Buildltl
ConceptAreas
GeometryandspatialrellSnl\lngInthreedimensions,logicInageometricalsetting.Usingvocabulary:cube,ftlc,edge,!!Ide,touching,ftbove,below,each,t•very.
ForEachGroup:
• Coloredcubes.Youcansolveeveryprobleminthisfamilybyusingasubset ofelevencubes:twoeachofred,blue,yellow,green,andorange,andonepurple.
Description
Thegroupneedstobuildasmallstructureout ofcoloredcubes.Eachcluetellssomethingaboutthestructure,forexample,"thereisaredblockbelowthegreenblock,"or"the twoorange
blocksshareanedge."Insome problems,studentshavetodeduce whatblockstheyneedfromtheirclues.Inoneproblem,eachcluerestrictsitsholdertotouchingonlyonecolorofblock.
Theseproblemsarepopularstarters.They'refun,andthefirstfewarepretty easywithout beingtrivial.
Purpose
Wecouldgoonforpagesabout theimportance
ofgeometry aspartofmathematicslearningatalllevels.Let'sjustmakethree points here:
• First,thecluesusemathematicallanguageandforceproblem-solverstousewords like
"face"and"edge"togettheircluesacrossto
others.Furthermore,studentsgetintogooddiscussionsaboutwhether"below"means"belowandnextto."
• Second,mostgeometryinstructionistwo-dimensional,yetweliveina30world.Learningtothinkinthreedimensionsispowerfulanduseful.
• Third,incorporatingmathlanguageand30thinkingwillhelpthosestudentswhowillneeditthemostthestudentswho don'toftenplaywithtoysthatenhancespatialvisualization
PossibleDebriefingQuestions
Howwould youmaketheseproblemsmoredifficult?
Didyouuseanywordsthat hadmorethanone
muMingtothegroup?
WhichWll$ ynurfavoriteproblem?Why?
page44
•BuildIt#1
BuildIt#1
..
,..
Therearesixblocksinall.Oneoftheblocksisyellow.
Thegreenblocksharesonefacewitheachoftheotherfiveblocks.
1
I
'lIc•
·I
------..----·------
,..j..
q,,...
•BuildIt#1
Thetworedblocksdonottoucheachother.
BuildIt#1•
Thetwoblueblocksdonottoucheachother.
------r------
1
I
BuildIt#1
Eachredblocksharesanedgewiththeyellowblock
BuildIt#1
Eachblueblocksharesoneedgewitheachoftheredblocks.
1
olitUnlvollyufCoHfoml•- ----;_------
•BuildIt#2
Therearesixblocksinall,ina
towersixblockshigh.
Thereisayellowblockontop.
BuildIt#2•
Theredblockisabovethegreenblock.
•BuildIt·#2.·
..
Oneoftheyellowsisabove thegreenblock;theother isbelowit.
BuildIt#2•
Eachoftheblueblockssharesafacewith thegreenblock
Buildlt#2
--
Notwoblocksofthesame
colortoucheachother.
page46
Buildlt#2
Therearetwoyellows,twoblues,onegreen,andoneredinthesetofblocks.
fromCt>tItToxt'fher• EQUALS,LawrenceHallofScience
•BuildIt#3
Thereisaredblockdirectlybelowayellowblock.
Thereisagreenblockonthebottomlevel.
BuildIt#3•
Thereisared blockdirectlyontopofayellowblock.
ThehighestblockisonthethirdleveL
I
------
•BuildIt#3
Therearesixblocksinall.
Anorangeblocksharesafacewithagreenblockandtwoothers.
BuildIt#3•
Ablueblocksharesafacewithayellowblock.
Thereisared blockonthebottomlevel.
------
Buildlt#3
Ablueblocktouchesredand
greenblocksonlyalongedges.
Therearethreeblocksonthe
bottomlevel.
Buildlt#3
Ayellowblocktouchesanorangeblockonlyalongan·edge.
------·---·------
f
.P1989TheRegentsuftheUniversityofCalifmia------•.- fr>mCtlll'/'o,<lltrr•6QUALS.t..wtonceHallofScience
:page47
l
·)··..·.-_:-_:··.
s·uildIt#4··_.
"lor"." ',,.-, ·-·' ''7",.••a -/
.....'. - ..- .-:---... .
Special Ruk•:
you may only touch tlworangeblock.
SpecialRule:
youmayonlytouchyellowblocks.
E.whyellowblock is(lbovearedblock;t'Vl'ryredblocksharesanl'dgt• with thl'blul' block.
Yourclue: theoneredblocksharesafacewiththeorangeblock
------r------
Help builditwith blocks,buttheblueblockistheonlyoneyou
"reallowed totouch.
Your clue: thegreenblock
sharesafacewith one ofthe twoyellowblocks.
Yourjobistohelpthegroupbuildit,butthegreen blockistheonlyonethat youareallowedtotouch.
Theblueblocksharesafacewith
theorangeblockand twoothers.
-.
._·Build_
'. ·.!::,.._:_::_ ;,:
_ .· --,·
. J ;' ·-.....·-
Buildlt#4
Don't passthisoneout-theseare
Youmayonlytouch thered
block
Thehighest blocks(neitherofwhichareblue)areonthethirdlevel.
instructionstotheteacher!
Notethateachplayercantouchonlyonecolorofblock;ifyoudon'tusetheoptionalclue,noonecantouchred.That'sintentional!
Minimumblocks:Oneblue,green,
.orange,red;twoyellows.
I•t·f'IHtlfful<•·.-··nhufiiii'Univt·rityofCCllifomia .. ------fromGelltTogtlbt!r•EQVAl.5,LawrenceHallofScience