a splash of color - complete mathcompletemath.onmason.com/files/2016/12/splash-of-color.pdf ·...

GeorgeMasonUniversityCOMPLETEMath©2015

ASplashofColor

CreatedbyKateBeckSpring2016

TheTaskCreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!

BigIdeas• Placevalueinapositionalnumbersystem.

StandardsofLearningforGrades3-4-5

3.1aReadandwrite6-digitnumeralsandidentifytheplacevalueandvalueofeachdigit.

4.1aIdentifyorallyandinwritingtheplacevalueforeachdigitinawholenumberexpressedthroughmillions.

StandardsofLearningforGrades6-7-86.5Investigateanddescribeconceptsofpositive

exponents.7.10Determinetheprobabilityofcompoundevents,

usingtheFundamentalCountingPrinciple.

ProcessGoals• ProblemSolvingandReasoning–Studentswillapplyanunderstandingofbase10placevaluetomake

senseofthebase16hexadecimalsystem.• ConnectionsandRepresentations–Studentswillrecognizeandusemathematicalconnectionsto

extendandgeneralizepatternsinapositionalnumbersystem.Theywilluseavarietyofrepresentationsastheyexplorebase16andcommunicatetheirthinking.

• Communication–Studentswilljustifytheirfindingsandpresenttheirresultstotheclasswithprecisemathematicallanguage.

RelatedTask–OutofthisWorldYourmissionistomakesenseoftheWoop/Zoobie/GlimnumbersystemandpresentittothemathematiciansonEarth.Youmusthelpthemunderstandthisnewwayofcounting.Peaceinoursolarsystemdependsonit!

RelatedTask–MayanMathStudytheMayancountingsystem.Completethefollowingtasks:

• DeterminethenumberthattheMayancountingsystemisbasedon.• MakeaplacevaluechartfortheMayansystem.• Chooseanumberthatfitseachcategorybelowinbase10andrecordtheequivalentnumberinthe

Mayansystem.*Anumberbetween40and100.*Anumberbetween100and500.*Anumberbetween500and1,000.*Anumberbetween1,000and10,000.

*Anumbergreaterthan10,000.


ASplashofColorLessonPlan

CreatedbyKateBeck

Spring2016

TheTaskCreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!

Materials• CopiesoftheSupplementalMaterialsforeach

student• Copiesofthetaskforeachstudentorpair• CopiesoftheRGBColorChartorthe

HexadecimalColorChartforeachstudentorpair

• Blankpaper• Chartpaper• Markers• Calculator

FacilitatingTaskNote:• Youmayconsiderexploringthesupplemental

materialswithyourstudents.ThesematerialswillwalkyourstudentsthroughanintroductiontothehexadecimalsystemandtheRGBcolorsystem.Thismaybedoneinalessonpriortothetaskoritmaybedoneatthestartofthetask.

• ChoosewhetheryouwantstudentstocompletethetaskbyconvertinghexadecimalvaluestoRGB(base10)valuesorRGB(base10)valuestohexadecimalvaluesandincludetheappropriatechartwiththetask.*Thesechartsarenotcorrelated.Simplychoosetheoneyouwilluse,anddonotincludetheotherwhendistributingthetasktothestudents.

• Studentscanworkindividuallyorinpairs.Giveeachstudentorpairacopyofthetask.

• Readthetasktogetherandanswerclarifyingquestions.

• Eachstudentorpairmaycreateitsdesigndirectlyonthetaskpaperoronalargechartpaperforpresentingtotheclass.

• Allow10minutesattheendofthelessonforpresentationsanddiscussion.Studentsorpairswillsharetheirdesignswiththeclass.

• Afterstudentshaveshared,discussthechallengesofconvertingbetweenbase10andthehexadecimalsystem.(Seeprompts/questionsbelow.)

Misconceptions• Thestudentsmaythinkthatthefirsttwo

columnsinthehexadecimalsystemarethesameasbase10(tensandones).

• ThestudentsmaygetconfusedbythehexadecimalRGBformat(#RRGGBB).Theymaythinkthatthesixnumbersrepresentsixplaceswithinthehexadecimalsystemratherthanthreetwodigithexadecimalnumbers.

SuggestedPromptsorQuestions• Whatpatternsdidyounoticeasyouconverted

betweenbase10andthehexadecimalsystem?• Howarebasetenandthehexadecimalsystem

thesame?• Howaretheydifferent?• Whatdidyoufindtrickiestaboutworkingwithin

eachsystem?• Hasanythingbecomecleareraboutbaseten

afterworkinginthehexadecimalsystem?


ASplashofColor Name Date CreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!


Extension:

*Whatisthehighestcolorvalueinthe#RRGGBBhexadecimalsystem?UsethisinformationtofigureouthowmanyRGBcolorsexist.


ASplashofColor Name Date Computerprogrammersuseahexadecimalnumbersystemwhenassigningcolorstoobjectsonthescreen.

What’sahexadecimalsystem?It’sanumbersystembasedon16.

Belowarethedigitsusedinthehexadecimalsystem:

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

whereAisthedigitthatstandsforthevalue10,Bfor11,andsoonuptoFfor15.

Justasourbase10numbersystemisapositionalnumbersystembasedon10,

theHexadecimalsystemisbasedonthenumber16.

Workwithyourgrouptoconvertthefollowinghexadecimalnumberstobaseten.

42166C16FE16

Now,convertthesebasetennumberstohexadecimals.

64 100 255

101=10100=1

tens ones

161=16160=1

sixteensones


It’stimetogetcolorful!

WeusetheRGBcolormodeltolabelcolors.R(red),G(green),andB(blue).Thesethreecolorsworktogethertocreatenewcolors.EachcolorhasanRvalue,aGvalue,andaBvalue.Thesevaluesareinwritteninbase10.

Forexample,

• RedhasanRGBvalueof255,0,0.

• YellowhasanRGBvalueof255,255,0.

• PinkhasanRGBvalueof255,192,203.

Whencodingwebpages,computerprogrammersusethehexadecimalsystemtotellthecomputerwhatcolortouse.Theywritethenumbersusingthisformat:

#RRGGBB

Let’sconvertpink’sRGBvaluetoit’shexadecimalequivalentsowecanaddittoapictureonourwebpage.

Givenpink’sRGBvalueof255,192,203,canyouconvertpinktoitshexadecimalequivalent?

Theredvalueinbase16.

Thegreenvalueinbase16.

Thebluevalueinbase16.


RGBColorChart

Reminder:Thenumbersonthischartarewritteninbase10.


HexadecimalColorChart


Extension:

*Whatisthehighestcolorvalueinthe#RRGGBBhexadecimalsystem?UsethisinformationtofigureouthowmanyRGBcolorsexist.

Solution:

Thehighestcolorvalueis#FFFFFFwhichcorrelatestotheRGBvalueof255255255.Sincethevaluesrangefrom0to255,thereare256possiblevalueseachforred,green,andblue.

Usingthefundamentalcountingprinciple,wecanfindthenumberofRGBcolorsthatexistbysolving:256x256x256=16,777,216possiblecolorcombinations.

a splash of color - complete mathcompletemath.onmason.com/files/2016/12/splash-of-color.pdf ·...

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