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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