TM CCSS Correlation-2019 - Literacy and Math Instructional

Common Core State Standards for MathematicsTransMath Third Edition, Grades 3–12

GRADES 3–12

CCSS

TransMathThirdEditionCorrelatedtotheCommonCoreStateStandardsforMathematics(CCSS)

Grades 3 - 12

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GRADE3CCSSLessonSubsection(andPageNumber)in

TransMath1WhereStandardisAddressed

LessonSubsection(andPageNumber)inTransMath2

WhereStandardisAddressed



CCSS.Math.Content.3.G.A.1Understandthatshapesindifferentcategories(e.g.,rhombuses,rectangles,andothers)mayshareattributes(e.g.,havingfoursides);andthatthesharedattributescandefinealargercategory(e.g.,quadrilaterals).Recognizerhombuses,rectangles,andsquaresasexamplesofquadrilaterals,anddrawexamplesofquadrilateralsthatdonotbelongtoanyofthesesubcategories.

Unit6:Lesson1,ProblemSolving(649-651);Lesson2,ProblemSolving(659-661);Lesson3,ProblemSolving(668-670);Lesson10,ProblemSolving(727-730);Unit7:Lesson1,ProblemSolving(747-749);Lesson2,ProblemSolving(756-757)

Unit3:Lesson12,BuildingNumberConcepts(350-354)Unit5:Lesson3,ProblemSolving(518-519);Lesson4,ProblemSolving(525-526);Lesson9,ProblemSolving(569-570);Lesson12,ProblemSolving(594-595)

CCSS.Math.Content.3.G.A.2Partitionshapesintopartswithequalareas.Expresstheareaofeachpartasaunitfractionofthewhole.Forexample,partitionashapeinto4partswithequalarea,anddescribetheareaofeachpartas1/4oftheareaoftheshape.

Unit1:Lesson2,BuildingNumberConcepts(16-18);Lesson2,ProblemSolving(19-20);Lesson3,BuildingNumberConcepts(23-26);Lesson4,BuildingNumberConcepts(32-34);Lesson4,ProblemSolving(35-37);Lesson5,BuildingNumberConcepts(40-43);Lesson6,BuildingNumberConcepts(48-50);Lesson8,BuildingNumberConcepts(65-67);Lesson10,BuildingNumberConcepts(81-88);Lesson10,ProblemSolving(89-92)

Unit1:Lesson1,BuildingNumberConcepts(9-13)

CCSS.Math.Content.3.MD.A.1Tellandwritetimetothenearestminuteandmeasuretimeintervalsinminutes.Solvewordproblemsinvolvingadditionandsubtractionoftimeintervalsinminutes,e.g.,byrepresentingtheproblemonanumberlinediagram.

CCSS.Math.Content.3.MD.A.2Measureandestimateliquidvolumesandmassesofobjectsusingstandardunitsofgrams(g);kilograms(kg);andliters(l).6Add,subtract,multiply,ordividetosolveone-stepwordproblemsinvolvingmassesorvolumesthataregiveninthesameunits,e.g.,byusingdrawings(suchasabeakerwithameasurementscale)torepresenttheproblem.7

Unit6:Lesson6,ProblemSolving(692-693);Lesson7,ProblemSolving(700-703)

CCSS.Math.Content.3.MD.B.3Drawascaledpicturegraphandascaledbargraphto

Unit1:Lesson5,ProblemSolving(41-42);Lesson6,ProblemSolving(50-51);Lesson7,

Unit8:Lesson1,ProblemSolving(866-867)


Grades 3 - 12

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WhereStandardisAddressedrepresentadatasetwithseveralcategories.Solveone-andtwo-step“howmanymore”and“howmanyless”problemsusinginformationpresentedinscaledbargraphs.Forexample,drawabargraphinwhicheachsquareinthebargraphmightrepresent5pets.

ProblemSolving(58-59)Unit2:Lesson2,ProblemSolving(144-145)

CCSS.Math.Content.3.MD.B.4Generatemeasurementdatabymeasuringlengthsusingrulersmarkedwithhalvesandfourthsofaninch.Showthedatabymakingalineplot,wherethehorizontalscaleismarkedoffinappropriateunits—wholenumbers,halves,orquarters.

Unit8:Lesson12,ProblemSolving(932-933);Unit9:Lesson7,BuildingNumberConcepts(1020-1022);Lesson7,ProblemSolving(1023-1025);Lesson8,ProblemSolving(1032-1033)

CCSS.Math.Content.3.MD.C.5Recognizeareaasanattributeofplanefiguresandunderstandconceptsofareameasurement.

Unit5:Lesson1,ProblemSolving(519-520);Lesson2,ProblemSolving(523-527);Lesson3,ProblemSolving(533-535);Lesson4,ProblemSolving(542-543);Lesson8,ProblemSolving(575-576);Lesson9,ProblemSolving(579-583);Lesson11,ProblemSolving(598-599);Lesson12,ProblemSolving(606-608);Lesson13,ProblemSolving(614-615);Lesson15,ProblemSolving(629-632)

CCSS.Math.Content.3.MD.C.5aAsquarewithsidelength1unit,called“aunitsquare,”issaidtohave“onesquareunit”ofarea,andcanbeusedtomeasurearea.

Unit3:Lesson13,ProblemSolving(346-351);Lesson14,ProblemSolving(354-357);Lesson15,ProblemSolving(364-369)Unit5:Lesson2,ProblemSolving(523-527);Lesson3,ProblemSolving(533-535);Lesson4,ProblemSolving(542-543)

CCSS.Math.Content.3.MD.C.5bAplanefigurewhichcanbecoveredwithoutgapsoroverlapsbynunitsquaresissaidtohaveanareaofnsquareunits.

Unit3:Lesson13,ProblemSolving(346-351);Lesson14,ProblemSolving(354-357);Lesson15,ProblemSolving(364-369)Unit5:Lesson2,ProblemSolving(523-527);Lesson3,ProblemSolving(533-535);Lesson4,ProblemSolving(542-543)

CCSS.Math.Content.3.MD.C.6Measureareasbycountingunitsquares(squarecm,squarem,squarein,squareft,andimprovisedunits).

Unit3:Lesson13,ProblemSolving(346-351);Lesson14,ProblemSolving(354-357);Lesson15,ProblemSolving(364-369)Unit5:Lesson1,ProblemSolving(519-520);Lesson2,ProblemSolving(523-527);Lesson


Grades 3 - 12

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WhereStandardisAddressed3,ProblemSolving(533-535);Lesson4,ProblemSolving(542-543)

CSS.Math.Content.3.MD.C.7Relateareatotheoperationsofmultiplicationandaddition.

Unit5:Lesson1,ProblemSolving(519-520);Lesson2,ProblemSolving(523-527);Lesson3,ProblemSolving(533-535);Lesson4,ProblemSolving(542-543);Lesson8,ProblemSolving(575-576);Lesson9,ProblemSolving(579-583);Lesson11,ProblemSolving(598-599);Lesson12,ProblemSolving(606-608);Lesson13,ProblemSolving(614-615);Lesson15,ProblemSolving(629-632)Unit6:Lesson8,BuildingNumberConcepts(706-708);Lesson9,BuildingNumberConcepts(714-717);Lesson10,BuildingNumberConcepts(722-726)

CCSS.Math.Content.3.MD.C.7aFindtheareaofarectanglewithwhole-numbersidelengthsbytilingit,andshowthattheareaisthesameaswouldbefoundbymultiplyingthesidelengths.

Unit3:Lesson13,ProblemSolving(346-351);Lesson14,ProblemSolving(354-357);Lesson15,ProblemSolving(364-369)Unit5:Lesson2,ProblemSolving(523-527);Lesson4,ProblemSolving(542-543)

CCSS.Math.Content.3.MD.C.7bMultiplysidelengthstofindareasofrectangleswithwholenumbersidelengthsinthecontextofsolvingrealworldandmathematicalproblems,andrepresentwhole-numberproductsasrectangularareasinmathematicalreasoning.

Unit3:Lesson13,ProblemSolving(346-351);Lesson14,ProblemSolving(354-357);Lesson15,ProblemSolving(364-369)Unit5:Lesson2,ProblemSolving(523-527);Lesson4,ProblemSolving(542-543);Lesson9,ProblemSolving(579-583);Lesson11,ProblemSolving(598-599);Lesson12,ProblemSolving(606-608);Lesson13,ProblemSolving(614-615);Lesson15,ProblemSolving(629-632)

CCSS.Math.Content.3.MD.C.7cUsetilingtoshowinaconcretecasethattheareaofarectanglewithwhole-numbersidelengthsaandb+cisthesumofa×banda×c.Useareamodelstorepresentthedistributivepropertyinmathematicalreasoning.

Unit3:Lesson13,ProblemSolving(346-351);Unit3:Lesson14,ProblemSolving(354-357);Unit3:Lesson15,ProblemSolving(364-369);Unit5:Lesson2,ProblemSolving(523-527);Unit5:Lesson12,ProblemSolving(606-608);Unit5:Lesson13,ProblemSolving(614-615)

CCSS.Math.Content.3.MD.C.7dRecognizeareaasadditive.Findareasofrectilinearfiguresbydecomposingthemintonon-overlappingrectanglesandaddingtheareasofthenon-overlappingparts,applyingthistechniquetosolverealworldproblems.

Unit5:Lesson4,ProblemSolving(542-543);Lesson12,ProblemSolving(606-608);Lesson13,ProblemSolving(614-615);Lesson15,ProblemSolving(629-632)


CSSS.Math.Content.3.MD.D.8Solverealworldandmathematicalproblemsinvolving

Unit5:Lesson6,ProblemSolving(558-561);Lesson7,ProblemSolving(568-569);Lesson



Grades 3 - 12

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WhereStandardisAddressedperimetersofpolygons,includingfindingtheperimetergiventhesidelengths,findinganunknownsidelength,andexhibitingrectangleswiththesameperimeteranddifferentareasorwiththesameareaanddifferentperimeters.

8,ProblemSolving(575-576);Lesson9,ProblemSolving(579-583);Lesson11,ProblemSolving(598-599);Lesson12,ProblemSolving(606-608);Lesson15,ProblemSolving(629-632)

CCSS.Math.Content.3.NBT.A.1Useplacevalueunderstandingtoroundwholenumberstothenearest10or100.

Unit1:Lesson10,BuildingNumberConcepts(77-82);Lesson11,ProblemSolving(91-92);Lesson12,ProblemSolving(98-99)Unit2:Lesson6,BuildingNumberConcepts(169-172);Lesson7,BuildingNumberConcepts(178-180);Lesson7,ProblemSolving(181-182);Lesson8,BuildingNumberConcepts(184-187);Lesson8,ProblemSolving(188-189);Lesson9,BuildingNumberConcepts(192-193);Lesson9,ProblemSolving(194-195);Lesson13,ProblemSolving(224-225);Lesson15,BuildingNumberConcepts(235-238)

CCSS.Math.Content.3.NBT.A.2Fluentlyaddandsubtractwithin1000usingstrategiesandalgorithmsbasedonplacevalue,propertiesofoperations,and/ortherelationshipbetweenadditionandsubtraction.

Unit1:Lesson3,BuildingNumberConcepts(27-29);Lesson4,BuildingNumberConcepts(34-35);Lesson6,BuildingNumberConcepts(47-49);Lesson7,BuildingNumberConcepts(54-57);Lesson8,BuildingNumberConcepts(62-64);Lesson9,BuildingNumberConcepts(69-72);Lesson11,BuildingNumberConcepts(87-90);Lesson15,BuildingNumberConcepts(113-115)Unit2:Lesson1,BuildingNumberConcepts(133-135);Lesson1,ProblemSolving(134-137);Lesson2,BuildingNumberConcepts(140-143);Lesson2,ProblemSolving(144-145);Lesson3,BuildingNumberConcepts(148-150);Lesson4,BuildingNumberConcepts(154-157);Lesson5,BuildingNumberConcepts(162-164);Lesson6,BuildingNumberConcepts(169-172);Lesson7,BuildingNumberConcepts(178-180);Lesson8,BuildingNumberConcepts(184-187);Lesson9,BuildingNumberConcepts


Grades 3 - 12

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WhereStandardisAddressed(192-193);Lesson10,BuildingNumberConcepts(198-201);Lesson11,BuildingNumberConcepts(206-208);Lesson11,ProblemSolving(209-210);Lesson12,BuildingNumberConcepts(213-216);Lesson12,ProblemSolving(217-218);Lesson13,BuildingNumberConcepts(221-223);Lesson14,BuildingNumberConcepts(228-230);Lesson14,ProblemSolving(231-232);Lesson15,BuildingNumberConcepts(235-238);Lesson15,ProblemSolving(239-240)

CCSS.Math.Content.3.NBT.A.3Multiplyone-digitwholenumbersbymultiplesof10intherange10–90(e.g.,9×80,5×60)usingstrategiesbasedonplacevalueandpropertiesofoperations.

Unit3:Lesson1,BuildingNumberConcepts(253-255);Lesson1,ProblemSolving(256-259);Lesson2,BuildingNumberConcepts(262-264);Lesson3,BuildingNumberConcepts(270-272);Lesson11,BuildingNumberConcepts(334-336);Lesson15,BuildingNumberConcepts(360-363);Lesson15,ProblemSolving(364-369)Unit4:Lesson2,BuildingNumberConcepts(391-394);Lesson3,ProblemSolving(403-404)

CCSS.Math.Content.3.NF.A.1Understandafraction1/basthequantityformedby1partwhenawholeispartitionedintobequalparts;understandafractiona/basthequantityformedbyapartsofsize1/b.

Unit8:Lesson1,BuildingNumberConcepts(837-841);Lesson2,BuildingNumberConcepts(847-849);Lesson3,BuildingNumberConcepts(854-857);Lesson4,BuildingNumberConcepts(864-868);Lesson6,BuildingNumberConcepts(881-884);Lesson7,BuildingNumberConcepts(890-892);Lesson8,BuildingNumberConcepts(897-899);Lesson9,BuildingNumberConcepts(905-907);Lesson10,BuildingNumberConcepts(913-915);Lesson11,BuildingNumberConcepts(920-922);Lesson12,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(936-940);Lesson14,BuildingNumberConcepts(943-945);Lesson15,BuildingNumberConcepts(950-954)

Unit1:Lesson2,BuildingNumberConcepts(16-18);Lesson3,BuildingNumberConcepts(23-26);Lesson4,BuildingNumberConcepts(32-34);Lesson5,BuildingNumberConcepts(40-43);Lesson6,BuildingNumberConcepts(48-50);Lesson7,BuildingNumberConcepts(56-58);Lesson8,BuildingNumberConcepts(65-67);Lesson9,BuildingNumberConcepts(72-75);Lesson10,BuildingNumberConcepts(81-88);Lesson10,ProblemSolving(89-92)Unit2:Lesson6,BuildingNumberConcepts(151-154)


Grades 3 - 12

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WhereStandardisAddressedUnit9:Lesson1,BuildingNumberConcepts(971-975);Lesson2,BuildingNumberConcepts(981-984)

CCSS.Math.Content.3.NF.A.2Understandafractionasanumberonthenumberline;representfractionsonanumberlinediagram.

Unit8:Lesson1,BuildingNumberConcepts(837-841);Lesson2,BuildingNumberConcepts(847-849);Lesson9,BuildingNumberConcepts(905-907);Lesson14,BuildingNumberConcepts(943-945);Lesson15,BuildingNumberConcepts(950-954)

Unit1:Lesson1,BuildingNumberConcepts(9-11);Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,BuildingNumberConcepts(81-88);Lesson10,ProblemSolving(89-92)Unit2:Lesson1,BuildingNumberConcepts(107-108);Lesson1,ProblemSolving(109-112);Lesson2,BuildingNumberConcepts(115-117);Lesson2,ProblemSolving(118-120);Lesson3,BuildingNumberConcepts(123-127);Lesson3,ProblemSolving(128-129);Lesson4,BuildingNumberConcepts(133-135);Lesson4,ProblemSolving(136-138);Lesson5,BuildingNumberConcepts(141-145);Lesson15,ProblemSolving(240-243)Unit3:Lesson1,BuildingNumberConcepts(255-259)Unit5:Lesson1,BuildingNumberConcepts(495-499);Lesson9,BuildingNumberConcepts(563-568);Lesson13,BuildingNumberConcepts(597-601)

CCSS.Math.Content.3.NF.A.2aRepresentafraction1/bonanumberlinediagrambydefiningtheintervalfrom0to1asthewholeandpartitioningitintobequalparts.Recognizethateachparthassize1/bandthattheendpointofthepartbasedat0locatesthenumber1/bonthenumberline.

Unit8:Lesson1,BuildingNumberConcepts(837-841);Lesson2,BuildingNumberConcepts(847-849);Lesson15,BuildingNumberConcepts(950-954)

Unit1:Lesson1,BuildingNumberConcepts(9-11);Lesson8,ProblemSolving(68-69);Lesson10,ProblemSolving(89-92)Unit2:Lesson2,ProblemSolving(118-120);Lesson3,ProblemSolving(128-129);Lesson4,ProblemSolving(136-138)

CCSS.Math.Content.3.NF.A.2bRepresentafractiona/bonanumberlinediagramby

Unit8:Lesson2,BuildingNumberConcepts(847-849);Lesson15,BuildingNumber

Unit1:Lesson1,BuildingNumberConcepts(9-11);Lesson8,ProblemSolving(68-69);


Grades 3 - 12

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WhereStandardisAddressedmarkingoffalengths1/bfrom0.Recognizethattheresultingintervalhassizea/bandthatitsendpointlocatesthenumbera/bonthenumberline.

Concepts(950-954)Unit9:Lesson7,BuildingNumberConcepts(1020-1022)

Lesson10,ProblemSolving(89-92)Unit2:Lesson2,ProblemSolving(118-120);Lesson3,ProblemSolving(128-129);Lesson4,ProblemSolving(136-138)

CCSS.Math.Content.3.NF.A.3Explainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.

Unit8:Lesson12,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(936-940);Lesson14,BuildingNumberConcepts(943-945);Lesson15,BuildingNumberConcepts(950-954)

Unit2:Lesson1,BuildingNumberConcepts(107-108);Lesson2,BuildingNumberConcepts(115-117);Lesson3,BuildingNumberConcepts(123-127);Lesson4,BuildingNumberConcepts(133-135);Lesson5,BuildingNumberConcepts(141-145);Lesson7,BuildingNumberConcepts(160-163);Lesson15,BuildingNumberConcepts(232-239)

CCSS.Math.Content.3.NF.A.3aUnderstandtwofractionsasequivalent(equal)iftheyarethesamesize,orthesamepointonanumberline.



CCSS.Math.Content.3.NF.A.3bRecognizeandgeneratesimpleequivalentfractions,e.g.,1/2=2/4,4/6=2/3.Explainwhythefractionsareequivalent,e.g.,byusingavisualfractionmodel.


Unit2:Lesson7,ProblemSolving(164-166)Unit3:Lesson7,BuildingNumberConcepts(307-310)

CCSS.Math.Content.3.NF.A.3cExpresswholenumbersasfractions,andrecognizefractionsthatareequivalenttowholenumbers.Examples:Express3intheform3=3/1;recognizethat6/1=6;locate4/4and1atthesamepointofanumberlinediagram.


Unit2:Lesson4,BuildingNumberConcepts(133-135);Lesson5,BuildingNumberConcepts(141-145)Unit3:Lesson1,BuildingNumberConcepts(255-259)Unit4:Lesson5,BuildingNumberConcepts(438-440)

CCSS.Math.Content.3.NF.A.3dComparetwofractionswiththesamenumeratororthesamedenominatorbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothesamewhole.




Grades 3 - 12

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WhereStandardisAddressedRecordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualfractionmodel.CCSS.Math.Content.3.OA.A.1Interpretproductsofwholenumbers,e.g.,interpret5×7asthetotalnumberofobjectsin5groupsof7objectseach.Forexample,describeacontextinwhichatotalnumberofobjectscanbeexpressedas5×7.

Unit4:Lesson1,BuildingNumberConcepts(383-385);Lesson2,BuildingNumberConcepts(391-394);Lesson2,ProblemSolving(395-397);Lesson3,BuildingNumberConcepts(400-402);Lesson3,ProblemSolving(403-404);Lesson4,BuildingNumberConcepts(407-409);Lesson4,ProblemSolving(410-411);Lesson5,ProblemSolving(414-417);Lesson6,ProblemSolving(426-427);Lesson7,ProblemSolving(432-435);Lesson11,ProblemSolving(465-467);Lesson12,ProblemSolving(470-473);Lesson13,ProblemSolving(481-483)Unit5:Lesson1,BuildingNumberConcepts(515-518);Lesson3,BuildingNumberConcepts(530-532);Lesson4,BuildingNumberConcepts(538-541);Lesson5,BuildingNumberConcepts(546-550);Lesson6,BuildingNumberConcepts(555-557);Lesson7,BuildingNumberConcepts(564-567);Lesson8,BuildingNumberConcepts(572-574);Lesson12,BuildingNumberConcepts(602-605);Lesson13,BuildingNumberConcepts(611-613);Lesson14,BuildingNumberConcepts(618-620);Lesson15,BuildingNumberConcepts(625-628)

CCSS.Math.Content.3.OA.A.2Interpretwhole-numberquotientsofwholenumbers,e.g.,interpret56÷8asthenumberofobjectsineachsharewhen56objectsarepartitionedequallyinto8shares,orasanumberofshareswhen56objectsarepartitionedintoequalsharesof8objectseach.Forexample,describeacontextinwhichanumberofsharesoranumberofgroupscanbeexpressedas56÷8.

Unit4:Lesson1,BuildingNumberConcepts(383-385);Lesson2,BuildingNumberConcepts(391-394);Lesson2,ProblemSolving(395-397);Lesson3,BuildingNumberConcepts(400-402);Lesson3,ProblemSolving(403-404);Lesson4,BuildingNumberConcepts(407-409);Lesson4,ProblemSolving(410-411);Lesson5,ProblemSolving(414-417);Lesson6,BuildingNumberConcepts(422-425);Lesson6,Problem


Grades 3 - 12

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WhereStandardisAddressedSolving(426-427);Lesson7,BuildingNumberConcepts(430-431);Lesson7,ProblemSolving(432-435);Lesson8,BuildingNumberConcepts(438-440);Lesson8,ProblemSolving(441-443);Lesson9,BuildingNumberConcepts(445-448);Lesson9,ProblemSolving(449-451);Lesson10,BuildingNumberConcepts(454-457);Lesson11,BuildingNumberConcepts(462-464);Lesson11,ProblemSolving(465-467);Lesson12,ProblemSolving(470-473);Lesson13,ProblemSolving(481-483);Lesson15,BuildingNumberConcepts(494-500)Unit5:Lesson11,BuildingNumberConcepts(593-597);Lesson12,BuildingNumberConcepts(602-605);Lesson13,BuildingNumberConcepts(611-613);Lesson14,BuildingNumberConcepts(618-620);Lesson15,BuildingNumberConcepts(625-628)

CCSS.Math.Content.3.OA.A.3Usemultiplicationanddivisionwithin100tosolvewordproblemsinsituationsinvolvingequalgroups,arrays,andmeasurementquantities,e.g.,byusingdrawingsandequationswithasymbolfortheunknownnumbertorepresenttheproblem.


CCSS.Math.Content.3.OA.A.4Determinetheunknownwholenumberinamultiplicationordivisionequationrelatingthreewholenumbers.Forexample,determinetheunknownnumberthatmakestheequationtrueineachoftheequations8×?=48,5=�÷3,6×6=?.


CCSS.Math.Content.3.OA.B.5Applypropertiesofoperationsasstrategiestomultiplyanddivide.2Examples:If6×4=24isknown,then4×6=24isalsoknown.(Commutativepropertyofmultiplication.)3×5×2canbefoundby3×5=15,then15×2=30,orby5×2=10,then3×10=30.(Associativepropertyof

Unit3:Lesson1,BuildingNumberConcepts(253-255);Lesson2,BuildingNumberConcepts(262-264);Lesson3,BuildingNumberConcepts(270-272);Lesson4,BuildingNumberConcepts(278-280)Unit4:Lesson3,ProblemSolving(403-404);Lesson4,ProblemSolving(410-411);Lesson


Grades 3 - 12

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WhereStandardisAddressedmultiplication.)Knowingthat8×5=40and8×2=16,onecanfind8×7as8×(5+2)=(8×5)+(8×2)=40+16=56.(Distributiveproperty.)

5,ProblemSolving(414-417);Lesson6,ProblemSolving(426-427);Lesson7,ProblemSolving(432-435);Lesson11,ProblemSolving(465-467);Lesson12,ProblemSolving(470-473);Lesson13,ProblemSolving(481-483);Lesson14,ProblemSolving(489-491);Lesson15,ProblemSolving(501-503)

CCSS.Math.Content.3.OA.CMultiplyanddividewithin100.

Unit5:Lesson14,BuildingNumberConcepts(618-620);Lesson15,BuildingNumberConcepts(625-628)

CCSS.Math.Content.3.OA.C.7Fluentlymultiplyanddividewithin100,usingstrategiessuchastherelationshipbetweenmultiplicationanddivision(e.g.,knowingthat8×5=40,oneknows40÷5=8)orpropertiesofoperations.BytheendofGrade3,knowfrommemoryallproductsoftwoone-digitnumbers.

Unit3:Lesson1,BuildingNumberConcepts(253-255);Lesson2,BuildingNumberConcepts(262-264);Lesson2,ProblemSolving(265-267);Lesson3,BuildingNumberConcepts(270-272);Lesson4,BuildingNumberConcepts(278-280)Unit4:Lesson1,BuildingNumberConcepts(383-385);Lesson2,BuildingNumberConcepts(391-394);Lesson3,BuildingNumberConcepts(400-402);Lesson4,BuildingNumberConcepts(407-409);Lesson6,BuildingNumberConcepts(422-425);Lesson7,BuildingNumberConcepts(430-431);Lesson8,BuildingNumberConcepts(438-440);Lesson9,BuildingNumberConcepts(445-448);Lesson10,BuildingNumberConcepts(454-457);Lesson11,BuildingNumberConcepts(462-464);Lesson13,BuildingNumberConcepts(476-480);Lesson13,ProblemSolving(481-483);Lesson15,BuildingNumberConcepts(494-500)Unit5:Lesson1,BuildingNumberConcepts(515-518);Lesson3,BuildingNumberConcepts(530-532);Lesson4,BuildingNumberConcepts(538-541);Lesson10,BuildingNumberConcepts(586-588);Lesson11,BuildingNumberConcepts(593-597);Lesson12,BuildingNumberConcepts(602-605);Lesson13,BuildingNumberConcepts


Grades 3 - 12

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WhereStandardisAddressed(611-613);Lesson14,BuildingNumberConcepts(618-620);Lesson15,BuildingNumberConcepts(625-628)Unit7:Lesson1,BuildingNumberConcepts(743-746)







CCSS.Math.Content.4.G.ADrawandidentifylinesandangles,andclassifyshapesbypropertiesoftheirlinesandangles.

Unit7:Lesson1,ProblemSolving(755-760);Lesson2,ProblemSolving(766-769);Lesson4,ProblemSolving(786-790);Lesson5,ProblemSolving(793-796);Lesson6,ProblemSolving(805-808)

CCSS.Math.Content.4.G.A.1Drawpoints,lines,linesegments,rays,angles(right,acute,obtuse);andperpendicularandparallellines.Identifytheseintwo-dimensionalfigures.

Unit3:Lesson1,ProblemSolving(260-262);Lesson4,ProblemSolving(283-285);Lesson6,BuildingNumberConcepts(297-301);Lesson6,ProblemSolving(302-304)Unit4:Lesson7,ProblemSolving(457-459);Lesson8,ProblemSolving(464-465);Lesson10,ProblemSolving(478-482)Unit5:Lesson1,ProblemSolving(500-501);Lesson2,ProblemSolving(508-510);Lesson3,ProblemSolving(518-519);Lesson4,ProblemSolving(525-526)


CCSS.Math.Content.4.G.A.2Classifytwo-dimensionalfiguresbasedonthepresenceorabsenceofparallelorperpendicularlines,orthepresenceorabsenceofanglesofaspecifiedsize.Recognizerighttrianglesasacategory,andidentifyrighttriangles.

Unit6:Lesson2,ProblemSolving(659-661);Lesson3,ProblemSolving(668-670)Unit7:Lesson1,ProblemSolving(747-749);Lesson2,ProblemSolving(756-757)

Unit3:Lesson12,BuildingNumberConcepts(350-354);Lesson13,ProblemSolving(365-366);Lesson15,ProblemSolving(382-385)Unit5:Lesson1,ProblemSolving(500-501);Lesson2,ProblemSolving(508-510);Lesson3,ProblemSolving(518-519);Lesson4,ProblemSolving(525-526);Lesson6,ProblemSolving(541-542);Lesson7,ProblemSolving(550-551;Lesson8,Problem


Grades 3 - 12

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WhereStandardisAddressedSolving(558-560);Lesson9,ProblemSolving(569-570);Lesson12,ProblemSolving(594-595);Lesson13,ProblemSolving(602-603);Lesson14,ProblemSolving(612-613);Lesson15,ProblemSolving(621-627)

CCSS.Math.Content.4.G.A.3Recognizealineofsymmetryforatwo-dimensionalfigureasalineacrossthefiguresuchthatthefigurecanbefoldedalongthelineintomatchingparts.Identifyline-symmetricfiguresanddrawlinesofsymmetry.

Unit7:Lesson4,ProblemSolving(770-772);Lesson6,ProblemSolving(785-787);Lesson7,ProblemSolving(790-793);Lesson8,ProblemSolving(799-803);Lesson9,ProblemSolving(810-812);Lesson10,ProblemSolving(821-824)


CCSS.Math.Content.4.MD.A.1Knowrelativesizesofmeasurementunitswithinonesystemofunitsincludingkm,m,cm;kg,g;lb,oz.;l,ml;hr,min,sec.Withinasinglesystemofmeasurement,expressmeasurementsinalargerunitintermsofasmallerunit.Recordmeasurementequivalentsinatwocolumntable.Forexample,knowthat1ftis12timesaslongas1in.Expressthelengthofa4ftsnakeas48in.Generateaconversiontableforfeetandincheslistingthenumberpairs(1,12);(2,24);(3,36);...

Unit3:Lesson1,ProblemSolving(256-259);Lesson2,ProblemSolving(265-267);Lesson3,ProblemSolving(273-275);Lesson15,ProblemSolving(364-369)Unit9:Lesson1,ProblemSolving(976-978);Lesson2,ProblemSolving(985-986);Lesson3,ProblemSolving(991-994);Lesson4,ProblemSolving(1001-1002);Lesson5,ProblemSolving(1005-1007;Lesson6,ProblemSolving(1016-1017);Lesson9,ProblemSolving(1036-1038);Lesson10,ProblemSolving(1045-1047)

CCSS.Math.Content.4.MD.A.2Usethefouroperationstosolvewordproblemsinvolvingdistances,intervalsoftime,liquidvolumes,massesofobjects,andmoney,includingproblemsinvolvingsimplefractionsordecimals,andproblemsthatrequireexpressingmeasurementsgiveninalargerunitintermsofasmallerunit.Representmeasurementquantitiesusingdiagramssuchasnumberlinediagramsthatfeatureameasurementscale.

Unit3:Lesson4,ProblemSolving(281-282);Lesson6,ProblemSolving(297-298)Unit9:Lesson1,ProblemSolving(976-978);Lesson2,ProblemSolving(985-986);Lesson3,ProblemSolving(991-994);Lesson4,ProblemSolving(1001-1002);Lesson5,ProblemSolving(1005-1007);Lesson6,ProblemSolving(1016-1017);Lesson9,ProblemSolving(1036-1038);Lesson10,ProblemSolving(1045-1047)

CCSS.Math.Content.4.MD.A.3Applytheareaandperimeterformulasforrectanglesinrealworldandmathematicalproblems.Forexample,findthewidthofarectangularroomgiventheareaoftheflooringandthelength,by

Unit5:Lesson2,ProblemSolving(523-527);Lesson6,ProblemSolving(558-561);Lesson7,ProblemSolving(568-569);Lesson8,ProblemSolving(575-576);Lesson9,ProblemSolving(579-583);Lesson11,




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WhereStandardisAddressedviewingtheareaformulaasamultiplicationequationwithanunknownfactor.

ProblemSolving(598-599);Lesson12,ProblemSolving(606-608);Lesson13,ProblemSolving(614-615);Lesson15,ProblemSolving(629-632)

CCSS.Math.Content.4.MD.C.5Recognizeanglesasgeometricshapesthatareformedwherevertworaysshareacommonendpoint,andunderstandconceptsofanglemeasurement:

Unit3:Lesson4,ProblemSolving(283-285);Lesson6,BuildingNumberConcepts(297-301);Lesson6,ProblemSolving(302-304);Lesson7,ProblemSolving(311-314)

CCSS.Math.Content.4.MD.C.5aAnangleismeasuredwithreferencetoacirclewithitscenteratthecommonendpointoftherays,byconsideringthefractionofthecirculararcbetweenthepointswherethetworaysintersectthecircle.Ananglethatturnsthrough1/360ofacircleiscalleda“one-degreeangle,”andcanbeusedtomeasureangles.


CCSS.Math.Content.4.MD.C.5bAnanglethatturnsthroughnone-degreeanglesissaidtohaveananglemeasureofndegrees.


CCSS.Math.Content.4.MD.C.6Measureanglesinwhole-numberdegreesusingaprotractor.Sketchanglesofspecifiedmeasure.

Unit3:Lesson4,ProblemSolving(283-285);Lesson6,BuildingNumberConcepts(297-301);Lesson6,ProblemSolving(302-304);Lesson7,ProblemSolving(311-314);Lesson12,BuildingNumberConcepts(350-354);Lesson12,ProblemSolving(355-357);13,ProblemSolving(365-366);Lesson15,ProblemSolving(382-385)Unit4:Lesson3,ProblemSolving(423-425);Lesson4,ProblemSolving(432-435);Lesson7,ProblemSolving(457-459);Lesson8,ProblemSolving(464-465);Lesson10,ProblemSolving(478-482)Unit5:Lesson1,ProblemSolving(500-501);Lesson2,ProblemSolving(508-510);Lesson7,ProblemSolving(550-551);Lesson9,ProblemSolving(569-570)


Grades 3 - 12

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WhereStandardisAddressedCCSS.Math.Content.4.MD.C.7Recognizeanglemeasureasadditive.Whenanangleisdecomposedintonon-overlappingparts,theanglemeasureofthewholeisthesumoftheanglemeasuresoftheparts.Solveadditionandsubtractionproblemstofindunknownanglesonadiagraminrealworldandmathematicalproblems,e.g.,byusinganequationwithasymbolfortheunknownanglemeasure.

Unit3:Lesson7,ProblemSolving(311-314);Lesson8,ProblemSolving(322-324);Lesson12,BuildingNumberConcepts(350-354);Lesson12,ProblemSolving(355-357)

CCSS.Math.Content.4.NBT.A.1Recognizethatinamulti-digitwholenumber,adigitinoneplacerepresentstentimeswhatitrepresentsintheplacetoitsright.Forexample,recognizethat700÷70=10byapplyingconceptsofplacevalueanddivision.


CCSS.Math.Content.4.NBT.A.2Readandwritemulti-digitwholenumbersusingbase-tennumerals,numbernames,andexpandedform.Comparetwomulti-digitnumbersbasedonmeaningsofthedigitsineachplace,using>,=,and<symbolstorecordtheresultsofcomparisons.

Unit1:Lesson1,BuildingNumberConcepts(9-13);Lesson2,BuildingNumberConcepts(18-21);Lesson3,BuildingNumberConcepts(27-29);Lesson4,BuildingNumberConcepts(34-35);Lesson6,BuildingNumberConcepts(47-49);Lesson7,BuildingNumberConcepts(54-57);Lesson9,BuildingNumberConcepts(69-72);Lesson12,BuildingNumberConcepts(95-97);Lesson13,BuildingNumberConcepts(102-103);Lesson15,BuildingNumberConcepts(113-115)

CCSS.Math.Content.4.NBT.A.3Useplacevalueunderstandingtoroundmulti-digitwholenumberstoanyplace.

Unit1:Lesson11,BuildingNumberConcepts(87-90);Lesson11,ProblemSolving(91-92);Lesson12,ProblemSolving(98-99);Lesson15,BuildingNumberConcepts(113-115)Unit2:Lesson7,ProblemSolving(181-182);Lesson8,ProblemSolving(188-189);Lesson9,ProblemSolving(194-195);Lesson13,ProblemSolving(224-225)Unit3:Lesson8,BuildingNumberConcepts(309-312);Lesson10,BuildingNumberConcepts(326-328);Lesson11,BuildingNumberConcepts(334-336);Lesson15,BuildingNumberConcepts(360-363)


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WhereStandardisAddressedUnit4:Lesson15,BuildingNumberConcepts(494-500)

CCSS.Math.Content.4.NBT.B.4Fluentlyaddandsubtractmulti-digitwholenumbersusingthestandardalgorithm.

Unit1:Lesson8,BuildingNumberConcepts(62-64);Lesson9,BuildingNumberConcepts(69-72);Lesson11,BuildingNumberConcepts(87-90);Lesson12,BuildingNumberConcepts(95-97);Lesson13,BuildingNumberConcepts(102-103);Lesson15,BuildingNumberConcepts(113-115)Unit2:Lesson11,ProblemSolving(209-210);Lesson12,ProblemSolving(217-218);Lesson14,ProblemSolving(231-232);Lesson15,ProblemSolving(239-240)

Unit4:Lesson9,BuildingNumberConcepts(468-470);Lesson9,ProblemSolving(471-472)

CCSS.Math.Content.4.NBT.B.5Multiplyawholenumberofuptofourdigitsbyaone-digitwholenumber,andmultiplytwotwo-digitnumbers,usingstrategiesbasedonplacevalueandthepropertiesofoperations.Illustrateandexplainthecalculationbyusingequations,rectangulararrays,and/orareamodels.

Unit3:Lesson2,ProblemSolving(265-267);Lesson4,ProblemSolving(281-282);Lesson5,BuildingNumberConcepts(285-288);Lesson6,BuildingNumberConcepts(293-296);Lesson7,BuildingNumberConcepts(301-304);Lesson7,ProblemSolving(305-306);Lesson8,BuildingNumberConcepts(309-312);Lesson8,ProblemSolving(313-315);Lesson9,BuildingNumberConcepts(318-320);Lesson9,ProblemSolving(321-323);Lesson10,BuildingNumberConcepts(326-328);Lesson11,BuildingNumberConcepts(334-336);Lesson11,ProblemSolving(337-338);Lesson15,BuildingNumberConcepts(360-363)


CCSS.Math.Content.4.NBT.B.6Findwhole-numberquotientsandremainderswithuptofour-digitdividendsandone-digitdivisors,usingstrategiesbasedonplacevalue,thepropertiesofoperations,and/ortherelationshipbetweenmultiplicationanddivision.Illustrateandexplainthecalculationbyusingequations,rectangulararrays,and/orareamodels.

Unit4:Lesson6,BuildingNumberConcepts(422-425);Lesson6,ProblemSolving(426-427);Lesson7,BuildingNumberConcepts(430-431);Lesson7,ProblemSolving(432-435);Lesson8,BuildingNumberConcepts(438-440);Lesson8,ProblemSolving(441-443);Lesson9,BuildingNumberConcepts(445-448);Lesson9,ProblemSolving(449-451);Lesson10,BuildingNumberConcepts



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WhereStandardisAddressed(454-457);Lesson11,BuildingNumberConcepts(462-464);Lesson11,ProblemSolving(465-467);Lesson12,ProblemSolving(470-473);Lesson13,BuildingNumberConcepts(476-480);Lesson13,ProblemSolving(481-483);Lesson14,ProblemSolving(489-491);Lesson15,BuildingNumberConcepts(494-500);Lesson15,ProblemSolving(501-503)

CCSS.Math.Content.4.NF.AExtendunderstandingoffractionequivalenceandordering.

Unit2:Lesson7,BuildingNumberConcepts(160-163);Lesson8,BuildingNumberConcepts(169-174);Lesson9,BuildingNumberConcepts(180-184);Lesson10,BuildingNumberConcepts(189-193);Lesson11,BuildingNumberConcepts(198-201);Lesson12,BuildingNumberConcepts(207-210);Lesson13,BuildingNumberConcepts(215-219)Unit5:Lesson7,BuildingNumberConcepts(545-549)

CCSS.Math.Content.4.NF.A.1Explainwhyafractiona/bisequivalenttoafraction(n×a)/(n×b)byusingvisualfractionmodels,withattentiontohowthenumberandsizeofthepartsdiffereventhoughthetwofractionsthemselvesarethesamesize.Usethisprincipletorecognizeandgenerateequivalentfractions.


Unit2:Lesson7,BuildingNumberConcepts(160-163);Lesson8,BuildingNumberConcepts(169-174);Lesson9,BuildingNumberConcepts(180-184);Lesson10,BuildingNumberConcepts(189-193);Lesson11,BuildingNumberConcepts(198-201);Lesson12,BuildingNumberConcepts(207-210);Lesson13,BuildingNumberConcepts(215-219);Lesson15,BuildingNumberConcepts(232-239);Lesson15,ProblemSolving(240-243)Unit3:Lesson5,BuildingNumberConcepts(288-292);Lesson7,BuildingNumberConcepts(307-310)


CCSS.Math.Content.4.NF.A.2Comparetwofractionswithdifferentnumeratorsanddifferentdenominators,e.g.,bycreatingcommondenominatorsornumerators,orbycomparingtoabenchmarkfractionsuchas1/2.


Unit2:Lesson2,BuildingNumberConcepts(115-117);Lesson2,ProblemSolving(118-120);Lesson3,BuildingNumberConcepts(123-127);Lesson3,ProblemSolving(128-129);Lesson4,BuildingNumberConcepts


Grades 3 - 12

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WhereStandardisAddressedRecognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothesamewhole.Recordtheresultsofcomparisonswithsymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualfractionmodel.

(133-135);Lesson4,ProblemSolving(136-138);Lesson5,BuildingNumberConcepts(141-145);Lesson6,BuildingNumberConcepts(151-154);Lesson15,BuildingNumberConcepts(232-239);Lesson15,ProblemSolving(240-243)

CCSS.Math.Content.4.NF.B.3Understandafractiona/bwitha>1asasumoffractions1/b.

Unit1:Lesson5,BuildingNumberConcepts(40-43);Lesson6,ProblemSolving(51-53);Lesson7,BuildingNumberConcepts(56-58);Lesson7,ProblemSolving(59-62);Lesson8,BuildingNumberConcepts(65-67);Lesson8,ProblemSolving(68-69);Lesson9,BuildingNumberConcepts(72-75);Lesson9,ProblemSolving(76-78);Lesson10,BuildingNumberConcepts(81-88);Lesson10,ProblemSolving(89-92)Unit2:Lesson4,ProblemSolving(136-138)Unit3:Lesson11,BuildingNumberConcepts(342-345)Unit4:Lesson5,BuildingNumberConcepts(438-440)

CCSS.Math.Content.4.NF.B.3aUnderstandadditionandsubtractionoffractionsasjoiningandseparatingpartsreferringtothesamewhole.



CCSS.Math.Content.4.NF.B.3bDecomposeafractionintoasumoffractionswiththesamedenominatorinmorethanoneway,recordingeachdecompositionbyanequation.Justifydecompositions,e.g.,byusingavisualfractionmodel.Examples:3/8=1/8+1/8+1/8;3/8=1/8+2/8;21/8=1+1+1/8=8/8+8/8+1/8.



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WhereStandardisAddressedCCSS.Math.Content.4.NF.B.3cAddandsubtractmixednumberswithlikedenominators,e.g.,byreplacingeachmixednumberwithanequivalentfraction,and/orbyusingpropertiesofoperationsandtherelationshipbetweenadditionandsubtraction.


Unit2:Lesson11,ProblemSolving(202-204)Unit4:Lesson1,BuildingNumberConcepts(397-401);Lesson1,ProblemSolving(402-403)

CCSS.Math.Content.4.NF.B.3dSolvewordproblemsinvolvingadditionandsubtractionoffractionsreferringtothesamewholeandhavinglikedenominators,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.


Unit2:Lesson6,ProblemSolving(155-157);Lesson11,ProblemSolving(202-204)Unit4:Lesson1,ProblemSolving(402-403)


CCSS.Math.Content.4.NF.B.4Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.

Unit1:Lesson3,BuildingNumberConcepts(23-26);Lesson5,BuildingNumberConcepts(40-43);Lesson7,BuildingNumberConcepts(56-58);Lesson8,BuildingNumberConcepts(65-67);Lesson9,BuildingNumberConcepts(72-75);Lesson10,BuildingNumberConcepts(81-88)Unit3:Lesson1,BuildingNumberConcepts(255-259)

CCSS.Math.Content.4.NF.B.4bUnderstandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5);recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)


CCSS.Math.Content.4.NF.B.4cSolvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?

Unit3:Lesson2,BuildingNumberConcepts(265-267);Lesson3,BuildingNumberConcepts(272-275);Lesson3,ProblemSolving(276-277)

CCSS.Math.Content.4.NF.C.5Expressafractionwithdenominator10asanequivalentfraction

Unit5:Lesson2,BuildingNumberConcepts(504-507);Lesson3,BuildingNumber


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WhereStandardisAddressedwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.4Forexample,express3/10as30/100,andadd3/10+4/100=34/100.

Concepts(513-517);Lesson4,BuildingNumberConcepts(522-524);Lesson5,BuildingNumberConcepts(529-533);Lesson6,BuildingNumberConcepts(538-540);Lesson7,BuildingNumberConcepts(545-549);Lesson8,BuildingNumberConcepts(554-557)Unit7:Lesson2,BuildingNumberConcepts(780-782);Lesson5,BuildingNumberConcepts(810-814);Lesson10,BuildingNumberConcepts(844-847)

CCSS.Math.Content.4.NF.C.6Usedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.


Unit5:Lesson2,BuildingNumberConcepts(504-507);Lesson3,BuildingNumberConcepts(513-517);Lesson4,BuildingNumberConcepts(522-524);Lesson5,BuildingNumberConcepts(529-533);Lesson6,BuildingNumberConcepts(538-540);Lesson7,BuildingNumberConcepts(545-549);Lesson8,BuildingNumberConcepts(554-557)Unit7:Lesson1,ProblemSolving(773-777)

CCSS.Math.Content.4.NF.C.7Comparetwodecimalstohundredthsbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualmodel.



CCSS.Math.Content.4.OA.A.2Multiplyordividetosolvewordproblemsinvolvingmultiplicativecomparison,e.g.,byusingdrawingsandequationswithasymbolfortheunknownnumbertorepresenttheproblem,distinguishingmultiplicativecomparisonfromadditivecomparison.1


CCSS.Math.Content.4.OA.B.4Findallfactorpairsforawholenumberintherange1–100.Recognizethatawholenumberisamultipleofeachofitsfactors.Determinewhetheragiven

Unit5:Lesson1,BuildingNumberConcepts(515-518);Lesson3,BuildingNumberConcepts(530-532);Lesson4,BuildingNumberConcepts(538-541);Lesson5,

Unit2:Lesson12,BuildingNumberConcepts(207-210);Lesson13,BuildingNumberConcepts(215-219)Unit3:Lesson5,BuildingNumberConcepts


Grades 3 - 12

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WhereStandardisAddressedwholenumberintherange1–100isamultipleofagivenone-digitnumber.Determinewhetheragivenwholenumberintherange1–100isprimeorcomposite

BuildingNumberConcepts(546-550);Lesson6,BuildingNumberConcepts(555-557);Lesson7,BuildingNumberConcepts(564-567);Lesson8,BuildingNumberConcepts(572-574);Lesson10,BuildingNumberConcepts(586-588);Lesson14,BuildingNumberConcepts(618-620);Lesson15,BuildingNumberConcepts(625-628)Unit6:Lesson1,BuildingNumberConcepts(645-648);Lesson2,BuildingNumberConcepts(654-658);Lesson4,BuildingNumberConcepts(673-676);Lesson5,BuildingNumberConcepts(681-683);Lesson6,BuildingNumberConcepts(687-691);Lesson10,BuildingNumberConcepts(722-726)Unit7:Lesson2,BuildingNumberConcepts(752-755);Lesson3,BuildingNumberConcepts(760-762);Lesson4,BuildingNumberConcepts(767-769);Lesson5,BuildingNumberConcepts(775-777);Lesson6,BuildingNumberConcepts(782-784);Lesson9,BuildingNumberConcepts(806-809);Lesson10,BuildingNumberConcepts(815-820)

(288-292)Unit9:Lesson9,BuildingNumberConcepts(1062-1065)

CCSS.Math.Content.4.OA.C.5Generateanumberorshapepatternthatfollowsagivenrule.Identifyapparentfeaturesofthepatternthatwerenotexplicitintheruleitself.Forexample,giventherule“Add3”andthestartingnumber1,generatetermsintheresultingsequenceandobservethatthetermsappeartoalternatebetweenoddandevennumbers.Explaininformallywhythenumberswillcontinuetoalternateinthisway.



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CCSS.Math.Content.5.G.A.1Useapairofperpendicularnumberlines,calledaxes,todefineacoordinatesystem,withtheintersectionofthelines(theorigin)arrangedtocoincidewiththe0oneachlineandagivenpointintheplanelocatedbyusinganorderedpairofnumbers,calleditscoordinates.Understandthatthefirstnumberindicateshowfartotravelfromtheorigininthedirectionofoneaxis,andthesecondnumberindicateshowfartotravelinthedirectionofthesecondaxis,withtheconventionthatthenamesofthetwoaxesandthecoordinatescorrespond(e.g.,x-axisandx-coordinate,y-axisandy-coordinate).

Unit8:Lesson8,ProblemSolving(923-925);Lesson10,ProblemSolving(934-939);Lesson11,ProblemSolving(944-950)Unit9:Lesson1,ProblemSolving(1004-1006);Lesson2,ProblemSolving(1014-1016)

CCSS.Math.Content.5.G.A.2Representrealworldandmathematicalproblemsbygraphingpointsinthefirstquadrantofthecoordinateplane,andinterpretcoordinatevaluesofpointsinthecontextofthesituation.


CCSS.Math.Content.5.G.B.3Understandthatattributesbelongingtoacategoryoftwodimensionalfiguresalsobelongtoallsubcategoriesofthatcategory.Forexample,allrectangleshavefourrightanglesandsquaresarerectangles,soallsquareshavefourrightangles.


CCSS.Math.Content.5.G.B.4Classifytwo-dimensionalfiguresinahierarchybasedonproperties.


CCSS.Math.Content.5.MD.A.1Convertamongdifferent-sizedstandardmeasurementunitswithinagivenmeasurementsystem(e.g.,convert5cmto0.05m);andusetheseconversionsinsolvingmulti-step,realworldproblems.

Unit3:Lesson2,ProblemSolving(265-267);Lesson3,ProblemSolving(273-275)Unit4:Lesson1,ProblemSolving(386-388)


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WhereStandardisAddressedCCSS.Math.Content.5.MD.C.3bAsolidfigurewhichcanbepackedwithoutgapsoroverlapsusingnunitcubesissaidtohaveavolumeofncubicunits.

CCSS.Math.Content.5.NBT.A.1Recognizethatinamulti-digitnumber,adigitinoneplacerepresents10timesasmuchasitrepresentsintheplacetoitsrightand1/10ofwhatitrepresentsintheplacetoitsleft.

Unit 5: Lesson4, BuildingNumberConcepts(522-524)

CCSS.Math.Content.5.NBT.A.2Explainpatternsinthenumberofzerosoftheproductwhenmultiplyinganumberbypowersof10,andexplainpatternsintheplacementofthedecimalpointwhenadecimalismultipliedordividedbyapowerof10.Usewhole-numberexponentstodenotepowersof10.

Unit3:Lesson3,BuildingNumberConcepts(270-272);Lesson15,BuildingNumberConcepts(360-363)Unit7:Lesson2,BuildingNumberConcepts(752-755);Lesson3,BuildingNumberConcepts(760-762);Lesson4,BuildingNumberConcepts(767-769)

CCSS.Math.Content.5.NBT.A.3Read,write,andcomparedecimalstothousandths.



CCSS.Math.Content.5.NBT.A.3bComparetwodecimalstothousandthsbasedonmeaningsofthedigitsineachplace,using>,=,and<symbolstorecordtheresultsofcomparisons.


CCSS.Math.Content.5.NBT.A.4Useplacevalueunderstandingtorounddecimalstoanyplace.


Unit5:Lesson12,BuildingNumberConcepts(589-593);Lesson15,BuildingNumberConcepts(616-620)Unit6:Lesson2,BuildingNumberConcepts(649-652);Lesson3,BuildingNumberConcepts(657-660);Lesson8,BuildingNumberConcepts(692-694);Lesson13,BuildingNumberConcepts(733-735);Lesson14,BuildingNumberConcepts(740-744);Lesson15,BuildingNumberConcepts(747-751)


CCSS.Math.Content.5.NBT.B.5Fluentlymultiplymulti-digitwholenumbersusingthestandardalgorithm.



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WhereStandardisAddressedCCSS.Math.Content.5.NBT.B.6Findwhole-numberquotientsofwholenumberswithuptofour-digitdividendsandtwo-digitdivisors,usingstrategiesbasedonplacevalue,thepropertiesofoperations,and/ortherelationshipbetweenmultiplicationanddivision.Illustrateandexplainthecalculationbyusingequations,rectangulararrays,and/orareamodels.


CCSS.Math.Content.5.NBT.B.7Add,subtract,multiply,anddividedecimalstohundredths,usingconcretemodelsordrawingsandstrategiesbasedonplacevalue,propertiesofoperations,and/ortherelationshipbetweenadditionandsubtraction;relatethestrategytoawrittenmethodandexplainthereasoningused.


Unit1:Lesson9,BuildingNumberConcepts(95-97);Lesson11,BuildingNumberConcepts(112-114);Lesson12,BuildingNumberConcepts(120-123);Lesson13,BuildingNumberConcepts(128-131);Lesson14,BuildingNumberConcepts(138-140);Lesson15,BuildingNumberConcepts(145-152)

CCSS.Math.Content.5.NF.A.1Addandsubtractfractionswithunlikedenominators(includingmixednumbers)byreplacinggivenfractionswithequivalentfractionsinsuchawayastoproduceanequivalentsumordifferenceoffractionswithlikedenominators.Forexample,2/3+5/4=8/12+15/12=23/12.(Ingeneral,a/b+c/d=(ad+bc)/bd.)

Unit9:Lesson4,BuildingNumberConcepts(997-1000);Lesson6,BuildingNumberConcepts(1012-1015);Lesson8,BuildingNumberConcepts(1028-1031);Lesson8,ProblemSolving(1032-1033);Lesson9,ProblemSolving(1036-1038);Lesson10,BuildingNumberConcepts(1041-1044)

Unit2:Lesson8,BuildingNumberConcepts(169-174);Lesson9,BuildingNumberConcepts(180-184);Lesson10,BuildingNumberConcepts(189-193);Lesson11,BuildingNumberConcepts(198-201);Lesson12,BuildingNumberConcepts(207-210);Lesson12,ProblemSolving(211-212);Lesson13,BuildingNumberConcepts(215-219);Lesson13,ProblemSolving(220-221);Lesson14,BuildingNumberConcepts(224-227);Lesson14,ProblemSolving(228-229);Lesson15,BuildingNumberConcepts(232-239);Lesson15,ProblemSolving(240-243)Unit4:Lesson2,BuildingNumberConcepts(406-411);Lesson2,ProblemSolving(412-413);Lesson3,BuildingNumberConcepts(416-422);Lesson4,BuildingNumberConcepts(428-431);Lesson8,BuildingNumberConcepts(462-463);Lesson9,ProblemSolving(471-472);Lesson10,BuildingNumberConcepts(475-477)



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WhereStandardisAddressedCCSS.Math.Content.5.NF.A.2Solvewordproblemsinvolvingadditionandsubtractionoffractionsreferringtothesamewhole,includingcasesofunlikedenominators,e.g.,byusingvisualfractionmodelsorequationstorepresenttheproblem.Usebenchmarkfractionsandnumbersenseoffractionstoestimatementallyandassessthereasonablenessofanswers.Forexample,recognizeanincorrectresult2/5+1/2=3/7,byobservingthat3/7<1/2.

Unit9:Lesson4,BuildingNumberConcepts(997-1000);Lesson6,BuildingNumberConcepts(1012-1015);Lesson8,BuildingNumberConcepts(1028-1031);Lesson9,ProblemSolving(1036-1038);Lesson10,BuildingNumberConcepts(1041-1044)

Unit2:Lesson8,ProblemSolving(175-177);Lesson9,ProblemSolving(185-186);Lesson12,ProblemSolving(211-212);Lesson13,ProblemSolving(220-221);Lesson14,ProblemSolving(228-229);Lesson15,ProblemSolving(240-243)Unit3:Lesson14,ProblemSolving(372-374)Unit4:Lesson2,ProblemSolving(412-413);Lesson9,BuildingNumberConcepts(468-470);Lesson9,ProblemSolving(471-472)

CCSS.Math.Content.5.NF.BApplyandextendpreviousunderstandingsofmultiplicationanddivisiontomultiplyanddividefractions.


CCSS.Math.Content.5.NF.B.3Interpretafractionasdivisionofthenumeratorbythedenominator(a/b=a÷b).Solvewordproblemsinvolvingdivisionofwholenumbersleadingtoanswersintheformoffractionsormixednumbers,e.g.,byusingvisualfractionmodelsorequationstorepresenttheproblem.Forexample,interpret3/4astheresultofdividing3by4,notingthat3/4multipliedby4equals3,andthatwhen3wholesaresharedequallyamong4peopleeachpersonhasashareofsize3/4.If9peoplewanttosharea50-poundsackofriceequallybyweight,howmanypoundsofriceshouldeachpersonget?Betweenwhattwowholenumbersdoesyouranswerlie?

Unit3:Lesson11,BuildingNumberConcepts(342-345)Unit5:Lesson9,BuildingNumberConcepts(563-568);Lesson10,BuildingNumberConcepts(573-576);Lesson14,BuildingNumberConcepts(606-611);Lesson15,BuildingNumberConcepts(616-620)Unit7:Lesson1,ProblemSolving(773-777);Lesson2,BuildingNumberConcepts(780-782);Lesson5,BuildingNumberConcepts(810-814);Lesson10,BuildingNumberConcepts(844-847)

CCSS.Math.Content.5.NF.B.4Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionorwholenumberbyafraction.


Unit3:Lesson4,BuildingNumberConcepts(280-282);Lesson7,BuildingNumberConcepts(307-310);Lesson13,BuildingNumberConcepts(360-364);Lesson14,BuildingNumberConcepts(369-371);Lesson15,BuildingNumberConcepts(376-381)Unit4:Lesson6,BuildingNumberConcepts(445-448);Lesson6,ProblemSolving(449-450);Lesson8,BuildingNumberConcepts



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WhereStandardisAddressed(462-463);Lesson10,BuildingNumberConcepts(475-477)

CCSS.Math.Content.5.NF.B.4bFindtheareaofarectanglewithfractionalsidelengthsbytilingitwithunitsquaresoftheappropriateunitfractionsidelengths,andshowthattheareaisthesameaswouldbefoundbymultiplyingthesidelengths.Multiplyfractionalsidelengthstofindareasofrectangles,andrepresentfractionproductsasrectangularareas.


CCSS.Math.Content.5.NF.B.5aComparingthesizeofaproducttothesizeofonefactoronthebasisofthesizeoftheotherfactor,withoutperformingtheindicatedmultiplication.


CCSS.Math.Content.5.NF.B.5bExplainingwhymultiplyingagivennumberbyafractiongreaterthan1resultsinaproductgreaterthanthegivennumber(recognizingmultiplicationbywholenumbersgreaterthan1asafamiliarcase);explainingwhymultiplyingagivennumberbyafractionlessthan1resultsinaproductsmallerthanthegivennumber;andrelatingtheprincipleoffractionequivalencea/b=(n×a)/(n×b)totheeffectofmultiplyinga/bby1.


CCSS.Math.Content.5.NF.B.6Solverealworldproblemsinvolvingmultiplicationoffractionsandmixednumbers,e.g.,byusingvisualfractionmodelsorequationstorepresenttheproblem.

Unit3:Lesson9,ProblemSolving(331-332);Lesson11,ProblemSolving(346-347);Lesson14,ProblemSolving(372-374)Unit4:Lesson6,ProblemSolving(449-450)


CCSS.Math.Content.5.NF.B.7aInterpretdivisionofaunitfractionbyanon-zerowholenumberandcomputesuchquotients.Forexample,createastorycontextfor(1/3)÷4,anduseavisualfractionmodeltoshowthequotient.Usetherelationshipbetweenmultiplicationanddivisiontoexplainthat(1/3)÷4=1/12because(1/12)×4=1/3.



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WhereStandardisAddressedCCSS.Math.Content.5.NF.B.7bInterpretdivisionofawholenumberbyaunitfraction,andcomputesuchquotients.Forexample,createastorycontextfor4÷(1/5);anduseavisualfractionmodeltoshowthequotient.Usetherelationshipbetweenmultiplicationanddivisiontoexplainthat4÷(1/5)=20because20×(1/5)=4.








CCSS.Math.Content.6.RP.AUnderstandratioconceptsanduseratioreasoningtosolveproblems.

Unit2:Lesson3,BuildingNumberConcepts(193-196);Lesson7,BuildingNumberConcepts(227-229);Lesson13,BuildingNumberConcepts(284-285)Unit3:Lesson1,ProblemSolving(331-335);Lesson2,ProblemSolving(342-344);Lesson4,ProblemSolving(358-361);Lesson6,ProblemSolving(374-380);Lesson8,ProblemSolving(392-396);Lesson10,ProblemSolving(414-417)

CCSS.Math.Content.6.RP.A.1Understandtheconceptofaratioanduseratiolanguagetodescribearatiorelationshipbetweentwoquantities.Forexample,“Theratioofwingstobeaksinthebirdhouseatthezoowas2:1,becauseforevery2wingstherewas1beak.”“ForeveryvotecandidateAreceived,candidateCreceivednearlythreevotes.”

Unit2:Lesson1,ProblemSolving(175-177);Lesson2,ProblemSolving(186-189);Lesson3,BuildingNumberConcepts(193-196);Lesson3,ProblemSolving(197-198);Lesson4,ProblemSolving(206-208);Lesson6,ProblemSolving(221-224);Lesson7,BuildingNumberConcepts(227-229);Lesson7,ProblemSolving(232-231);Lesson13,BuildingNumberConcepts(284-285);Lesson15,ProblemSolving(308-313)Unit3:Lesson1,ProblemSolving(331-335);Lesson2,ProblemSolving(342-344);Lesson4,ProblemSolving(358-361);Lesson6,ProblemSolving(374-380);Lesson8,Problem


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WhereStandardisAddressedSolving(392-396);Lesson10,ProblemSolving(414-417)

CCSS.Math.Content.6.RP.A.2Understandtheconceptofaunitratea/bassociatedwitharatioa:bwithb≠0,anduseratelanguageinthecontextofaratiorelationship.Forexample,“Thisrecipehasaratioof3cupsofflourto4cupsofsugar,sothereis3/4cupofflourforeachcupofsugar.”“Wepaid$75for15hamburgers,whichisarateof$5perhamburger.”1

Unit2:Lesson3,ProblemSolving(197-198);Lesson4,ProblemSolving(206-208);Lesson6,ProblemSolving(221-224);Lesson7,ProblemSolving(232-231);Lesson15,ProblemSolving(308-313)Unit3:Lesson2,ProblemSolving(342-344);Lesson4,ProblemSolving(358-361);Lesson6,ProblemSolving(374-380);Lesson8,ProblemSolving(392-396);Lesson10,ProblemSolving(414-417)

CCSS.Math.Content.6.RP.A.3Useratioandratereasoningtosolvereal-worldandmathematicalproblems,e.g.,byreasoningabouttablesofequivalentratios,tapediagrams,doublenumberlinediagrams,orequations.

Unit2:Lesson3,ProblemSolving(197-198);Lesson4,ProblemSolving(206-208);Lesson6,ProblemSolving(221-224);Lesson7,ProblemSolving(232-231);Lesson10,ProblemSolving(254-256);Lesson11,ProblemSolving(268-270);Lesson12,ProblemSolving(278-280);Lesson13,ProblemSolving(286-289);Lesson14,ProblemSolving(297-298);Lesson15,ProblemSolving(308-313)Unit3:Lesson2,ProblemSolving(342-344);Lesson4,ProblemSolving(358-361);Lesson6,ProblemSolving(374-380);Lesson8,ProblemSolving(392-396);Lesson10,ProblemSolving(414-417);Lesson3,ProblemSolving(453-456)Unit7:Lesson9,BuildingNumberConcepts(831-833);Lesson10,BuildingNumberConcepts(839-843)

CCSS.Math.Content.6.RP.A.3aMaketablesofequivalentratiosrelatingquantitieswithwholenumbermeasurements,findmissingvaluesinthetables,andplotthepairsofvaluesonthecoordinateplane.Usetablestocompareratios.



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WhereStandardisAddressed Unit3:Lesson1,ProblemSolving(331-335);

Lesson2,ProblemSolving(342-344);Lesson4,ProblemSolving(358-361);Lesson6,ProblemSolving(374-380);Lesson8,ProblemSolving(392-396);Lesson10,ProblemSolving(414-417)

CCSS.Math.Content.6.RP.A.3bSolveunitrateproblemsincludingthoseinvolvingunitpricingandconstantspeed.Forexample,ifittook7hourstomow4lawns,thenatthatrate,howmanylawnscouldbemowedin35hours?Atwhatratewerelawnsbeingmowed?

Unit2:Lesson4,ProblemSolving(206-208);Lesson6,ProblemSolving(221-224);Lesson7,ProblemSolving(232-231);Lesson15,ProblemSolving(308-313)Unit3:Lesson1,ProblemSolving(331-335);Lesson2,ProblemSolving(342-344);Lesson4,ProblemSolving(358-361);Lesson6,ProblemSolving(374-380);Lesson8,ProblemSolving(392-396);Lesson10,ProblemSolving(414-417)Unit8:Lesson6,ProblemSolving(912-915)

CCSS.Math.Content.6.RP.A.3cFindapercentofaquantityasarateper100(e.g.,30%ofaquantitymeans30/100timesthequantity);solveproblemsinvolvingfindingthewhole,givenapartandthepercent.

Unit4:Lesson1,ProblemSolving(433-435);Lesson2,ProblemSolving(441-445);Lesson3,ProblemSolving(453-456)

CCSS.Math.Content.6.RP.A.3cFindapercentofaquantityasarateper100(e.g.,30%ofaquantitymeans30/100timesthequantity);solveproblemsinvolvingfindingthewhole,givenapartandthepercent.

Unit7:Lesson1,BuildingNumberConcepts(769-772);Lesson1,ProblemSolving(773-777);Lesson2,BuildingNumberConcepts(780-782);Lesson3,BuildingNumberConcepts(790-792);Lesson5,BuildingNumberConcepts(810-814);Lesson10,BuildingNumberConcepts(844-847)

CCSS.Math.Content.6.EE.AApplyandextendpreviousunderstandingsofarithmetictoalgebraicexpressions.

Unit4:Lesson4,BuildingNumberConcepts(460-463)Unit5:Lesson6,BuildingNumberConcepts(588-594);Lesson7,BuildingNumberConcepts(597-601);Lesson8,BuildingNumberConcepts(608-612);Lesson10,BuildingNumberConcepts(622-627)Unit6:Lesson1,BuildingNumberConcepts(643-650);Lesson3,BuildingNumberConcepts(664-670);Lesson4,Building


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WhereStandardisAddressedNumberConcepts(678-683);Lesson5,BuildingNumberConcepts(686-689);Lesson7,BuildingNumberConcepts(703-709);Lesson10,BuildingNumberConcepts(728-732)

CCSS.Math.Content.6.EE.A.1Writeandevaluatenumericalexpressionsinvolvingwhole-numberexponents.


Unit4:Lesson4,BuildingNumberConcepts(460-463)Unit5:Lesson6,BuildingNumberConcepts(588-594);Lesson7,BuildingNumberConcepts(597-601);Lesson8,BuildingNumberConcepts(608-612);Lesson10,BuildingNumberConcepts(622-627)

CCSS.Math.Content.6.EE.A.2Write,read,andevaluateexpressionsinwhichlettersstandfornumbers.

Unit2:Lesson11,BuildingNumberConcepts(262-267);Lesson12,BuildingNumberConcepts(274-277)Unit4:Lesson4,BuildingNumberConcepts(460-463);Lesson7,BuildingNumberConcepts(489-491);Lesson9,BuildingNumberConcepts(508-510);Lesson10,BuildingNumberConcepts(518-523)Unit5:Lesson6,BuildingNumberConcepts(588-594);Lesson7,BuildingNumberConcepts(597-601);Lesson8,BuildingNumberConcepts(608-612);Lesson10,BuildingNumberConcepts(622-627)Unit6:Lesson4,BuildingNumberConcepts(678-683);Lesson5,BuildingNumberConcepts(686-689);Lesson7,BuildingNumberConcepts(703-709);Lesson10,BuildingNumberConcepts(728-732)

CCSS.Math.Content.6.EE.A.2aWriteexpressionsthatrecordoperationswithnumbersandwithlettersstandingfornumbers.Forexample,expressthecalculation“Subtractyfrom5”as5–y.

Unit2:Lesson11,BuildingNumberConcepts(262-267);Lesson12,BuildingNumberConcepts(274-277)Unit4:Lesson10,BuildingNumberConcepts(518-523)Unit5:Lesson6,BuildingNumberConcepts(588-594);Lesson7,BuildingNumberConcepts(597-601);Lesson8,BuildingNumberConcepts(608-612);Lesson10,


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WhereStandardisAddressedBuildingNumberConcepts(622-627)Unit6:Lesson1,BuildingNumberConcepts(643-650)Unit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915)

CCSS.Math.Content.6.EE.A.2bIdentifypartsofanexpressionusingmathematicalterms(sum,term,product,factor,quotient,coefficient);viewoneormorepartsofanexpressionasasingleentity.Forexample,describetheexpression2(8+7)asaproductoftwofactors;view(8+7)asbothasingleentityandasumoftwoterms.

Unit2:Lesson11,BuildingNumberConcepts(262-267);Lesson12,BuildingNumberConcepts(274-277)Unit5:Lesson6,BuildingNumberConcepts(588-594);Lesson7,BuildingNumberConcepts(597-601);Lesson8,BuildingNumberConcepts(608-612);Lesson10,BuildingNumberConcepts(622-627)Unit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915)

CCSS.Math.Content.6.EE.A.2cEvaluateexpressionsatspecificvaluesoftheirvariables.Includeexpressionsthatarisefromformulasusedinreal-worldproblems.Performarithmeticoperations,includingthoseinvolvingwholenumberexponents,intheconventionalorderwhentherearenoparenthesestospecifyaparticularorder(OrderofOperations).Forexample,usetheformulasV=s3andA=6s2tofindthevolumeandsurfaceareaofacubewithsidesoflengths=1/2.

Unit5:Lesson1,BuildingNumberConcepts(541-545);Lesson2,BuildingNumberConcepts(553-555);Lesson3,BuildingNumberConcepts(561-564);Lesson10,BuildingNumberConcepts(622-627)Unit6:Lesson1,BuildingNumberConcepts(643-650);Lesson3,BuildingNumberConcepts(664-670)Unit7:Lesson1,BuildingNumberConcepts(751-754);Lesson2,BuildingNumberConcepts(763-765);Lesson3,BuildingNumberConcepts(772-777);Lesson4,BuildingNumberConcepts(780-785);Lesson8,BuildingNumberConcepts(822-825);Lesson9,BuildingNumberConcepts(831-833);Lesson10,BuildingNumberConcepts


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WhereStandardisAddressed(839-843)Unit10:Lesson7,BuildingNumberConcepts(1211-1214)

CCSS.Math.Content.6.EE.A.3Applythepropertiesofoperationstogenerateequivalentexpressions.Forexample,applythedistributivepropertytotheexpression3(2+x)toproducetheequivalentexpression6+3x;applythedistributivepropertytotheexpression24x+18ytoproducetheequivalentexpression6(4x+3y);applypropertiesofoperationstoy+y+ytoproducetheequivalentexpression3y.

Unit5:Lesson7,BuildingNumberConcepts(597-601);Lesson8,BuildingNumberConcepts(608-612);Lesson10,BuildingNumberConcepts(622-627)Unit7:Lesson2,BuildingNumberConcepts(763-765);Lesson3,BuildingNumberConcepts(772-777);Lesson4,BuildingNumberConcepts(780-785);Lesson8,BuildingNumberConcepts(822-825);Lesson9,BuildingNumberConcepts(831-833);Lesson10,BuildingNumberConcepts(839-843)

CCSS.Math.Content.6.EE.A.4Identifywhentwoexpressionsareequivalent(i.e.,whenthetwoexpressionsnamethesamenumberregardlessofwhichvalueissubstitutedintothem).Forexample,theexpressionsy+y+yand3yareequivalentbecausetheynamethesamenumberregardlessofwhichnumberystandsfor.


CCSS.Math.Content.6.EE.BReasonaboutandsolveone-variableequationsandinequalities.

Unit2:Lesson1,BuildingNumberConcepts(171-174);Lesson2,BuildingNumberConcepts(181-185);Lesson4,BuildingNumberConcepts(202-205);Lesson5,BuildingNumberConcepts(211-213);Lesson6,BuildingNumberConcepts(218-220);Lesson9,BuildingNumberConcepts(244-248);Lesson14,BuildingNumberConcepts(293-296);Lesson15,BuildingNumberConcepts(301-307)Unit3:Lesson1,BuildingNumberConcepts(325-330);Lesson2,BuildingNumberConcepts(339-341);Lesson3,BuildingNumberConcepts(348-351);Lesson4,BuildingNumberConcepts(355-357);Lesson


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WhereStandardisAddressed5,BuildingNumberConcepts(365-369);Lesson7,BuildingNumberConcepts(383-386);Lesson7,ProblemSolving(387-389);Lesson9,BuildingNumberConcepts(400-402);Lesson9,ProblemSolving(403-404);Lesson10,BuildingNumberConcepts(408-413)Unit7:Lesson3,BuildingNumberConcepts(772-777);Lesson4,BuildingNumberConcepts(780-785);Lesson6,BuildingNumberConcepts(801-804);Lesson7,BuildingNumberConcepts(811-815);Lesson8,BuildingNumberConcepts(822-825);Lesson9,BuildingNumberConcepts(831-833);Lesson10,BuildingNumberConcepts(839-843)Unit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915)

CCSS.Math.Content.6.EE.B.5Understandsolvinganequationorinequalityasaprocessofansweringaquestion:whichvaluesfromaspecifiedset,ifany,maketheequationorinequalitytrue?Usesubstitutiontodeterminewhetheragivennumberinaspecifiedsetmakesanequationorinequalitytrue.

Unit2:Lesson1,BuildingNumberConcepts(171-174);Lesson2,BuildingNumberConcepts(181-185);Lesson4,BuildingNumberConcepts(202-205);Lesson5,BuildingNumberConcepts(211-213);Lesson6,BuildingNumberConcepts(218-220);Lesson9,BuildingNumberConcepts(244-248)Unit3:Lesson1,BuildingNumberConcepts(325-330);Lesson2,BuildingNumberConcepts(339-341);Lesson3,BuildingNumberConcepts(348-351);Lesson4,BuildingNumberConcepts(355-357);Lesson5,BuildingNumberConcepts(365-369);Lesson7,BuildingNumberConcepts(383-386);Lesson7,ProblemSolving(387-389)Lesson9,BuildingNumberConcepts(400-


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WhereStandardisAddressed402);Lesson9,ProblemSolving(403-404);Lesson10,BuildingNumberConcepts(408-413)Unit7:Lesson3,BuildingNumberConcepts(772-777);Lesson4,BuildingNumberConcepts(780-785);Lesson6,BuildingNumberConcepts(801-804);Lesson7,BuildingNumberConcepts(811-815);Lesson8,BuildingNumberConcepts(822-825);Lesson9,BuildingNumberConcepts(831-833);Lesson10,BuildingNumberConcepts(839-843)Unit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915)

CCSS.Math.Content.6.EE.B.6Usevariablestorepresentnumbersandwriteexpressionswhensolvingareal-worldormathematicalproblem;understandthatavariablecanrepresentanunknownnumber,or,dependingonthepurposeathand,anynumberinaspecifiedset.


CCSS.Math.Content.6.EE.B.7Solvereal-worldandmathematicalproblemsbywritingandsolvingequationsoftheformx+p=qandpx=qforcasesinwhichp,qandxareallnonnegativerationalnumbers.

Unit2:Lesson14,BuildingNumberConcepts(293-296);Lesson15,BuildingNumberConcepts(301-307)Unit4:Lesson1,BuildingNumberConcepts(429-432);Lesson3,BuildingNumberConcepts(448-452);Lesson5,BuildingNumberConcepts(471-475);Lesson6,BuildingNumberConcepts(480-483);Lesson8,BuildingNumberConcepts(498-501);Lesson10,BuildingNumberConcepts(518-523)Unit7:Lesson7,BuildingNumberConcepts(811-815)


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WhereStandardisAddressedUnit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915)

CCSS.Math.Content.6.EE.B.8Writeaninequalityoftheformx>corx<ctorepresentaconstraintorconditioninareal-worldormathematicalproblem.Recognizethatinequalitiesoftheformx>corx<chaveinfinitelymanysolutions;representsolutionsofsuchinequalitiesonnumberlinediagrams.

Unit3:Lesson1,BuildingNumberConcepts(325-330);Lesson2,BuildingNumberConcepts(339-341);Lesson3,BuildingNumberConcepts(348-351);Lesson4,BuildingNumberConcepts(355-357);Lesson5,BuildingNumberConcepts(365-369);Lesson7,BuildingNumberConcepts(383-386);Lesson7,ProblemSolving(387-389);Lesson9,BuildingNumberConcepts(400-402);Lesson9,ProblemSolving(403-404);Lesson10,BuildingNumberConcepts(408-413)

CCSS.Math.Content.6.EE.CRepresentandanalyzequantitativerelationshipsbetweendependentandindependentvariables.


CCSS.Math.Content.6.EE.C.9Usevariablestorepresenttwoquantitiesinareal-worldproblemthatchangeinrelationshiptooneanother;writeanequationtoexpressonequantity,thoughtofasthedependentvariable,intermsoftheotherquantity,thoughtofastheindependentvariable.Analyzetherelationshipbetweenthedependentandindependentvariablesusinggraphsandtables,andrelatethesetotheequation.Forexample,inaprobleminvolvingmotionatconstantspeed,listandgraphorderedpairsofdistancesandtimes,andwritetheequationd=65ttorepresenttherelationshipbetweendistanceandtime.



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WhereStandardisAddressedCCSS.Math.Content.6.G.ASolvereal-worldandmathematicalproblemsinvolvingarea,surfacearea,andvolume.

Unit2:Lesson8,BuildingNumberConcepts(234-237)Unit6:Lesson1,ProblemSolving(651-653);Lesson2,ProblemSolving(656-661);Lesson3,ProblemSolving(671-675);Lesson9,ProblemSolving(717-724);Lesson10,ProblemSolving(733-739)

CCSS.Math.Content.6.G.A.1Findtheareaofrighttriangles,othertriangles,specialquadrilaterals,andpolygonsbycomposingintorectanglesordecomposingintotrianglesandothershapes;applythesetechniquesinthecontextofsolvingreal-worldandmathematicalproblems.



Unit2:Lesson8,BuildingNumberConcepts(234-237);Lesson15,BuildingNumberConcepts(301-307)Unit10:Lesson1,BuildingNumberConcepts(1159-1167);Lesson2,BuildingNumberConcepts(1170-1175);Lesson3,BuildingNumberConcepts(1178-1185)

CCSS.Math.Content.6.G.A.2Findthevolumeofarightrectangularprismwithfractionaledgelengthsbypackingitwithunitcubesoftheappropriateunitfractionedgelengths,andshowthatthevolumeisthesameaswouldbefoundbymultiplyingtheedgelengthsoftheprism.ApplytheformulasV=lwhandV=bhtofindvolumesofrightrectangularprismswithfractionaledgelengthsinthecontextofsolvingreal-worldandmathematicalproblems.


CCSS.Math.Content.6.G.A.3Drawpolygonsinthecoordinateplanegivencoordinatesforthevertices;usecoordinatestofindthelengthofasidejoiningpointswiththesamefirstcoordinateorthesamesecondcoordinate.Applythesetechniquesinthecontextofsolvingreal-worldandmathematicalproblems.


CCSS.Math.Content.6.G.A.4Representthree-dimensionalfiguresusingnetsmadeupofrectanglesandtriangles,andusethenetstofindthesurfaceareaofthesefigures.Applythesetechniquesinthecontextofsolvingreal-worldandmathematicalproblems.

Unit3:Lesson2,ProblemSolving(265-267) Unit5:Lesson1,ProblemSolving(546-550);Lesson2,ProblemSolving(556-558);Lesson3,ProblemSolving(565-567)


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WhereStandardisAddressedCCSS.Math.Content.6.NS.AApplyandextendpreviousunderstandingsofmultiplicationanddivisiontodividefractionsbyfractions.


CCSS.Math.Content.6.NS.A.1Interpretandcomputequotientsoffractions,andsolvewordproblemsinvolvingdivisionoffractionsbyfractions,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,createastorycontextfor(2/3)÷(3/4)anduseavisualfractionmodeltoshowthequotient;usetherelationshipbetweenmultiplicationanddivisiontoexplainthat(2/3)÷(3/4)=8/9because3/4of8/9is2/3.(Ingeneral,(a/b)÷(c/d)=ad/bc.)Howmuchchocolatewilleachpersongetif3peopleshare1/2lbofchocolateequally?Howmany3/4-cupservingsarein2/3ofacupofyogurt?Howwideisarectangularstripoflandwithlength3/4miandarea1/2squaremi?

Unit3:Lesson8,BuildingNumberConcepts(317-321);Lesson9,BuildingNumberConcepts(326-330);Lesson9,ProblemSolving(331-332);Lesson10,BuildingNumberConcepts(335-337);Lesson11,ProblemSolving(346-347);Lesson13,BuildingNumberConcepts(360-364);Lesson14,BuildingNumberConcepts(369-371);Lesson14,ProblemSolving(372-374);Lesson15,BuildingNumberConcepts(376-381)Unit4:Lesson7,BuildingNumberConcepts(453-456);Lesson8,BuildingNumberConcepts(462-463);Lesson10,BuildingNumberConcepts(475-477)


CCSS.Math.Content.6.NS.B.2Fluentlydividemulti-digitnumbersusingthestandardalgorithm.



CCSS.Math.Content.6.NS.B.3Fluentlyadd,subtract,multiply,anddividemulti-digitdecimalsusingthestandardalgorithmforeachoperation.

Unit6:Lesson1,BuildingNumberConcepts(639-643);Lesson2,BuildingNumberConcepts(649-652);Lesson3,BuildingNumberConcepts(657-660);Lesson7,BuildingNumberConcepts(687-689);Lesson12,BuildingNumberConcepts(725-727);Lesson13,BuildingNumberConcepts(733-735);Lesson13,ProblemSolving(736-737);Lesson14,BuildingNumberConcepts(740-744);Lesson15,BuildingNumberConcepts(747-751)

Unit1:Lesson9,BuildingNumberConcepts(95-97);Lesson12,BuildingNumberConcepts(120-123);Lesson14,BuildingNumberConcepts(138-140);Lesson14,ProblemSolving(141-142);Lesson15,BuildingNumberConcepts(145-152)


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WhereStandardisAddressedCCSS.Math.Content.6.NS.B.4Findthegreatestcommonfactoroftwowholenumberslessthanorequalto100andtheleastcommonmultipleoftwowholenumberslessthanorequalto12.Usethedistributivepropertytoexpressasumoftwowholenumbers1–100withacommonfactorasamultipleofasumoftwowholenumberswithnocommonfactor.Forexample,express36+8as4(9+2).

Unit6:Lesson1,BuildingNumberConcepts(645-648);Lesson2,BuildingNumberConcepts(654-658);Lesson3,BuildingNumberConcepts(664-667);Lesson4,BuildingNumberConcepts(673-676);Lesson5,BuildingNumberConcepts(681-683);Lesson6,BuildingNumberConcepts(687-691);Lesson10,BuildingNumberConcepts(722-726)Unit7:Lesson5,BuildingNumberConcepts(775-777);Lesson6,BuildingNumberConcepts(782-784);Lesson8,BuildingNumberConcepts(796-798);Lesson9,BuildingNumberConcepts(806-809);Lesson10,BuildingNumberConcepts(815-820)

Unit3:Lesson5,BuildingNumberConcepts(288-292);Lesson7,BuildingNumberConcepts(307-310);Lesson8,BuildingNumberConcepts(317-321)Unit4:Lesson4,BuildingNumberConcepts(428-431)

CCSS.Math.Content.6.NS.C.5Understandthatpositiveandnegativenumbersareusedtogethertodescribequantitieshavingoppositedirectionsorvalues(e.g.,temperatureabove/belowzero,elevationabove/belowsealevel,credits/debits,positive/negativeelectriccharge);usepositiveandnegativenumberstorepresentquantitiesinreal-worldcontexts,explainingthemeaningof0ineachsituation.

Unit8:Lesson1,BuildingNumberConcepts(863-865);Lesson3,BuildingNumberConcepts(878-881);Lesson3,ProblemSolving(882-883);Lesson4,BuildingNumberConcepts(886-888);Lesson5,BuildingNumberConcepts(895-899)

CCSS.Math.Content.6.NS.C.6Understandarationalnumberasapointonthenumberline.Extendnumberlinediagramsandcoordinateaxesfamiliarfrompreviousgradestorepresentpointsonthelineandintheplanewithnegativenumbercoordinates

Unit8:Lesson1,BuildingNumberConcepts(863-865);Lesson2,BuildingNumberConcepts(870-875);Lesson3,BuildingNumberConcepts(878-881);Lesson4,BuildingNumberConcepts(886-888);Lesson11,ProblemSolving(944-950);Lesson12,ProblemSolving(953-956);Lesson15,ProblemSolving(983-987)

CCSS.Math.Content.6.NS.C.6aRecognizeoppositesignsofnumbersasindicatinglocationsonoppositesidesof0onthenumberline;recognizethattheoppositeoftheoppositeofanumberisthenumberitself,e.g.,–(–3)=3,andthat0isitsownopposite.

Unit8:Lesson1,BuildingNumberConcepts(863-865);Lesson11,ProblemSolving(944-950);Lesson12,ProblemSolving(953-956);Lesson15,ProblemSolving(983-987)


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WhereStandardisAddressedCCSS.Math.Content.6.NS.C.6bUnderstandsignsofnumbersinorderedpairsasindicatinglocationsinquadrantsofthecoordinateplane;recognizethatwhentwoorderedpairsdifferonlybysigns,thelocationsofthepointsarerelatedbyreflectionsacrossoneorbothaxes.

Unit8:Lesson11,ProblemSolving(944-950);Lesson12,ProblemSolving(953-956);Lesson15,ProblemSolving(983-987)Unit9:Lesson1,ProblemSolving(1004-1006);Lesson2,ProblemSolving(1014-1016);Lesson3,ProblemSolving(1019-1023);Lesson4,ProblemSolving(1031-1032);Lesson5,ProblemSolving(1035-1038);Lesson7,ProblemSolving(1050-1053);Lesson8,ProblemSolving(1056-1059);Lesson10,ProblemSolving(1071-1076)

CCSS.Math.Content.6.NS.C.6cFindandpositionintegersandotherrationalnumbersonahorizontalorverticalnumberlinediagram;findandpositionpairsofintegersandotherrationalnumbersonacoordinateplane.

Unit8:Lesson3,ProblemSolving(882-883);Lesson6,ProblemSolving(908-910);Lesson8,ProblemSolving(923-925);Lesson10,ProblemSolving(934-939);Lesson11,ProblemSolving(944-950);Lesson12,ProblemSolving(953-956);Lesson15,ProblemSolving(983-987)

CCSS.Math.Content.6.NS.C.7aInterpretstatementsofinequalityasstatementsabouttherelativepositionoftwonumbersonanumberlinediagram.Forexample,interpret–3>–7asastatementthat–3islocatedtotherightof–7onanumberlineorientedfromlefttoright.


CCSS.Math.Content.6.NS.C.7cUnderstandtheabsolutevalueofarationalnumberasitsdistancefrom0onthenumberline;interpretabsolutevalueasmagnitudeforapositiveornegativequantityinareal-worldsituation.Forexample,foranaccountbalanceof–30dollars,write|–30|=30todescribethesizeofthedebtindollars.


CCSS.Math.Content.6.NS.C.8Solvereal-worldandmathematicalproblemsbygraphingpointsinallfourquadrantsofthecoordinateplane.Includeuseofcoordinatesandabsolutevaluetofinddistancesbetweenpointswiththe

Unit9:Lesson1,ProblemSolving(1013-1015);Lesson2,ProblemSolving(1022-1024);Lesson3,ProblemSolving(1032-1034);Lesson13,BuildingNumberConcepts(1119-1120)


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WhereStandardisAddressedsamefirstcoordinateorthesamesecondcoordinate.

CCSS.Math.Content.6.SP.ADevelopunderstandingofstatisticalvariability.


CCSS.Math.Content.6.SP.A.2Understandthatasetofdatacollectedtoanswerastatisticalquestionhasadistributionwhichcanbedescribedbyitscenter,spread,andoverallshape.



CCSS.Math.Content.6.SP.A.3Recognizethatameasureofcenterforanumericaldatasetsummarizesallofitsvalueswithasinglenumber,whileameasureofvariationdescribeshowitsvaluesvarywithasinglenumber.



CCSS.Math.Content.6.SP.BSummarizeanddescribedistributions.


CCSS.Math.Content.6.SP.B.4Displaynumericaldatainplotsonanumberline,includingdotplots,histograms,andboxplots.


CCSS.Math.Content.6.SP.B.5Summarizenumericaldatasetsinrelationtotheircontext,suchasby:


CCSS.Math.Content.6.SP.B.5aReportingthenumberofobservations.



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WhereStandardisAddressedCCSS.Math.Content.6.SP.B.5cGivingquantitativemeasuresofcenter(medianand/ormean)andvariability(interquartilerangeand/ormeanabsolutedeviation);aswellasdescribinganyoverallpatternandanystrikingdeviationsfromtheoverallpatternwithreferencetothecontextinwhichthedataweregathered.

Unit8:Lesson1,ProblemSolving(842-844);Lesson2,ProblemSolving(850-851);Lesson3,ProblemSolving(858-861);Lesson4,ProblemSolving(869-871);Lesson5,ProblemSolving(874-876);Lesson6,ProblemSolving(885-887);Lesson7,ProblemSolving(893-894);Lesson11,ProblemSolving(923-925);Lesson12,ProblemSolving(932-933);Lesson14,ProblemSolving(946-947);Lesson15,ProblemSolving(955-958)Unit9:Lesson8,ProblemSolving(1032-1033)








CCSS.Math.Content.7.RP.A.1Computeunitratesassociatedwithratiosoffractions,includingratiosoflengths,areasandotherquantitiesmeasuredinlikeordifferentunits.Forexample,ifapersonwalks1/2mileineach1/4hour,computetheunitrateasthecomplexfraction1/2/1/4milesperhour,equivalently2milesperhour.


CCSS.Math.Content.7.RP.A.2Recognizeandrepresentproportionalrelationshipsbetweenquantities.

Unit2:Lesson6,ProblemSolving(221-224);Lesson7,ProblemSolving(232-231);Lesson15,ProblemSolving(308-313);Lesson2,BuildingNumberConcepts(439-440)

CCSS.Math.Content.7.RP.A.2aDecidewhethertwoquantitiesareinaproportionalrelationship,e.g.,bytestingforequivalentratiosinatableorgraphingonacoordinateplaneandobservingwhetherthegraphisastraightlinethroughtheorigin.



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WhereStandardisAddressedCCSS.Math.Content.7.RP.A.2cRepresentproportionalrelationshipsbyequations.Forexample,iftotalcosttisproportionaltothenumbernofitemspurchasedataconstantpricep,therelationshipbetweenthetotalcostandthenumberofitemscanbeexpressedast=pn.

Unit2:Lesson4,ProblemSolving(206-208);Lesson6,ProblemSolving(221-224);Lesson7,ProblemSolving(232-231);Lesson15,ProblemSolving(308-313)Unit4:Lesson2,BuildingNumberConcepts(439-440);Lesson2,ProblemSolving(441-445);Lesson3,ProblemSolving(453-456);Lesson4,ProblemSolving(464-467);Lesson6,ProblemSolving(484-486);Lesson7,ProblemSolving(492-495);Lesson8,ProblemSolving(502-505);Lesson9,ProblemSolving(511-514);Lesson10,ProblemSolving(524-529)

CCSS.Math.Content.7.RP.A.3Useproportionalrelationshipstosolvemultistepratioandpercentproblems.Examples:simpleinterest,tax,markupsandmarkdowns,gratuitiesandcommissions,fees,percentincreaseanddecrease,percenterror.

Unit4:Lesson2,BuildingNumberConcepts(439-440);Lesson2,ProblemSolving(441-445);Lesson3,ProblemSolving(453-456);Lesson4,ProblemSolving(464-467);Lesson6,ProblemSolving(484-486);Lesson7,ProblemSolving(492-495);Lesson8,ProblemSolving(502-505);Lesson9,ProblemSolving(511-514);Lesson10,ProblemSolving(524-529)

CCSS.Math.Content.7.EE.AUsepropertiesofoperationstogenerateequivalentexpressions.


CCSS.Math.Content.7.EE.A.1Applypropertiesofoperationsasstrategiestoadd,subtract,factor,andexpandlinearexpressionswithrationalcoefficients.



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WhereStandardisAddressedCCSS.Math.Content.7.EE.1.2:Understandthatrewritinganexpressionindifferentformsinaproblemcontextcanshedlightontheproblemandhowthequantitiesinitarerelated.Forexample,a+0.05a=1.05ameansthat"increaseby5%"isthesameas"multiplyby1.05."

LessonSubsection:Level3Unit5:Lessons6,7,8:587–594,596–601,607–612

CCSS.Math.Content.7.EE.BSolvereal-lifeandmathematicalproblemsusingnumericalandalgebraicexpressionsandequations.


CCSS.Math.Content.7.EE.B.3Solvemulti-stepreal-lifeandmathematicalproblemsposedwithpositiveandnegativerationalnumbersinanyform(wholenumbers,fractions,anddecimals);usingtoolsstrategically.Applypropertiesofoperationstocalculatewithnumbersinanyform;convertbetweenformsasappropriate;andassessthereasonablenessofanswersusingmentalcomputationandestimationstrategies.Forexample:Ifawomanmaking$25anhourgetsa10%raise,shewillmakeanadditional1/10ofhersalaryanhour,or$2.50,foranewsalaryof$27.50.Ifyouwanttoplaceatowelbar93/4incheslonginthecenterofadoorthatis271/2incheswide,youwillneedtoplacethebarabout9inchesfromeachedge;thisestimatecanbeusedasacheckontheexactcomputation.

Unit6:Lesson3,BuildingNumberConcepts(664-670)Unit8:Lesson12,BuildingNumberConcepts(962-964);Lesson13,BuildingNumberConcepts(970-974);Lesson14,BuildingNumberConcepts(981-983);Lesson15,BuildingNumberConcepts(989-993)


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WhereStandardisAddressedCCSS.Math.Content.7.EE.B.4Usevariablestorepresentquantitiesinareal-worldormathematicalproblem,andconstructsimpleequationsandinequalitiestosolveproblemsbyreasoningaboutthequantities.

Unit4:Lesson3,BuildingNumberConcepts(448-452);Lesson5,BuildingNumberConcepts(471-475);Lesson6,BuildingNumberConcepts(480-483);Lesson8,BuildingNumberConcepts(498-501);Lesson10,BuildingNumberConcepts(518-523)Unit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915);Lesson7,ProblemSolving(921-925);Lesson8,ProblemSolving(933-935)

CCSS.Math.Content.7.EE.B.4aSolvewordproblemsleadingtoequationsoftheformpx+q=randp(x+q)=r,wherep,q,andrarespecificrationalnumbers.Solveequationsoftheseformsfluently.Compareanalgebraicsolutiontoanarithmeticsolution,identifyingthesequenceoftheoperationsusedineachapproach.Forexample,theperimeterofarectangleis54cm.Itslengthis6cm.Whatisitswidth?

Unit8:Lesson1,ProblemSolving(869-871);Lesson2,ProblemSolving(878-800);Lesson3,ProblemSolving(887-891);Lesson4,ProblemSolving(894-898);Lesson5,ProblemSolving(901-904);Lesson6,ProblemSolving(912-915);Lesson7,ProblemSolving(921-925);Lesson8,ProblemSolving(933-935)

CCSS.Math.Content.7.G.A.1Solveproblemsinvolvingscaledrawingsofgeometricfigures,includingcomputingactuallengthsandareasfromascaledrawingandreproducingascaledrawingatadifferentscale.

Unit3:Lesson12,ProblemSolving(341-343)Unit6:Lesson7,ProblemSolving(700-703);Lesson8,ProblemSolving(709-711);Lesson9,ProblemSolving(718-719);Lesson10,ProblemSolving(727-730)


CCSS.Math.Content.7.G.A.2Draw(freehand,withrulerandprotractor,andwithtechnology)geometricshapeswithgivenconditions.Focusonconstructingtrianglesfromthreemeasuresofanglesorsides,noticingwhentheconditionsdetermineauniquetriangle,morethanonetriangle,ornotriangle.

Unit4:Lesson7,ProblemSolving(457-459);Lesson10,ProblemSolving(478-482)Unit5:Lesson2,ProblemSolving(508-510);Lesson3,ProblemSolving(518-519);Lesson12,ProblemSolving(594-595)


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WhereStandardisAddressedCCSS.Math.Content.7.G.BSolvereal-lifeandmathematicalproblemsinvolvinganglemeasure,area,surfacearea,andvolume.

Unit2:Lesson8,BuildingNumberConcepts(234-237)Unit6:Lesson8,ProblemSolving(712-714)

CCSS.Math.Content.7.G.B.4Knowtheformulasfortheareaandcircumferenceofacircleandusethemtosolveproblems;giveaninformalderivationoftherelationshipbetweenthecircumferenceandareaofacircle.



CCSS.Math.Content.7.G.B.5Usefactsaboutsupplementary,complementary,vertical,andadjacentanglesinamulti-stepproblemtowriteandsolvesimpleequationsforanunknownangleinafigure.

Unit7:Lesson2,ProblemSolving(766-769);Lesson4,ProblemSolving(786-790);Lesson5,ProblemSolving(793-796);Lesson6,ProblemSolving(805-808);Lesson7,ProblemSolving(816-819);Lesson8,ProblemSolving(826-828);Lesson9,ProblemSolving(834-836);Lesson10,ProblemSolving(844-851)

CCSS.Math.Content.7.G.B.6Solvereal-worldandmathematicalproblemsinvolvingarea,volumeandsurfaceareaoftwo-andthree-dimensionalobjectscomposedoftriangles,quadrilaterals,polygons,cubes,andrightprisms.

Unit5:Lesson5,ProblemSolving(578-583);Lesson7,ProblemSolving(602-605);Lesson8,ProblemSolving(613-614);Lesson9,ProblemSolving(617-619);Lesson10,ProblemSolving(628-632);Lesson3,ProblemSolving(671-675);Lesson8,ProblemSolving(712-714);Lesson9,ProblemSolving(717-724);Lesson10,ProblemSolving(733-739)

CCSS.Math.Content.7.NS.AApplyandextendpreviousunderstandingsofoperationswithfractionstoadd,subtract,multiply,anddividerationalnumbers.



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WhereStandardisAddressedCCSS.Math.Content.7.NS.A.1Applyandextendpreviousunderstandingsofadditionandsubtractiontoaddandsubtractrationalnumbers;representadditionandsubtractiononahorizontalorverticalnumberlinediagram.

Unit8:Lesson2,BuildingNumberConcepts(870-875);Lesson5,BuildingNumberConcepts(895-899);Lesson6,BuildingNumberConcepts(904-907);Lesson7,BuildingNumberConcepts(913-916);Lesson8,BuildingNumberConcepts(919-922);Lesson9,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(959-964);Lesson14,BuildingNumberConcepts(967-971);Lesson15,BuildingNumberConcepts(974-982)

CCSS.Math.Content.7.NS.A.1aDescribesituationsinwhichoppositequantitiescombinetomake0.Forexample,ahydrogenatomhas0chargebecauseitstwoconstituentsareoppositelycharged.

Unit8:Lesson2,BuildingNumberConcepts(870-875);Lesson5,BuildingNumberConcepts(895-899);Lesson6,BuildingNumberConcepts(904-907);Lesson7,BuildingNumberConcepts(913-916);Lesson8,BuildingNumberConcepts(919-922);Lesson9,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(959-964);Lesson14,BuildingNumberConcepts(967-971);Lesson15,BuildingNumberConcepts(974-982)

CCSS.Math.Content.7.NS.A.1bUnderstandp+qasthenumberlocatedadistance|q|fromp,inthepositiveornegativedirectiondependingonwhetherqispositiveornegative.Showthatanumberanditsoppositehaveasumof0(areadditiveinverses).Interpretsumsofrationalnumbersbydescribingreal-worldcontexts.

Unit8:Lesson5,BuildingNumberConcepts(895-899);Lesson6,BuildingNumberConcepts(904-907);Lesson7,BuildingNumberConcepts(913-916);Lesson8,BuildingNumberConcepts(919-922);Lesson9,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(959-964);Lesson14,BuildingNumberConcepts(967-971);Lesson15,BuildingNumberConcepts(974-982)Unit9:Lesson3,ProblemSolving(1019-1023);Lesson4,ProblemSolving(1031-1032);Lesson5,ProblemSolving(1035-1038);Lesson6,BuildingNumberConcepts


Grades 3 - 12

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WhereStandardisAddressed(1043-1047);Lesson10,BuildingNumberConcepts(1068-1070)

CCSS.Math.Content.7.NS.A.1cUnderstandsubtractionofrationalnumbersasaddingtheadditiveinverse,p–q=p+(–q).Showthatthedistancebetweentworationalnumbersonthenumberlineistheabsolutevalueoftheirdifference,andapplythisprincipleinreal-worldcontexts.

Unit8:Lesson7,BuildingNumberConcepts(913-916);Lesson8,BuildingNumberConcepts(919-922);Lesson9,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(959-964);Lesson14,BuildingNumberConcepts(967-971);Lesson15,BuildingNumberConcepts(974-982)Unit9:Lesson3,ProblemSolving(1019-1023);Lesson4,ProblemSolving(1031-1032);Lesson5,ProblemSolving(1035-1038);Lesson6,BuildingNumberConcepts(1043-1047);Lesson10,BuildingNumberConcepts(1068-1070)


CCSS.Math.Content.7.NS.A.1dApplypropertiesofoperationsasstrategiestoaddandsubtractrationalnumbers.

Unit8:Lesson9,BuildingNumberConcepts(928-931);Lesson13,BuildingNumberConcepts(959-964);Lesson14,BuildingNumberConcepts(967-971);Lesson15,BuildingNumberConcepts(974-982)Unit9:Lesson6,BuildingNumberConcepts(1043-1047);Lesson10,BuildingNumberConcepts(1068-1070)


CCSS.Math.Content.7.NS.A.2Applyandextendpreviousunderstandingsofmultiplicationanddivisionandoffractionstomultiplyanddividerationalnumbers.



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WhereStandardisAddressedCCSS.Math.Content.7.NS.A.2aUnderstandthatmultiplicationisextendedfromfractionstorationalnumbersbyrequiringthatoperationscontinuetosatisfythepropertiesofoperations,particularlythedistributiveproperty,leadingtoproductssuchas(–1)(–1)=1andtherulesformultiplyingsignednumbers.Interpretproductsofrationalnumbersbydescribingreal-worldcontexts.


CCSS.Math.Content.7.NS.A.2bUnderstandthatintegerscanbedivided,providedthatthedivisorisnotzero,andeveryquotientofintegers(withnon-zerodivisor)isarationalnumber.Ifpandqareintegers,then–(p/q)=(–p)/q=p/(–q).Interpretquotientsofrationalnumbersbydescribingrealworldcontexts.


CCSS.Math.Content.7.NS.A.2cApplypropertiesofoperationsasstrategiestomultiplyanddividerationalnumbers.



CCSS.Math.Content.7.NS.A.2dConvertarationalnumbertoadecimalusinglongdivision;knowthatthedecimalformofarationalnumberterminatesin0soreventuallyrepeats.

Unit5:Lesson9,BuildingNumberConcepts(563-568);Lesson10,BuildingNumberConcepts(573-576)Unit7:Lesson2,BuildingNumberConcepts(780-782)


CCSS.Math.Content.7.NS.A.3Solvereal-worldandmathematicalproblemsinvolvingthefouroperationswithrationalnumbers.



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WhereStandardisAddressedCCSS.Math.Content.7.SP.A.1Understandthatstatisticscanbeusedtogaininformationaboutapopulationbyexaminingasampleofthepopulation;generalizationsaboutapopulationfromasamplearevalidonlyifthesampleisrepresentativeofthatpopulation.Understandthatrandomsamplingtendstoproducerepresentativesamplesandsupportvalidinferences.


CCSS.Math.Content.7.SP.A.2Usedatafromarandomsampletodrawinferencesaboutapopulationwithanunknowncharacteristicofinterest.Generatemultiplesamples(orsimulatedsamples)ofthesamesizetogaugethevariationinestimatesorpredictions.Forexample,estimatethemeanwordlengthinabookbyrandomlysamplingwordsfromthebook;predictthewinnerofaschoolelectionbasedonrandomlysampledsurveydata.Gaugehowfarofftheestimateorpredictionmightbe.


CCSS.Math.Content.7.SP.C.5Understandthattheprobabilityofachanceeventisanumberbetween0and1thatexpressesthelikelihoodoftheeventoccurring.Largernumbersindicategreaterlikelihood.Aprobabilitynear0indicatesanunlikelyevent,aprobabilityaround1/2indicatesaneventthatisneitherunlikelynorlikely,andaprobabilitynear1indicatesalikelyevent.

Unit7:Lesson1,ProblemSolving(773-777);Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,BuildingNumberConcepts(800-804);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,BuildingNumberConcepts(825-828);Lesson7,ProblemSolving(829-831);Lesson10,ProblemSolving(848-851)


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WhereStandardisAddressedCCSS.Math.Content.7.SP.C.6Approximatetheprobabilityofachanceeventbycollectingdataonthechanceprocessthatproducesitandobservingitslong-runrelativefrequency,andpredicttheapproximaterelativefrequencygiventheprobability.Forexample,whenrollinganumbercube600times,predictthata3or6wouldberolledroughly200times,butprobablynotexactly200times.


CCSS.Math.Content.7.SP.C.7Developaprobabilitymodelanduseittofindprobabilitiesofevents.Compareprobabilitiesfromamodeltoobservedfrequencies;iftheagreementisnotgood,explainpossiblesourcesofthediscrepancy

Unit7:Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,BuildingNumberConcepts(825-828)

CCSS.Math.Content.7.SP.C.7aDevelopauniformprobabilitymodelbyassigningequalprobabilitytoalloutcomes,andusethemodeltodetermineprobabilitiesofevents.Forexample,ifastudentisselectedatrandomfromaclass,findtheprobabilitythatJanewillbeselectedandtheprobabilitythatagirlwillbeselected.

Unit7:Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807;Lesson6,ProblemSolving(819-822);Lesson7,BuildingNumberConcepts(825-828);Lesson10,ProblemSolving(848-851)

CCSS.Math.Content.7.SP.C.7bDevelopaprobabilitymodel(whichmaynotbeuniform)byobservingfrequenciesindatageneratedfromachanceprocess.Forexample,findtheapproximateprobabilitythataspinningpennywilllandheadsuporthatatossedpapercupwilllandopen-enddown.Dotheoutcomesforthespinningpennyappeartobeequallylikelybasedontheobservedfrequencies?


CCSS.Math.Content.7.SP.C.8Findprobabilitiesofcompoundeventsusingorganizedlists,tables,treediagrams,andsimulation.



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WhereStandardisAddressedCCSS.Math.Content.7.SP.C.8aUnderstandthat,justaswithsimpleevents,theprobabilityofacompoundeventisthefractionofoutcomesinthesamplespaceforwhichthecompoundeventoccurs.

Unit7:Lesson4,BuildingNumberConcepts(800-804);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,BuildingNumberConcepts(825-828);Lesson10,ProblemSolving(848-851)

CCSS.Math.Content.7.SP.C.8bRepresentsamplespacesforcompoundeventsusingmethodssuchasorganizedlists,tablesandtreediagrams.Foraneventdescribedineverydaylanguage(e.g.,“rollingdoublesixes”);identifytheoutcomesinthesamplespacewhichcomposetheevent.

Unit7:Lesson4,BuildingNumberConcepts(800-804);Lesson4,ProblemSolving(805-807);Lesson7,BuildingNumberConcepts(825-828);Lesson10,ProblemSolving(848-851)







CCSS.Math.Content.8.EE.A.1Knowandapplythepropertiesofintegerexponentstogenerateequivalentnumericalexpressions.Forexample,32×3–5=3–3=1/33=1/27


CCSS.Math.Content.8.EE.A.2Usesquarerootandcuberootsymbolstorepresentsolutionstoequationsoftheformx2=pandx3=p,wherepisapositiverationalnumber.Evaluatesquarerootsofsmallperfectsquaresandcuberootsofsmallperfectcubes.Knowthat√2isirrational.


CCSS.Math.Content.8.EE.B.5Graphproportionalrelationships,interpretingtheunitrateastheslopeofthegraph.Comparetwodifferentproportionalrelationshipsrepresentedindifferentways.Forexample,compareadistance-timegraphtoadistance-timeequationtodeterminewhichoftwomovingobjectshasgreaterspeed.



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WhereStandardisAddressedCCSS.Math.Content.8.EE.C.7Solvelinearequationsinonevariable.


CCSS.Math.Content.8.EE.C.7aGiveexamplesoflinearequationsinonevariablewithonesolution,infinitelymanysolutions,ornosolutions.Showwhichofthesepossibilitiesisthecasebysuccessivelytransformingthegivenequationintosimplerforms,untilanequivalentequationoftheformx=a,a=a,ora=bresults(whereaandbaredifferentnumbers).


CCSS.Math.Content.8.EE.C.7bSolvelinearequationswithrationalnumbercoefficients,includingequationswhosesolutionsrequireexpandingexpressionsusingthedistributivepropertyandcollectingliketerms.

Unit7:Lesson6,BuildingNumberConcepts(801-804);Lesson7,BuildingNumberConcepts(811-815);Lesson8,BuildingNumberConcepts(822-825);Lesson9,BuildingNumberConcepts(831-833);Lesson10,BuildingNumberConcepts(839-843)Unit8:Lesson1,BuildingNumberConcepts(863-868);Lesson2,BuildingNumberConcepts(874-877);Lesson3,BuildingNumberConcepts(883-886);Lesson6,BuildingNumberConcepts(909-911);Lesson7,BuildingNumberConcepts(918-920);Lesson8,BuildingNumberConcepts(928-932);Lesson9,BuildingNumberConcepts(938-941);Lesson11,BuildingNumberConcepts(954-956);Lesson12,BuildingNumberConcepts(962-964);Lesson13,BuildingNumberConcepts(970-974);Lesson14,BuildingNumberConcepts(981-983);Lesson15,BuildingNumberConcepts(989-993)Unit9:Lesson12,BuildingNumberConcepts(1109-1111);Lesson12,ProblemSolving(1112-1116);Lesson13,BuildingNumberConcepts(1119-1120);Lesson13,ProblemSolving(1121-1123);Lesson14,BuildingNumberConcepts(1127-1132);Lesson15,BuildingNumberConcepts(1137-1141);


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WhereStandardisAddressedLesson15,ProblemSolving(1142-1148)Unit10:Lesson8,BuildingNumberConcepts(1220-1222)

CCSS.Math.Content.8.EE.C.8aUnderstandthatsolutionstoasystemoftwolinearequationsintwovariablescorrespondtopointsofintersectionoftheirgraphs,becausepointsofintersectionsatisfybothequationssimultaneously.


CCSS.Math.Content.8.F.ADefine,evaluate,andcomparefunctions.

Unit9:Lesson1,BuildingNumberConcepts(1009-1012);Lesson2,BuildingNumberConcepts(1019-1021);Lesson3,BuildingNumberConcepts(1028-1031);Lesson4,BuildingNumberConcepts(1038-1041);Lesson5,BuildingNumberConcepts(1044-1048);Lesson6,BuildingNumberConcepts(1053-1055);Lesson14,BuildingNumberConcepts(1127-1132);Lesson15,BuildingNumberConcepts(1137-1141)

CCSS.Math.Content.8.F.A.1Understandthatafunctionisarulethatassignstoeachinputexactlyoneoutput.Thegraphofafunctionisthesetoforderedpairsconsistingofaninputandthecorrespondingoutput.1

Unit4:Lesson6,BuildingNumberConcepts(480-483);Lesson8,BuildingNumberConcepts(498-501);Lesson10,BuildingNumberConcepts(518-523)Unit9:Lesson1,BuildingNumberConcepts(1009-1012);Lesson2,BuildingNumberConcepts(1019-1021);Lesson3,BuildingNumberConcepts(1028-1031);Lesson4,BuildingNumberConcepts(1038-1041);Lesson5,BuildingNumberConcepts(1044-1048);Lesson6,BuildingNumberConcepts(1053-1055);Lesson10,BuildingNumberConcepts(1088-1093);Lesson11,BuildingNumberConcepts(1098-1100);Lesson15,BuildingNumberConcepts(1137-1141)

CCSS.Math.Content.8.F.A.2Comparepropertiesoftwofunctionseachrepresentedinadifferentway(algebraically,graphically,numericallyintables,orbyverbal

Unit9:Lesson6,ProblemSolving(1056-1059);Lesson7,ProblemSolving(1066-1067);Lesson8,BuildingNumberConcepts(1071-1074);Lesson8,ProblemSolving(1075-1076);


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WhereStandardisAddresseddescriptions).Forexample,givenalinearfunctionrepresentedbyatableofvaluesandalinearfunctionrepresentedbyanalgebraicexpression,determinewhichfunctionhasthegreaterrateofchange.

Lesson9,BuildingNumberConcepts(1079-1082);Lesson9,ProblemSolving(1083-1085);Lesson10,BuildingNumberConcepts(1088-1093);Lesson11,BuildingNumberConcepts(1098-1100);Lesson11,ProblemSolving(1101-1105);Lesson13,BuildingNumberConcepts(1119-1120);Lesson14,BuildingNumberConcepts(1127-1132);Lesson15,BuildingNumberConcepts(1137-1141)

CCSS.Math.Content.8.F.A.3Interprettheequationy=mx+basdefiningalinearfunction,whosegraphisastraightline;giveexamplesoffunctionsthatarenotlinear.Forexample,thefunctionA=s2givingtheareaofasquareasafunctionofitssidelengthisnotlinearbecauseitsgraphcontainsthepoints(1,1);(2,4)and(3,9);whicharenotonastraightline.

Unit9:Lesson7,BuildingNumberConcepts(1062-1065);Lesson8,BuildingNumberConcepts(1071-1074);Lesson9,BuildingNumberConcepts(1079-1082);Lesson10,BuildingNumberConcepts(1088-1093);Lesson11,BuildingNumberConcepts(1098-1100);Lesson13,BuildingNumberConcepts(1119-1120);Lesson14,BuildingNumberConcepts(1127-1132);Lesson15,BuildingNumberConcepts(1137-1141)Unit10:Lesson4,ProblemSolving(1188-1192);Lesson6,ProblemSolving(1203-1208);Lesson7,ProblemSolving(1215-1217);Lesson8,ProblemSolving(1223-1226);Lesson10,ProblemSolving(1241-1247)

CCSS.Math.Content.8.F.BUsefunctionstomodelrelationshipsbetweenquantities.



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WhereStandardisAddressedCCSS.Math.Content.8.F.B.4Constructafunctiontomodelalinearrelationshipbetweentwoquantities.Determinetherateofchangeandinitialvalueofthefunctionfromadescriptionofarelationshiporfromtwo(x,y)values,includingreadingthesefromatableorfromagraph.Interprettherateofchangeandinitialvalueofalinearfunctionintermsofthesituationitmodels,andintermsofitsgraphoratableofvalues.

Unit9:Lesson4,BuildingNumberConcepts(1038-1041);Lesson5,BuildingNumberConcepts(1044-1048);Lesson6,BuildingNumberConcepts(1053-1055);Lesson6,ProblemSolving(1056-1059);Lesson7,BuildingNumberConcepts(1062-1065);Lesson7,ProblemSolving(1066-1067);Lesson8,BuildingNumberConcepts(1071-1074);Lesson8,ProblemSolving(1075-1076);Lesson9,BuildingNumberConcepts(1079-1082);Lesson9,ProblemSolving(1083-1085);Lesson10,BuildingNumberConcepts(1088-1093);Lesson11,BuildingNumberConcepts(1098-1100);Lesson11,ProblemSolving(1101-1105);Lesson12,ProblemSolving(1112-1116);Lesson13,ProblemSolving(1121-1123);Lesson14,ProblemSolving(1133-1134);Lesson15,ProblemSolving(1142-1148)

CCSS.Math.Content.8.F.B.5Describequalitativelythefunctionalrelationshipbetweentwoquantitiesbyanalyzingagraph(e.g.,wherethefunctionisincreasingordecreasing,linearornonlinear).Sketchagraphthatexhibitsthequalitativefeaturesofafunctionthathasbeendescribedverbally.

Unit9:Lesson3,BuildingNumberConcepts(1028-1031);Lesson4,BuildingNumberConcepts(1038-1041);Lesson5,BuildingNumberConcepts(1044-1048);Lesson6,BuildingNumberConcepts(1053-1055);Lesson6,ProblemSolving(1056-1059);Lesson7,BuildingNumberConcepts(1062-1065);Lesson7,ProblemSolving(1066-1067);Lesson8,BuildingNumberConcepts(1071-1074);Lesson8,ProblemSolving(1075-1076);Lesson9,BuildingNumberConcepts(1079-1082);Lesson9,ProblemSolving(1083-1085);Lesson10,BuildingNumberConcepts(1088-1093);Lesson11,BuildingNumberConcepts(1098-1100);Lesson11,ProblemSolving(1101-1105);Lesson12,ProblemSolving(1112-1116);Lesson13,ProblemSolving(1121-1123);Lesson14,ProblemSolving(1133-1134);Lesson15,BuildingNumberConcepts(1137-1141);Lesson15,Problem


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WhereStandardisAddressedSolving(1142-1148);Lesson4,ProblemSolving(1188-1192)Unit10:Lesson6,ProblemSolving(1203-1208);Lesson7,ProblemSolving(1215-1217);Lesson8,ProblemSolving(1223-1226);Lesson10,ProblemSolving(1241-1247)

CCSS.Math.Content.8.G.A.1Verifyexperimentallythepropertiesofrotations,reflections,andtranslations:


Unit4:Lesson3,ProblemSolving(423-425);Lesson4,ProblemSolving(432-435);Lesson10,ProblemSolving(478-482)Unit5:Lesson6,ProblemSolving(541-542)Unit9:Lesson7,ProblemSolving(1050-1053)

CCSS.Math.Content.8.G.A.1aLinesaretakentolines,andlinesegmentstolinesegmentsofthesamelength.

Unit4:Lesson3,ProblemSolving(423-425);Unit9:Lesson5,ProblemSolving(1035-1038);Lesson7,ProblemSolving(1050-1053)

CCSS.Math.Content.8.G.A.2Understandthatatwo-dimensionalfigureiscongruenttoanotherifthesecondcanbeobtainedfromthefirstbyasequenceofrotations,reflections,andtranslations;giventwocongruentfigures,describeasequencethatexhibitsthecongruencebetweenthem.

Unit6:Lesson4,ProblemSolving(677-678);Lesson6,ProblemSolving(692-693)Unit7:Lesson8,ProblemSolving(799-803);Lesson9,ProblemSolving(810-812);Lesson10,ProblemSolving(821-824)


CCSS.Math.Content.8.G.A.3Describetheeffectofdilations,translations,rotations,andreflectionsontwo-dimensionalfiguresusingcoordinates.


Unit4:Lesson10,ProblemSolving(478-482);Lesson4,ProblemSolving(1031-1032)Unit9:Lesson8,ProblemSolving(1056-1059);Lesson10,ProblemSolving(1071-1076)


CCSS.Math.Content.8.G.A.4Understandthatatwo-dimensionalfigureissimilartoanotherifthesecondcanbeobtainedfromthefirstbyasequenceofrotations,reflections,translations,anddilations;giventwosimilartwodimensionalfigures,describeasequencethatexhibitsthesimilaritybetweenthem.


CCSS.Math.Content.8.G.A.5Useinformalargumentstoestablishfactsabouttheanglesumandexteriorangleoftriangles,abouttheanglescreatedwhenparallellinesarecutbya

Unit7:Lesson1,ProblemSolving(755-760);Lesson2,ProblemSolving(766-769);Lesson4,ProblemSolving(786-790);Lesson5,ProblemSolving(793-796);Lesson6,Problem


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WhereStandardisAddressedtransversal,andtheangle-anglecriterionforsimilarityoftriangles.Forexample,arrangethreecopiesofthesametrianglesothatthesumofthethreeanglesappearstoformaline,andgiveanargumentintermsoftransversalswhythisisso.

Solving(805-808);Lesson9,ProblemSolving(834-836)

CCSS.Math.Content.8.G.BUnderstandandapplythePythagoreanTheorem.


CCSS.Math.Content.8.G.B.7ApplythePythagoreanTheoremtodetermineunknownsidelengthsinrighttrianglesinreal-worldandmathematicalproblemsintwoandthreedimensions.


CCSS.Math.Content.8.G.CSolvereal-worldandmathematicalproblemsinvolvingvolumeofcylinders,cones,andspheres.


CCSS.Math.Content.8.G.C.9Knowtheformulasforthevolumesofcones,cylinders,andspheresandusethemtosolvereal-worldandmathematicalproblems.


CCSS.Math.Content.8.NS.A.1Knowthatnumbersthatarenotrationalarecalledirrational.Understandinformallythateverynumberhasadecimalexpansion;forrationalnumbersshowthatthedecimalexpansionrepeatseventually,andconvertadecimalexpansionwhichrepeatseventuallyintoarationalnumber.


CCSS.Math.Content.8.NS.A.2Userationalapproximationsofirrationalnumberstocomparethesizeofirrationalnumbers,locatethemapproximatelyonanumberlinediagram,andestimatethevalueofexpressions(e.g.,π2).Forexample,bytruncatingthedecimal



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WhereStandardisAddressedexpansionof√2,showthat√2isbetween1and2,thenbetween1.4and1.5,andexplainhowtocontinueontogetbetterapproximations.CCSS.Math.Content.8.SP.AInvestigatepatternsofassociationinbivariatedata.


CCSS.Math.Content.8.SP.A.1Constructandinterpretscatterplotsforbivariatemeasurementdatatoinvestigatepatternsofassociationbetweentwoquantities.Describepatternssuchasclustering,outliers,positiveornegativeassociation,linearassociation,andnonlinearassociation.




CCSS.Math.Content.8.SP.A.2Knowthatstraightlinesarewidelyusedtomodelrelationshipsbetweentwoquantitativevariables.Forscatterplotsthatsuggestalinearassociation,informallyfitastraightline,andinformallyassessthemodelfitbyjudgingtheclosenessofthedatapointstotheline.


CCSS.Math.Content.HSA-CED.ACreateequationsthatdescribenumbersorrelationships


CCSS.Math.Content.HSA-CED.A.1Createequationsandinequalitiesinonevariableandusethemtosolveproblems.Includeequationsarisingfromlinearandquadraticfunctions,andsimplerationalandexponentialfunctions.



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WhereStandardisAddressedCCSS.Math.Content.HSA-CED.A.2Createequationsintwoormorevariablestorepresentrelationshipsbetweenquantities;graphequationsoncoordinateaxeswithlabelsandscales.


CCSS.Math.Content.HSA-CED.A.4Rearrangeformulastohighlightaquantityofinterest,usingthesamereasoningasinsolvingequations.Forexample,rearrangeOhm’slawV=IRtohighlightresistanceR.


CCSS.Math.Content.HSA-REI.AUnderstandsolvingequationsasaprocessofreasoningandexplainthereasoning

Unit8:Lesson1,BuildingNumberConcepts(863-868);Lesson2,BuildingNumberConcepts(874-877);Lesson3,BuildingNumberConcepts(883-886);Lesson6,BuildingNumberConcepts(909-911);Lesson7,BuildingNumberConcepts(918-920);Lesson8,BuildingNumberConcepts(928-932);Lesson9,BuildingNumberConcepts(938-941);Lesson9,ProblemSolving(942-943);Lesson11,BuildingNumberConcepts(954-956);Lesson12,BuildingNumberConcepts(962-964);Lesson13,BuildingNumberConcepts(970-974);Lesson14,BuildingNumberConcepts(981-983);Lesson14,ProblemSolving(984-986);Lesson15,BuildingNumberConcepts(989-993);Lesson15,ProblemSolving(994-997)

CCSS.Math.Content.HSA-REI.A.1Explaineachstepinsolvingasimpleequationasfollowingfromtheequalityofnumbersassertedatthepreviousstep,startingfromtheassumptionthattheoriginalequationhasasolution.Constructaviableargumenttojustifyasolutionmethod.



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WhereStandardisAddressedCCSS.Math.Content.HSA-REI.BSolveequationsandinequalitiesinonevariable

Unit8:Lesson1,BuildingNumberConcepts(863-868);Lesson2,BuildingNumberConcepts(874-877);Lesson3,BuildingNumberConcepts(883-886);Lesson6,BuildingNumberConcepts(909-911);Lesson7,BuildingNumberConcepts(918-920);Lesson8,BuildingNumberConcepts(928-932);Lesson9,BuildingNumberConcepts(938-94);Lesson14,ProblemSolving(984-986);Lesson15,ProblemSolving(994-997)

CCSS.Math.Content.HSA-REI.B.3Solvelinearequationsandinequalitiesinonevariable,includingequationswithcoefficientsrepresentedbyletters.

Unit8:Lesson9,ProblemSolving(942-943);Lesson12,BuildingNumberConcepts(962-964);Lesson13,BuildingNumberConcepts(970-974);Lesson14,BuildingNumberConcepts(981-983);Lesson14,ProblemSolving(984-986);Lesson15,BuildingNumberConcepts(989-993);Lesson15,ProblemSolving(994-997)Unit9:Lesson12,BuildingNumberConcepts(1109-1111);Lesson12,ProblemSolving(1112-1116);Lesson13,ProblemSolving(1121-1123);Lesson15,ProblemSolving(1142-1148)Unit10:Lesson7,BuildingNumberConcepts(1211-1214);Lesson8,BuildingNumberConcepts(1220-1222)

CCSS.Math.Content.HSA-REI.C.6Solvesystemsoflinearequationsexactlyandapproximately(e.g.,withgraphs);focusingonpairsoflinearequationsintwovariables.


GRADE9-12CCSSLessonSubsection(andPageNumber)in







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CCSS.MATH.PRACTICE.MP1Makesenseofproblemsandpersevereinsolvingthem.Mathematicallyproficientstudentsstartbyexplainingtothemselvesthemeaningofaproblemandlookingforentrypointstoitssolution.Theyanalyzegivens,constraints,relationships,andgoals.Theymakeconjecturesabouttheformandmeaningofthesolutionandplanasolutionpathwayratherthansimplyjumpingintoasolutionattempt.Theyconsideranalogousproblems,andtryspecialcasesandsimplerformsoftheoriginalprobleminordertogaininsightintoitssolution.Theymonitorandevaluatetheirprogressandchangecourseifnecessary.Olderstudentsmight,dependingonthecontextoftheproblem,transformalgebraicexpressionsorchangetheviewingwindowontheirgraphingcalculatortogettheinformationtheyneed.Mathematicallyproficientstudentscanexplaincorrespondencesbetweenequations,verbaldescriptions,tables,andgraphsordrawdiagramsofimportantfeaturesandrelationships,graphdata,andsearchforregularityortrends.Youngerstudentsmightrelyonusingconcreteobjectsorpicturestohelpconceptualizeandsolveaproblem.Mathematicallyproficientstudentschecktheiranswerstoproblemsusingadifferentmethod,andtheycontinuallyaskthemselves,"Doesthismakesense?"Theycanunderstandtheapproachesofotherstosolvingcomplexproblemsandidentifycorrespondencesbetweendifferentapproaches.

Unit1:Lesson1,ProblemSolving(14-15);Lesson2,ProblemSolving(22-24);Lesson3,ProblemSolving(30-31);Lesson4,ProblemSolving(36-38);Lesson8,ProblemSolving(65-66);Lesson9,ProblemSolving(72-74);Lesson13,ProblemSolving(104-105);Lesson14,ProblemSolving(108-110);Lesson15,ProblemSolving(117-120);Lesson8,ProblemSolving(313-315)

Unit1:Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,ProblemSolving(89-92);Lesson10,BuildingNumberConcepts(189-193);Lesson11,BuildingNumberConcepts(198-201);Lesson12,BuildingNumberConcepts(207-210);Lesson13,BuildingNumberConcepts(215-219);Lesson14,BuildingNumberConcepts(224-227);Lesson15,BuildingNumberConcepts(232-239);Lesson1,ProblemSolving(773-777)Unit7:Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,ProblemSolving(829-831);Lesson8,ProblemSolving(834-836);Lesson9,ProblemSolving(839-841);Lesson10,ProblemSolving(848-851)



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WhereStandardisAddressedCCSS.MATH.PRACTICE.MP2Reasonabstractlyandquantitatively.Mathematicallyproficientstudentsmakesenseofquantitiesandtheirrelationshipsinproblemsituations.Theybringtwocomplementaryabilitiestobearonproblemsinvolvingquantitativerelationships:theabilitytodecontextualize—toabstractagivensituationandrepresentitsymbolicallyandmanipulatetherepresentingsymbolsasiftheyhavealifeoftheirown,withoutnecessarilyattendingtotheirreferents—andtheabilitytocontextualize,topauseasneededduringthemanipulationprocessinordertoprobeintothereferentsforthesymbolsinvolved.Quantitativereasoningentailshabitsofcreatingacoherentrepresentationoftheproblemathand;consideringtheunitsinvolved;attendingtothemeaningofquantities,notjusthowtocomputethem;andknowingandflexiblyusingdifferentpropertiesofoperationsandobjects.

Unit1:Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,ProblemSolving(89-92)Unit2:Lesson6,BuildingNumberConcepts(151-154)Unit7:Lesson1,ProblemSolving(773-777);Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,ProblemSolving(829-831);Lesson8,ProblemSolving(834-836);Lesson9,ProblemSolving(839-841);Lesson10,ProblemSolving(848-851)


CCSS.MATH.PRACTICE.MP3Constructviableargumentsandcritiquethereasoningofothers.Mathematicallyproficientstudentsunderstandandusestatedassumptions,definitions,andpreviouslyestablishedresultsinconstructingarguments.Theymakeconjecturesandbuildalogicalprogressionofstatementstoexplorethetruthoftheirconjectures.Theyareabletoanalyzesituationsbybreakingthemintocases,andcanrecognizeandusecounterexamples.Theyjustifytheirconclusions,communicatethemtoothers,andrespondtotheargumentsofothers.Theyreasoninductivelyaboutdata,makingplausibleargumentsthattakeintoaccountthecontextfromwhichthedataarose.Mathematicallyproficientstudentsare

Unit1:Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,ProblemSolving(89-92)Unit2:Lesson3,BuildingNumberConcepts(123-127);Lesson4,BuildingNumberConcepts(133-135);Lesson5,BuildingNumberConcepts(141-145);Lesson6,BuildingNumberConcepts(151-154);Lesson14,BuildingNumberConcepts(224-227);Lesson15,BuildingNumberConcepts(232-239);


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WhereStandardisAddressedalsoabletocomparetheeffectivenessoftwoplausiblearguments,distinguishcorrectlogicorreasoningfromthatwhichisflawed,and—ifthereisaflawinanargument—explainwhatitis.Elementarystudentscanconstructargumentsusingconcretereferentssuchasobjects,drawings,diagrams,andactions.Suchargumentscanmakesenseandbecorrect,eventhoughtheyarenotgeneralizedormadeformaluntillatergrades.Later,studentslearntodeterminedomainstowhichanargumentapplies.Studentsatallgradescanlistenorreadtheargumentsofothers,decidewhethertheymakesense,andaskusefulquestionstoclarifyorimprovethearguments.

Lesson1,ProblemSolving(773-777);Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,ProblemSolving(829-831);Lesson8,ProblemSolving(834-836);Lesson9,ProblemSolving(839-841);Lesson10,ProblemSolving(848-851)

CCSS.MATH.PRACTICE.MP4Modelwithmathematics.Mathematicallyproficientstudentscanapplythemathematicstheyknowtosolveproblemsarisingineverydaylife,society,andtheworkplace.Inearlygrades,thismightbeassimpleaswritinganadditionequationtodescribeasituation.Inmiddlegrades,astudentmightapplyproportionalreasoningtoplanaschooleventoranalyzeaprobleminthecommunity.Byhighschool,astudentmightusegeometrytosolveadesignproblemoruseafunctiontodescribehowonequantityofinterestdependsonanother.Mathematicallyproficientstudentswhocanapplywhattheyknowarecomfortablemakingassumptionsandapproximationstosimplifyacomplicatedsituation,realizingthatthesemayneedrevisionlater.Theyareabletoidentifyimportantquantitiesinapracticalsituationandmaptheirrelationshipsusingsuchtoolsasdiagrams,two-waytables,graphs,flowchartsandformulas.Theycananalyzethoserelationshipsmathematicallytodraw





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WhereStandardisAddressedconclusions.Theyroutinelyinterprettheirmathematicalresultsinthecontextofthesituationandreflectonwhethertheresultsmakesense,possiblyimprovingthemodelifithasnotserveditspurpose.CCSS.MATH.PRACTICE.MP5Useappropriatetoolsstrategically.Mathematicallyproficientstudentsconsidertheavailabletoolswhensolvingamathematicalproblem.Thesetoolsmightincludepencilandpaper,concretemodels,aruler,aprotractor,acalculator,aspreadsheet,acomputeralgebrasystem,astatisticalpackage,ordynamicgeometrysoftware.Proficientstudentsaresufficientlyfamiliarwithtoolsappropriatefortheirgradeorcoursetomakesounddecisionsaboutwheneachofthesetoolsmightbehelpful,recognizingboththeinsighttobegainedandtheirlimitations.Forexample,mathematicallyproficienthighschoolstudentsanalyzegraphsoffunctionsandsolutionsgeneratedusingagraphingcalculator.Theydetectpossibleerrorsbystrategicallyusingestimationandothermathematicalknowledge.Whenmakingmathematicalmodels,theyknowthattechnologycanenablethemtovisualizetheresultsofvaryingassumptions,exploreconsequences,andcomparepredictionswithdata.Mathematicallyproficientstudentsatvariousgradelevelsareabletoidentifyrelevantexternalmathematicalresources,suchasdigitalcontentlocatedonawebsite,andusethemtoposeorsolveproblems.Theyareabletousetechnologicaltoolstoexploreanddeepentheirunderstandingofconcepts.





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WhereStandardisAddressedCCSS.MATH.PRACTICE.MP6Attendtoprecision.Mathematicallyproficientstudentstrytocommunicatepreciselytoothers.Theytrytousecleardefinitionsindiscussionwithothersandintheirownreasoning.Theystatethemeaningofthesymbolstheychoose,includingusingtheequalsignconsistentlyandappropriately.Theyarecarefulaboutspecifyingunitsofmeasure,andlabelingaxestoclarifythecorrespondencewithquantitiesinaproblem.Theycalculateaccuratelyandefficiently,expressnumericalanswerswithadegreeofprecisionappropriatefortheproblemcontext.Intheelementarygrades,studentsgivecarefullyformulatedexplanationstoeachother.Bythetimetheyreachhighschooltheyhavelearnedtoexamineclaimsandmakeexplicituseofdefinitions.

Unit1:Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,ProblemSolving(89-92)Unit2:Lesson5,BuildingNumberConcepts(141-145);Lesson6,BuildingNumberConcepts(151-154);Lesson9,BuildingNumberConcepts(180-184);Lesson10,BuildingNumberConcepts(189-193);Lesson11,BuildingNumberConcepts(198-201);Lesson12,BuildingNumberConcepts(207-210);Lesson13,BuildingNumberConcepts(215-219);Lesson14,BuildingNumberConcepts(224-227);Lesson15,BuildingNumberConcepts(232-239)Unit7:Lesson1,ProblemSolving(773-777);Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,ProblemSolving(829-831);Lesson8,ProblemSolving(834-836);Lesson9,ProblemSolving(839-841);Lesson10,ProblemSolving(848-851)


CCSS.MATH.PRACTICE.MP7Lookforandmakeuseofstructure.Mathematicallyproficientstudentslookcloselytodiscernapatternorstructure.Youngstudents,forexample,mightnoticethatthreeandsevenmoreisthesameamountassevenandthreemore,ortheymaysortacollectionofshapesaccordingtohowmanysidestheshapeshave.Later,studentswillsee7×8equalsthewellremembered7×5+7×3,in

Unit1:Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,ProblemSolving(89-92);

Unit4:Lesson1,BuildingNumberConcepts(429-432);Lesson2,BuildingNumberConcepts(439-440);Lesson3,BuildingNumberConcepts(448-452);Lesson4,BuildingNumberConcepts(460-463);Lesson5,BuildingNumberConcepts(471-475);Lesson6,BuildingNumberConcepts(480-483);Lesson7,BuildingNumberConcepts(489-491);Lesson8,BuildingNumberConcepts(498-501);Lesson9,Building


Grades 3 - 12

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WhereStandardisAddressedpreparationforlearningaboutthedistributiveproperty.Intheexpressionx2+9x+14,olderstudentscanseethe14as2×7andthe9as2+7.Theyrecognizethesignificanceofanexistinglineinageometricfigureandcanusethestrategyofdrawinganauxiliarylineforsolvingproblems.Theyalsocanstepbackforanoverviewandshiftperspective.Theycanseecomplicatedthings,suchassomealgebraicexpressions,assingleobjectsorasbeingcomposedofseveralobjects.Forexample,theycansee5-3(x-y)2as5minusapositivenumbertimesasquareandusethattorealizethatitsvaluecannotbemorethan5foranyrealnumbersxandy.


NumberConcepts(508-510);Lesson10,BuildingNumberConcepts(518-523)

CCSS.MATH.PRACTICE.MP8Lookforandexpressregularityinrepeatedreasoning.Mathematicallyproficientstudentsnoticeifcalculationsarerepeated,andlookbothforgeneralmethodsandforshortcuts.Upperelementarystudentsmightnoticewhendividing25by11thattheyarerepeatingthesamecalculationsoverandoveragain,andconcludetheyhavearepeatingdecimal.Bypayingattentiontothecalculationofslopeastheyrepeatedlycheckwhetherpointsareonthelinethrough(1,2)withslope3,middleschoolstudentsmightabstracttheequation(y-2)/(x-1)=3.Noticingtheregularityinthewaytermscancelwhenexpanding(x-1)(x+1);(x-1)(x2+x+1);and(x-1)(x3+x2+x+1)mightleadthemtothegeneralformulaforthesumofageometricseries.Astheyworktosolveaproblem,mathematicallyproficientstudentsmaintainoversightoftheprocess,whileattendingtothedetails.Theycontinuallyevaluatethereasonablenessoftheirintermediateresults.

Unit1:Lesson1,ProblemSolving(12-13);Lesson2,ProblemSolving(19-20);Lesson3,ProblemSolving(27-29);Lesson4,ProblemSolving(35-37);Lesson6,ProblemSolving(51-53);Lesson7,ProblemSolving(59-62);Lesson8,ProblemSolving(68-69);Lesson9,ProblemSolving(76-78);Lesson10,ProblemSolving(89-92);Unit7:Lesson1,ProblemSolving(773-777);Lesson2,ProblemSolving(783-787);Lesson3,ProblemSolving(793-797);Lesson4,ProblemSolving(805-807);Lesson6,ProblemSolving(819-822);Lesson7,ProblemSolving(829-831);Lesson8,ProblemSolving(834-836);Lesson9,ProblemSolving(839-841);Lesson10,ProblemSolving(848-851)


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TM CCSS Correlation-2019 - Literacy and Math Instructional