbehalfwayupanddowneachedgeandgoonlyhalfwaythroughthepiece.Becarefulnottocuttoofar!

1 32

FractalCutoutCard



4

5) Onceyou’vemadethetwocuts,foldoverandcreasetheflaps.Howcanyoutell

whichonestofoldover?Youwanttoendupwithsomethinglookinglikeastaircase.

6) Next,youunfoldtheflaps,andinvertthem.Whenyouopenupthepaper,itshouldlooklike6.

7) Repeatthesamecutting,foldingandinverting,butthistimeyouneedtomakefour

cutsinsteadoftwo.Foldandfliptheflapsinsidethemselveslikebelow.

8) Repeatthisagain,makingeightcutstotaltohaveyourfinalproduct.

4 65

7 8

FractalCutoutCard



5

Chooseapieceofheavierpaperinadifferentcolor,andfolditinhalf.Placethefractalcutoutinsideit,likethepagesofabook.Openitgently,andapplygluetothesolidareasofthefractalcutout,andthenglueitinplaceinsidethefoldedouterpaper.

Trydifferentcuttingpatterns,suchastheonesbelow.