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George Mason University COMPLETE Math © 2015 Mayan Math Created by Kate Beck Spring 2016 The Task Study the Mayan counting system. Complete the following tasks: • Determine the number that the Mayan counting system is based on. • Make a place value chart for the Mayan system. • Choose a number that fits each category below in base 10 and record the equivalent number in the Mayan system. * A number between 40 and 100. * A number between 100 and 500. * A number between 500 and 1,000. * A number between 1,000 and 10,000. * A number greater than 10,000. Big Ideas • Place value in a positional number system. Standards of Learning for Grades 3-4-5 3.1a Read and write 6-digit numerals and identify the place value and value of each digit. 4.1a Identify orally and in writing the place value for each digit in a whole number expressed through millions. Standards of Learning for Grades 6-7-8 6.5 Investigate and describe concepts of positive exponents. 7.1a Investigate and describe the concept of negative exponents for powers of 10. 7.1b Determine scientific notation for numbers greater than zero. Process Goals • Problem Solving and Reasoning – Students will apply an understanding of base 10 place value to make sense of the Mayan number system (base 5 within base 20). • Connections and Representations – Students will recognize and use mathematical connections to extend and generalize patterns in a positional number system. They will use a variety of representations as they explore base 20 and communicate their thinking. • Communication – Students will justify their findings and present their results to the class with precise mathematical language. Related Task – Out of this World Your mission is to make sense of the Woop/Zoobie/Glim number system and present it to the mathematicians on Earth. You must help them understand this new way of counting. Peace in our solar system depends on it! Related Task – A Splash of Color Create a colorful design for your iPhone screen. Use the chart to help you choose your colors and be sure to include at least 8 different colors. Label each component of your design with the RGB value as well as the hexadecimal #RRGGBB value. Finally, color your design!

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Page 1: 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!

Page 2: 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

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?

Page 3: 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

completelycorrect.• Studentsmaybeconfusedbythevertical

positionalsystem,astheyareusedtothehorizontalpositionalsystemthatweuse.

• WhatdidyoufindtrickiestabouttheMayansystem?

• HasanythingbecomecleareraboutbasetenafterworkingintheMayansystem?

Page 4: 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 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

Page 5: 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

MayanCountingSystem

0-19: Somelargernumbers:

Page 6: 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

MayanMathSolutionStrategies

• TheMayannumbersystemisabase5withinabase20system.Studentsmightidentifyonlyoneoftheseelementsastheyaremakingsenseofthesystem.

• Placevaluechart:

Page 7: 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

ExamplesofMayannumbersthatfiteachcategory:

• Anumberbetween40and100

60

(3x20)+(0x1)=60

• Anumberbetween100and500:

465

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

Page 8: 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

• Anumberbetween500and1,000

644

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

• Anumberbetween1,000and10,000

9,100

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

Page 9: 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

• Anumbergreaterthan10,000

20,007

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


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