Mathematics | Grade 7 · Mathematics | Grade 7 The descriptions below provide an overview of the...

Mathematics | Grade 7 The descriptions below provide an overview of the mathematical concepts and skills that students explore throughout the 7th grade.

Ratios and Proportional Relationships Students extend their understanding of ratios from 6th grade and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.

The Number System Students develop a unified understanding of numbers, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percent as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. These properties are further explored with respect to negative numbers. This exploration is carried out in problems from everyday contexts so that the student can gain a deeper understanding and appreciation for the mathematical concepts being studied.

Expressions and Equations By applying the properties of operations as strategies, students explore working with expressions, equations, and inequalities. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve multi-step real-world problems. They use variables to represent quantities and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Geometry Students continue their work with area from 6th grade, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity, they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Statistics and Probability Students continue their work from 6th grade in order to build a strong foundation for statistics and probability needed for high school. Students understand that statistics can be used to gain information about a population through sampling. They work with drawing inferences about a population based on a sample and use measures of center and of variability to draw informal comparative inferences about two populations. Students investigate the chance processes and develop, use, and evaluate probability models. Students summarize numerical data sets with respect to their context using quantitative measures and describe any overall patterns or deviations from the overall pattern.

(From TDOE Math Standards)

7THGRADEMATHPACINGGUIDE:1stNineWeeks UNITONE:TheNumberSystemWeek Lesson Standards LearningTarget Other

Materials/ProjectsWEEKONE

GoalsExpectationsPre-AssessmentSTARTesting(FallBenchmarkWindowTBA)

WEEKTWO

L1:UnderstandAdditionofPositiveandNegativeIntegers

7.NS.A.1a7.NS.A.1b

ICAN:● Understandthatthesumofanumberandits

oppositeiszeroinmathematicalandreal-worldsituations.

● Representp+qasthenumberlocateda

distance fromponanumberline● AddandsubtractIntegers.● Representadditionandsubtractionof

integersonhorizontaland/orverticalnumberlines.

● Applypropertiesofoperationstoaddandsubtractintegers.

EngageNY:Module2,TopicAIllustrativeMathematics

Week Lesson Standards LearningTarget OtherMaterials/Projects

WEEKTHREE

L2:UnderstandSubtractionofPositiveandNegativeIntegers

7.NS.A.1c

ICAN:● Understandtherelationshipbetweenaddition

andsubtraction.● AddandsubtractIntegers.● Representadditionandsubtractionofintegers

onhorizontaland/orverticalnumberlines.● Applypropertiesofoperationstoaddand

subtractintegersSubtractrationalnumbersbyaddingtheadditiveinverse.

● Usesubtractionandabsolutevaluetofindthedistancebetweentwonumbersonanumberline.

● Findthedistancebetweentwopointsonacoordinateplanethathaveeitherthesamex-ory-value.



WEEKFOUR

L3:AddandSubtractPositiveandNegativeIntegers

7.NS.A.1a7.NS.A.1b7.NS.A.1c7.NS.A.1d

ICAN:● Understandthatthesumofanumberandits


● Representp+qasthenumberlocateda

distance fromponanumberline.● AddandsubtractIntegers.● Representadditionandsubtractionofintegers

onhorizontaland/orverticalnumberlines● Applypropertiesofoperationstoaddand

subtractintegers.● Understandthatthesumofanumberandits


● Usesubtractionandabsolutevaluetofindthedistancebetweentwonumbersonanumberline.

● Findthedistancebetweentwopointsonacoordinateplanethathaveeitherthesamex-ory-value.



WEEKFIVE

L4:MultiplyandDividePositiveandNegativeIntegers

7.NS.A.2a7.NS.A.2b*7.NS.A.2c

ICAN:

● Developrulesformultiplyinganddividingintegersusingpatterns.

● Identifyequivalentnumberstoshowthat

(usingnumbers,notvariables).

● Multiplyanddivideintegersresultinginintegeranswers.

*Willneedsupplementalresourcetoaddress.EngageNY:Module2,TopicBIllustrativeMathematics

WEEKSIX

L5:TerminatingandRepeatingDecimals

7.NS.A.2d

ICAN:● Convertapositiveproperfractiontoa

terminatingdecimal.● Convertapositiveimproperfractiontoawhole

numberdecimalusinglongdivision.● Convertapositiveproperfractiontoa

repeatingdecimal;usesymbolsforrepeatingdecimals.

● Convertpositiveproperandimproperfractionstorepeatingandnon-repeatingdecimals.

EngageNY:Module2,TopicBIllustrativeMathematics


WEEKEIGHT

L7:AddandSubtractRationalNumbers

7.NS.A.1a7.NS.A.1b7.NS.A.1c7.NS.A.1d

ICAN:● Connectaddingandsubtractingpositiveand

negativefractionstowhatstudentsalreadyknowaboutaddingandsubtractingfractionsandaddingandsubtractingintegers.

● Useanumberlinewitheasyfractionstoconnecttodistancemodel.

● Addandsubtractpositiveandnegativeproperfractions.

● Addandsubtractpositiveandnegativeimproperfractions.

● Addandsubtractpositiveandnegativemixednumbers.


7THGRADEMATHPACINGGUIDE:2ndNineWeeksWeek Lesson Standards LearningTarget Other


L8:SolveProblemswithRationalNumbers;Unit1Assessment

7.EE.B.3a7.EE.B.3b7.NS.A.37.NS.A.1d7.NS.A.2c

ICAN:● Solveproblemsinvolvingnegativeintegers.● Usewhole-numberapproximationstoestimate,

andthencomparetheestimatetotheactualresultofcomputation.

● Connectpreviousone-ortwo-stepequation-solvingtosolvingequationswithpositiveandnegativefractions.

● Connectpreviousequation-solvingtosolvingequationswithpositiveandnegativedecimals.


UNITTWO:RatiosandProportionalRelationshipsWEEKTWO:

L9:RatiosInvolvingComplexFractions

7.RP.A.1

ICAN:● Computeunitratesinvolvingratioswitha

fractioninthedenominator.● Computeunitratesinvolvingratioswitha

fractioninthenumerator.● Computeunitratesinvolvingrationswith

fractionsinboththenumeratoranddenominator.

EngageNY:Module1,TopicCIllustrativeMathematics

WEEKTHREE

L10:UnderstandProportionalRelationships

7.RP.A.2a7.RP.A.2b

ICAN:● Determinewhethertwoquantitiesareina

proportionalrelationshipbylookingatvaluesinatable,alineinthecoordinateplane,andanequation.(Useequivalentfractionrelationshipsandmultiplication/divisiontofindproportionalratios.)

● Identifytheconstantofproportionality(unitrate)inatableandrepresentedbyanequation.



WEEKFOUR

L11:EquationsforProportionalRelationships

7.RP.A.2c7.RP.A.2d7.RP.A.2b

ICAN:● Representproportionalrelationshipsby

equations.● Graphproportionalequationsrepresentingreal-

worldsituationsonacoordinategrid.● Explainwhatagivenpoint(x,y)onthegraphof

theequationofaproportionalrelationshipmeansintermsofareal-worldsituation.


WEEKFIVE

L12:ProblemSolvingwithProportionalRelationships

7.RP.A.37.RP.A.2c

ICAN:● Setupandsolvemulti-stepsimpleinterest

problems.● Setupandsolvemulti-stepsimpletaxproblems.● Setupandsolvemulti-stepproblemsinvolving

markupandmarkdowns.● Setupandsolvemulti-stepproblemsinvolving

gratuities,commissionsandfees.

EngageNY:Module1,TopicCEngageNY:Module4,TopicAEngageNY:Module4,TopicDIllustrativeMathematics

WEEKSIX

L13:ProportionalRelationships;InterimAssessment

7.RP.A.37.RP.A.2c

ICAN:● Setupandsolvemulti-stepproblemsinvolving

percentincreaseanddecrease.● Setupandsolvemulti-stepproblemsinvolving

percenterror.

EngageNY:Module1,TopicCEngageNY:Module4,TopicBEngageNY:Module4,TopicDIllustrativeMathematics

UNITTHREE:ExpressionsandEquationsWeek Lesson Standards LearningTarget Other

Materials/ProjectsWEEKSEVEN

L14:EquivalentLinearExpressions

7.EE.A.17.EE.A.2

ICAN:● Addandsubtractlinearexpressionswith

fractionalanddecimalcoefficientsbycombiningliketerms.

● Simplifyexpressionsthatincludethedistributiveproperty,multiplevariableterms,andnegativenumbers.

● Applypropertiesofsimplifyingexpressionstocontextssuchasperimetersandareasoftrianglesandrectangles.

● Determinewhethertwoexpressionsareequivalent.

● Writeequivalentexpressionsforlinearexpressions.


WEEKEIGHT

L15:WritingLinearExpressions

7.EE.A.27.EE.A.1

ICAN:● Rewriteexpressionsindifferentformstobetter

understandrelationshipswithincontexts.● Incorporateexpressionsrepresentinglengthand

widthintotheformulasforperimeterandareaoftrianglesandrectangles.


WEEKNINE

†Thesedaysarebuiltintoaccommodateforpossibledaysneededfortesting,review,re-teachingthroughouttheunit.

7THGRADEMATHPACINGGUIDE:3rdNineWeeksWeek Lesson Standards LearningTarget Other


L16:SolveProblemswithEquations

7.EE.B.3a7.EE.B.3b7.EE.B.4a7.NS.A.3

ICAN:● Solveproblemsinvolvingrationalnumbers.● Convertamongfractions,decimals,andpercents

asneededtosolvetheproblems.● Estimatethereasonablenessofanswers.● Solvewordproblemsleadingtoequationsofthe

form��+ � = �and�(�+ �) = �,wherep,q,andrareintegers,fractions,ordecimals.

● Solveusingestimatesforthefractionsanddecimalsfirsttogetanestimatedsolution.


WEEKTWO

L17:SolveProblemswithInequalities;InterimAssessment

7.EE.B.3a7.EE.B.3b7.EE.B.4b

ICAN:● Writeandsolvereal-lifeinequalitiesthatleadto

theform𝑝𝑥 + 𝑞 < 𝑟or𝑝𝑥 + 𝑞 > 𝑟,wherep,q,andrareintegers,fractions,ordecimals.

● Graphandinterpretthesolutionsetofaninequality.


UNITFOUR:GeometryWEEKTHREE

L18:ProblemSolvingwithAngles

7.G.B.47.EE.B.4a

ICAN:● Writeequationstofindunknownanglemeasure

usingpropertiesofsupplementaryandcomplementaryangles.

● Writeequationstofindunknownanglemeasureusingpropertiesofverticalangles.

● Writeequationstofindunknownanglemeasureusingpropertiesofadjacentangles.

● Writeequationstofindunknownanglesinmorecomplexfigurescombiningsupplementary,complementary,vertical,andadjacentangles.

EngageNY:Module3,TopicBEngageNY:Module6,TopicAIllustrativeMathematics

Week Lesson Standards LearningTarget Other

Materials/ProjectsWEEKFOUR

L19:UnderstandConditionsforDrawingTriangles

7.G.A.2*.

ICAN:● Constructtrianglesgivenanglemeasure,side

lengths,orcongruence.● Determinewhetherornotitispossibletodrawa

trianglewithgivencharacteristics.Ifso,drawthetriangle.Ifnot,explainwhynot.

● Determinewhetheratriangleisunique,ifyoucandrawmorethanonevarietyofthattriangle,orifnosuchtriangleexists.

● Drawaquadrilateralwhengivenadescriptionofsidelengthsandanglemeasures.

*Willneedsupplementalresourcetoaddress.EngageNY:Module6,TopicBIllustrativeMathematics

WEEKFIVE

L20:AreaofComposedFigures

7.G.B.5

ICAN:● Findtheareasoftwo-dimensionalobjects

composedoftriangles,quadrilaterals,andpolygons.

● Applyformulastosolvereal-worldandmathematicalproblems.

EngageNY:Module3,TopicCEngageNY:Module6,TopicDIllustrativeMathematics

WEEKSIX

L21:AreaandCircumferenceofaCircle

7.G.B.3

ICAN:● Understandtherelationshipbetweentheradius

anddiameterofacircle.● Understandthattheratioofthecircumference

ofacircletoitsdiametercanbeexpressedaspi.● Discoveranexpressionfortheareaofacircle

usingtheareaofaparallelogram.● Solvereal-worldproblemsinvolvingthe

circumferenceofacircleandtheareaofacircle.



WEEKSEVEN

L22:ScaleDrawings

7.G.A.17.RP.A.1

ICAN:● Understandthatascaleisaratio.● Computeactuallengthsfromascaledrawing

involvinggeometricfigures.● Computeactualareasfromascaledrawing

involvinggeometricfigures.● Reproduceascaledrawingusingadifferent

scale.● Determinethescaleofadrawinggiventheratios

oflengthsandareasinthedrawingandtheactualdimensions.

EngageNY:Module1,TopicDEngageNY:Module4,TopicCIllustrativeMathematics

WEEKEIGHT

L23:VolumeofSolids

7.G.B.5

ICAN:● Findthevolumesofcubesandrightprismsby

multiplyingtheareaofthebasebytheheight.(FocusonV=Bh,notlxwxh.)

● Findthevolumeofcubesandrightprismsinreal-worldsituations.


WEEKNINE

†Thesedaysarebuiltintoaccommodateforpossibledaysneededfortesting,review,re-teachingthroughouttheunit.

7THGRADEMATHPACINGGUIDE:4thNineWeeks


WEEKONE

L24:SurfaceAreaofSolids;InterimAssessment

7.G.B.5

ICAN:● Usetwo-dimensionalformulastocalculate

surfaceareasofcubesandrightprisms.


UNITFIVE:StatisticsandProbabilityWEEKTWO

L26:UnderstandRandomSamples

7.SP.A.1

ICAN:● Understandthatarepresentativesamplecanbe

usedtomakepredictionsaboutlargepopulation.● Describedifferentwaysoffindingasampleand

determinewhichsampleisthemostrepresentativeofagivenpopulation.

● Createarepresentativesampleanduseittomakepredictionsaboutapopulation.


WEEKTHREE

L27:MakingStatisticalInferences

7.SP.A.2

ICAN:● Usedatafromtwosamplestowriteratiosthat

canbeeasilyusedtomakeanestimateaboutapopulation.

● Compareestimatesmadefrommultiplesamplesofthesamesizetogaugethevariationintheestimates.

● Predicttheaccuracyoftheestimatesmadebyvarioussamples.



WEEKFOUR

L28:FindMeasuresofCenterandVariability

7.SP.B.3

ICAN:● Usevisualrepresentations,suchasdotplots,to

comparetworeal-worldnumericaldatasetswithsimilaranddifferingvariabilities.

● Comparedatasetsandmeasurethedifferencebetweenthecenters.

● Representthedifferencebetweencentersofdatasetsbyusingthemean.

● Describethevariationindatasets.

EngageNY:Module5,TopicDIllustrativeMathematics

WEEKFIVE

L29:UseMeasureofCenterandVariabilitytoCompareData

7.SP.B.4

ICAN:● Usedatagatheredfromtwopopulationsto

comparethemean,median,andmode.● Describewhichmeasureofcenteristhebestto

representdata.● Usedatagatheredfromtwopopulationsto

comparethemeasuresofvariabilityincludingrangeandinterquartilerange.

EngageNY:Module5,TopicDIllustrativeMathematics

WEEKSIX

L30:UnderstandProbabilityConcepts

7.SP.C.5

ICAN:● Understandthatprobabilityofachanceeventis

between0and1,with0beingimpossible,closetozerobeingunlikely,closeto½beingneitherunlikelynorlikely,near1beinglikely,and1beingcertain.

● Representthelikelihoodofaneventonanumberline.

● Determineiftheprobabilityofaneventiscloserto0orto1foragivensituation.

● Determineiftheeventisimpossible,unlikely,equallylikely,verylikely,orcertainforagivenevent.

● Connectprobabilitiesof0,¼,½,¾,and1toequivalentdecimalandpercentrepresentations.


Week Lesson Standards LearningTarget Other

Materials/ProjectsWEEKSEVEN

L31:ExperimentalProbability

7.SP.C.6

ICAN:● Performanexperimentmultipletimestogather

dataforanumberofoutcomesandcalculatetheexperimentalprobability.

● Calculatetheexperimentalprobabilityofaneventusingthecombineddataofmanygroupsthencomparethisprobabilitytotheindividualprobabilities.

● Describesomereasonswhytheexperimentalgroupsmightbedifferent.

● Describetheprobabilityyouwouldexpectfor1,000outcomesor10,000outcomes.

● Makeaconjectureabouttheoutcomeofasimilarexperimentwithdifferentnumbers.


WEEKEIGHT

L32:ProbabilityModels

7.SP.C.7a7.SP.C.7b7.SP.C.6

ICAN:● Findtheoreticalprobabilitiesusingreal-world

situations.● Developauniformprobabilitymodelandusethe

modeltodeterminetheprobabilityofevents.● Developaprobabilitymodelandusethemodel

todetermineprobabilitiesofevents.● Comparethepredictedprobabilitiesto

experimentalresultsandexplainpossiblediscrepancies.



WEEKNINE

L33B:SummarizeDataSets

7.SP.D.8a7.SP.D.8b

ICAN:● Usemeasuresofcenterandvariabilityto

describepatternsanddeviationsindata.● Drawconclusionsandjustifyreasoningin

referencetodata.● Analyzethecontextinwhichthedatawere

gathered.● Determinewhichmeasureofcenterorvariability

bestrepresentsthedata.

L33A:ProbabilityandCompoundEvents

Previewof:8.SP.B.4

ICAN:● Listthepossibleoutcomeofacompoundevent

usingorganizedlists,tables,andtreediagrams.● Identifythedesiredoutcomesandtotalnumber

ofoutcomesfromorganizedlists,tables,andtreediagrams.

● Identifytheprobabilityofacompoundeventusingorganizedlists,tables,andtreediagrams.

*Willbedroppedin2017-18SY.EngageNY:Module5,TopicAIllustrativeMathematics

L25:UnderstandPlaneSectionsofPrismsandPyramids

Extensionof:7.G.B.5

ICAN:● Describetheintersectionofaplaneandaright

rectangularprism.● Describetheintersectionofaplaneandaright

rectangularpyramid.● Describetheintersectionofaplaneparallelto

thebaseofaconeorcylinder.● Understandthatintersectionsmaybeparallel,

perpendicular,orneitherparallelorperpendiculartothebaseofthesolid.

DroppedEngageNY:Module6,TopicCIllustrativeMathematics

†Pleasenote,therearetwolessons--nolongerpartoftheTennesseeStateStandards—thatwerenotscheduledwithinthePacingGuide’stimeline.TherearealsotwoweeksbuiltintothePacingGuide,markedfortestingand/oradditionalinstruction.TheuseofthistimeisleftuptoteacherdiscretionastowhethertomoveforwardinthePacingGuideoruseitfortesting,re-teaching,etc.

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