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Addition:PartialSums
Manytimesitiseasiertobreakapart
addends.Oftenitmakessensetobreak
themapartbytheirplacevalue.Consider
248+345
248=200+40+8
Subtraction:CountUporCountBack
Whensubtracting,wecancountbacktofind
thedifferenceoftwonumbers.Inmany
situations,itiseasiertocountup.
Consider536–179
RepeatedAddition:
345=300+40+5
345=500+80+13=593
Sometimeswemightusepartialsumsin
differentwaystomakeaneasierproblem.
Consider484+276
484=400+84
276=260+16
345=660+100=760
Addition:Adjusting
Wecanadjustaddendstomakethemeasier
toworkwith.Wecanadjustbygivinga
valuefromoneaddendtoanother.
Consider326+274.Wecantake1from326
andgiveitto274.
MoreFriendly
Problem
326+274
-1+1
325+275 =600
Consider173+389.Wecantake27from
389andgiveitto173tomake200.
MoreFriendly
Problem
173+389
+27-27
200+362 =562
WhatIsMultiplication?
Multiplicationhasdifferentrepresentations
basedonthecontext.Regardlessofthe
representation,theproductofany2factors
remainsthesame.Representationsfor3rd
gradeinclude:
6+6+6+6
4+4+4+4+4+4
Wecancountupfromonenumbertothe
other.Thedifferenceis300+21+36or357.
(above)
EqualGroups/Sets:
4groupsof6hearts
These
examples
arefor
6x4.
6groupsof4hearts
Area/ArrayModel:
Wecancountbackfromonenumbertothe
other.Thedifferenceis-300(landat236),-36
(landat200),–21(endat179).
Subtraction:Adjusting
Wecanuse“friendliernumbers”tosolve
problems.4,000–563canbechallengingto
regroup.Butthedifferencebetweenthese
numbersisthesameasthedifferencebetween
3,999–562.Now,wedon’tneedtoregroup.
(Originalproblem)
4,000-563=
(Compensation)
-1
-1
3,999-562=3,437
6
4
6x4=24squareunits-or-
4x6=24squareunits
TheCommutativeProperty
Thispropertyallowsustoreversetheorder
offactors.Itisusefulinmanysituations.
Examplesaboveshowthat6x4isequalto
4x6regardlessoftherepresentation.
Multiplication:Area/ArrayModel
Thearea/arraymodelformultiplication
andthedistributivepropertyareusedto
solvemultiplicationproblems.
Modelfor8x7:
In8x6,wecanbreakthe8into(5+3).8
x6becomes(5x6)+(3x6).
8x7=
(8x5)+(8x2)=
40+16=
56
8x6
(5x6)+(3x6)
30+18
48
Thisisthesame
modelwithout
innersquares.Itis
consideredan
“openmodel.”
Studentsmovefromarea/arraymodels
toworkingwithpartialproductsandthe
distributiveproperty.
8x7
(8x5)+(8x2)
40+16
56
Division:ThinkMultiplication
Multiplicationanddivisionarerelated.
Whenworkingwithdivision,it
sometimesmakessenseto“think
multiplication.”12÷4couldbethought
ofas“4timeswhatequals12.”
3x4=12
3x4tens=12tens
3x40=120
7
Developing
Computational
Fluency
Grade3
ElementaryMathematicsOffice
HowardCountyPublicSchoolSystem
Howmanygroupsof4arein12hearts?
Whatis12÷4?
Whattimes4equals12?
Multiplication:Multiplesof10
3x1=3
3x1ten=3tens
3x10=30
TheDistributiveProperty
Thispropertyallowsustobreakapart
factors.Itcanmakecomputationmore
efficient.Itwillbeusedlaterinalgebra.
3x4=12sothereare3groupsof4hearts.
Thisbrochurehighlightssomeofthemethods
fordevelopingcomputationalfluency.Formore
informationaboutcomputationandelementary
mathematicsvisit
https://hcpss.instructure.com/courses/34429/pa
ges/grade-3-star-mathematics-overview