Download - Mayan Mathcompletemath.onmason.com/files/2016/12/Mayan-Math.pdf · number in the Mayan system. * A number between 40 and 100. * A number between 100 and 500. * A number between 500

GeorgeMasonUniversityCOMPLETEMath©2015

MayanMath

CreatedbyKateBeckSpring2016

TheTask

StudytheMayancountingsystem.Completethefollowingtasks:• DeterminethenumberthattheMayancountingsystemisbasedon.• MakeaplacevaluechartfortheMayansystem.• Chooseanumberthatfitseachcategorybelowinbase10andrecordtheequivalentnumberinthe

Mayansystem.*Anumberbetween40and100.*Anumberbetween100and500.*Anumberbetween500and1,000.*Anumberbetween1,000and10,000.*Anumbergreaterthan10,000.

BigIdeas

• Placevalueinapositionalnumbersystem.

StandardsofLearningforGrades3-4-53.1aReadandwrite6-digitnumeralsandidentify

theplacevalueandvalueofeachdigit.4.1aIdentifyorallyandinwritingtheplacevalue

foreachdigitinawholenumberexpressedthroughmillions.

StandardsofLearningforGrades6-7-86.5Investigateanddescribeconceptsofpositive

exponents.7.1aInvestigateanddescribetheconceptofnegative

exponentsforpowersof10.7.1bDeterminescientificnotationfornumbers

greaterthanzero.

ProcessGoals• ProblemSolvingandReasoning–Studentswillapplyanunderstandingofbase10placevaluetomake

senseoftheMayannumbersystem(base5withinbase20).• ConnectionsandRepresentations–Studentswillrecognizeandusemathematicalconnectionsto

extendandgeneralizepatternsinapositionalnumbersystem.Theywilluseavarietyofrepresentationsastheyexplorebase20andcommunicatetheirthinking.

• Communication–Studentswilljustifytheirfindingsandpresenttheirresultstotheclasswithprecisemathematicallanguage.

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

RelatedTask–ASplashofColorCreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!


MayanMathLessonPlan

CreatedbyKateBeck

Spring2016

TheTask

StudytheMayancountingsystem.Completethefollowingtasks:• DeterminethenumberthattheMayancountingsystemisbasedon.• MakeaplacevaluechartfortheMayansystem.• Chooseanumberthatfitseachcategorybelowinbase10andrecordtheequivalent

numberintheMayansystem.*Anumberbetween40and100.*Anumberbetween100and500.*Anumberbetween500and1,000.*Anumberbetween1,000and10,000.*Anumbergreaterthan10,000.

Materials

• Copiesofthetaskforeachpair/group• CopiesoftheMayanNumberSystemsheetfor

eachpair/group• Graphpaper• Blankpaper• Calculators• 1largesheetofpaperforeachpair/groupon

whichtocreatetheplacevaluechart.• 5largepiecesofchartpaperlabeledwitheach

headingfromthetask(e.g.Anumberbetween40and100)thatarehungindifferentplacesaroundtheclassroom.

• Markers• Seashellsorasimilarmanipulativethatcanbe

usedtorepresenttheshellintheMayansystem• OrangeCuisenairerodsorother“sticks”that

canbeusedtorepresent5intheMayansystem• Roundchips(coloredchipsortwo-sided

countersthatcanbeusedtorepresentthedotsintheMayansystem)

FacilitatingTask• Dividetheclassintopairsorgroupsof3

students.Giveeachgroupacopyofthetask.• Readthetasktogetherandanswerclarifying

questions.• Makematerialsavailabletothegroups.• EachgroupwillexploretheMayansystemand

createtheirplacevaluechartsonalargesheetofpaper.

• Studentsmaywishtousethemanipulativestocreatetheirnumbersontheirplacevaluechartsbeforerecordingthem.

• Eachgroupwillrecordfivenumbersthatfitthecategoriesonseparatesheetsofpaperandattachthesesheetstotheappropriatechart.

• Allow10-15minutesattheendofthelessonfordiscussion.Discusstheplacevaluechartsandthenumbersthatthestudentscreated.

• Asthegroupspresent,drawconnectionsbetweentheMayancountingsystemandourbase10decimalsystem(seeprompts/questionsbelow).

• Anextensiontothistaskistohaveeachstudentcreatehisorherown“ancient”world(i.e.inabaseotherthan10or20).Theycanexplorethatworldbycreatingnumbers.

Misconceptions• StudentsmaythinktheMayansonlyusedzero

inthe“ones”place.Theymaycreatenumbersinwhichtheyjustleaveablankplaceratherthaninsertingashell.

• Studentsmaybeconfusedbythebase5withinabase20system.So,theymaysaythatit’sbasedonfive,whichisnotincorrectbutisnot

SuggestedPromptsorQuestions• WhatpatternsdoyounoticewithintheMayan

system?• Howdidyoufigureoutwhatnumberthe

systemwasbasedon?• HowistheMayansystemsimilartoourbase10

system?• Howisitdifferent?


completelycorrect.• Studentsmaybeconfusedbythevertical

positionalsystem,astheyareusedtothehorizontalpositionalsystemthatweuse.

• WhatdidyoufindtrickiestabouttheMayansystem?

• HasanythingbecomecleareraboutbasetenafterworkingintheMayansystem?


MayanMath Name Date TheancientMayancivilizationexistedfromaround2,000B.C.untilaround900A.D.inmodern-dayMexicoandCentralAmerica.TheMayansusedasophisticatedcountingsystemtocreatetheircalendarandmakeastronomicalobservations.Theyevendevelopedtheconceptofzerowhichtheyrepresentedusingashell:

StudytheMayancountingsystem.Completethefollowingtasks:

• DeterminethenumberthattheMayancountingsystemisbasedon.

• MakeaplacevaluechartfortheMayansystem.

• Chooseanumberthatfitseachcategorybelowinbase10andrecordtheequivalentnumberintheMayansystem.

o Anumberbetween40and100.

o Anumberbetween100and500

o Anumberbetween500and1,000

o Anumberbetween1,000and10,000

o Anumbergreaterthan10,000


MayanCountingSystem

0-19: Somelargernumbers:


MayanMathSolutionStrategies

• TheMayannumbersystemisabase5withinabase20system.Studentsmightidentifyonlyoneoftheseelementsastheyaremakingsenseofthesystem.

• Placevaluechart:


ExamplesofMayannumbersthatfiteachcategory:

• Anumberbetween40and100

60

(3x20)+(0x1)=60

• Anumberbetween100and500:

465

(1x400)+(3x20)+(5x1)=465


• Anumberbetween500and1,000

644

(1x400)+(12x20)+(4x1)=644

• Anumberbetween1,000and10,000

9,100

(1x8,000)+(2x400)+(15x20)+(0x1)=9,100


• Anumbergreaterthan10,000

20,007

(2x8,000)+(10x400)+(0x20)+(7x1)=20,007