Grade 4 Math Pacing 1St Six Weeks

$Grade 4 Math Pacing 1St Six Weeks$

Grade 4 Math Pacing—1st Six Weeks

Math Domains / Math Pacing / Math Standards / Resources
= Focus Standard / = Supporting Standard

= Additional Standard / Task Arc
To access tasks:
username: tneducation
password: fastestimproving / Additional Tasks
Place Value System
(Through Adding and Subtracting Whole Numbers; Perimeter)
Rationale
Students need a firm foundation in place value and whole numbers, as well as operations with whole numbers. This is the foundation for fractions, and eventually, decimals. / 6 weeks / Generalize place value understanding for multi-digit whole numbers

4.NBT.A.1

Recognizethatinamulti-digitwholenumber,adigitinoneplacerepresentstentimeswhatitrepresentsintheplacetoitsright.For example,recognizethat700÷70=10byapplyingconceptsofplacevalueanddivision.

4.NBT.A.2

Readandwritemulti-digitwholenumbersusingbase-tennumerals,numbernames,andexpandedform.Comparetwomulti-digit numbersbasedonmeaningsofthedigitsineachplace,using,=,andsymbolstorecordtheresultsofcomparisons.

4.NBT.A.3

Useplace valueunderstandingtoroundmulti-digitwholenumberstoanyplace.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

4.NBT.B.4

Fluentlyaddandsubtractmulti-digitwholenumbersusingthestandardalgorithm.

Use the four operations with whole numbers to solve problems—Embedded in every six weeks

4.OA.A.3

Solvemultistepwordproblemsposedwithwholenumbersandhavingwhole-numberanswersusingthefouroperations,including problemsinwhichremaindersmustbeinterpreted.Representtheseproblemsusingequationswithaletter standingfortheunknown quantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.

Gain familiarity with factors and multiples

4.OA.B.4

Findallfactorpairsforawholenumberintherange1–100.Recognizethatawholenumberisamultipleofeach ofitsfactors. Determinewhetheragivenwholenumberintherange1–100isamultipleofagivenone-digitnumber.Determinewhetheragiven wholenumberintherange1–100isprimeorcomposite.

/ Whole Number Place Values
(4.NBT.A.1, 4.NBT.A.2, 4.NBT.A.3)
/ Number Forms Task

Fluency Tasks

Grade 4 Math Pacing—2nd Six Weeks

Math Domains / Math Pacing / Math Standards / Resources
= Focus Standard / = Supporting Standard

= Additional Standard / Task Arc
To access tasks:
username: tneducation
password: fastestimproving / Additional Tasks
Place Value System
(Multiplication and Division; Area of Rectangles)
Rationale
Students should extend the knowledge that they have of whole number place value, as well as multiplication from third grade to relate skills within multiplication (such as area), and make relevant connections to division. / 6 weeks / Use the four operations with whole numbers to solve problems

4.OA.A.1

Interpreta multiplicationequationasa comparison,e.g., interpret35=5×7asastatementthat35is5timesas manyas7and7times asmanyas5.Representverbalstatementsofmultiplicativecomparisonsasmultiplicationequations.

4.OA.A.2

Multiplyordividetosolvewordproblemsinvolvingmultiplicativecomparison,e.g.,byusingdrawingsandequationswithasymbolfor theunknownnumbertorepresenttheproblem,distinguishingmultiplicativecomparisonfromadditivecomparison.

Use place value knowledge/properties of operations to perform multi-digit arithmetic

4.NBT.B.5

Multiplyawholenumberofuptofourdigitsbyaone-digitwholenumber,andmultiplytwotwo-digitnumbers,usingstrategiesbased onplacevalueandthepropertiesofoperations.Illustrateandexplainthecalculationbyusingequations,rectangulararrays,and/or areamodels.

Use the four operations with whole numbers to solve problems

4.OA.A.3

Solvemultistepwordproblemsposedwithwholenumbersandhavingwhole-numberanswersusingthefouroperations,including problemsinwhichremaindersmustbeinterpreted.Representtheseproblemsusingequationswithaletter standingfortheunknown quantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.

Use PV knowledge/properties of operations to perform multi-digit arithmetic

4.NBT.B.6

Findwhole-numberquotientsandremainderswithuptofour-digitdividendsandone-digitdivisors,usingstrategiesbasedonplace value,thepropertiesofoperations,and/ortherelationshipbetweenmultiplicationanddivision.Illustrateandexplainthecalculationby usingequations,rectangulararrays,and/orareamodels.

*Grade4expectationsinthisdomainarelimitedtowholenumberslessthanor equalto1,000,000.
Solve measurement conversion problems going from larger unit to smaller unit

4.MD.A.3

Applytheareaandperimeterformulas forrectanglesinreal worldandmathematicalproblems. Forexample,findthewidthofa rectangularroomgiventhe areaoftheflooringandthelength,byviewingtheareaformulaasamultiplicationequation withan unknownfactor.

/ Multiplication: Exploration of Multiplicative Comparisons and the Link to Division
(4.OA.A.1, 4.OA.A.2)
/ Comparing Reading Books Task

Raffle Tickets Task

Redwood Tree Task

Grade 4 Math Pacing—3rd Six Weeks

Math Domains / Math Pacing / Math Standards / Resources
= Focus Standard / = Supporting Standard

= Additional Standard / Task Arc
To access tasks:
username: tneducation
password: fastestimproving / Additional Tasks
Fractions: Decomposing/Composing, Relation to Division
(Add’l: Line Plots)
Rationale
Students need a strong foundation in fractions in order to conceptually understand decimals. / 6 weeks / Extend understanding of fraction equivalence and ordering

4.NF.A.1

Explainwhyafractiona/bisequivalenttoafraction(n×a)/(n×b)byusingvisualfractionmodels, withattentiontohowthenumber andsizeofthepartsdiffereventhoughthetwofractionsthemselvesarethesame size. Usethisprincipletorecognizeandgenerate equivalentfractions.

4.NF.A.2

Comparetwofractionswithdifferentnumeratorsanddifferentdenominators,e.g.,bycreatingcommondenominatorsornumerators, orbycomparingtoabenchmarkfractionsuchas1/2.Recognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothe samewhole.Recordtheresultsofcomparisonswith symbols,=,or,andjustifytheconclusions,e.g.,byusingavisualfractionmodel.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers

4.NF.B.3a/3b/3c/3d

Understanda fractiona/bwitha1asa sumoffractions1/b.

a.Understandadditionandsubtractionoffractionsasjoiningandseparatingpartsreferringtothesamewhole.
b.Decomposeafractionintoasumoffractionswiththesamedenominatorinmorethanoneway,recordingeachdecompositionby anequation.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.
c.Addandsubtractmixednumberswithlikedenominators,e.g.,byreplacingeachmixednumberwithanequivalentfraction,and/or byusingpropertiesofoperationsandtherelationshipbetweenadditionandsubtraction.
d.Solvewordproblemsinvolvingadditionandsubtractionoffractionsreferringtothe samewholeandhavinglikedenominators,e.g., byusingvisualfraction modelsandequationstorepresenttheproblem.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers

4.NF.B.4a/4b/4c

Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.

a. Understandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodelto represent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).
b.Understandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.For example,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5), recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)
c. Solvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfraction modelsandequationsto representtheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef, andtherewillbe5peopleatthe party,howmanypoundsof roastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?
Represent and interpret data

4.MD.B.4

Makealineplottodisplayadata setofmeasurementsinfractionsofaunit(1/2,1/4,1/8).Solveproblemsinvolvingadditionand subtractionoffractionsbyusinginformationpresentedinlineplots.Forexample,fromalineplotfindandinterpretthedifferencein lengthbetweenthelongestandshortestspecimensinaninsectcollection.

/ Building Non-Unit Fractions
/ Pizza Task

Adding/Multiplying Mixed Numbers Task

Portion of a Whole Task

Star Bar Task

Grade 4 Math Pacing—4th Six Weeks

Math Domains / Math Pacing / Math Standards / Resources
= Focus Standard / = Supporting Standard

= Additional Standard / Task Arc
To access tasks:
username: tneducation
password: fastestimproving / Additional Tasks
Fractions
(Multiplication by a whole number; Decimals)
Rationale
Students need to enter decimals after a firm conceptual understanding of whole #s and fractions. Connections back to these concepts will be important for students to understand decimals to the depth that is necessary for future yrs. / 6 weeks / Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers

4.NF.B.4a/4b/4c

Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.

4.NF.C.6

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.5
Expressafractionwithdenominator10asan equivalentfractionwithdenominator100,andusethistechniquetoaddtwofractions withrespectivedenominators10and100.4Forexample,express3/10as30/100,andadd3/10+4/100=34/100.

(Studentswhocangenerateequivalentfractionscandevelopstrategiesforaddingfractionswithunlikedenominatorsingeneral.But additionandsubtractionwithunlikedenominatorsingeneralisnotarequirementatthisgrade.)

4.NF.C.7

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

**Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

4.MD.A.1

Knowrelativesizesof measurementunitswithinonesystemofunitsincludingkm,m,cm;kg,g;lb,oz.;l,ml;hr,min,sec.Withina single systemofmeasurement,expressmeasurementsinalargerunitintermsofasmallerunit.Recordmeasurementequivalentsinatwo columntable.Forexample,knowthat1ftis12timesas longas1in.Expressthelengthofa4ftsnakeas48in.Generateaconversion tableforfeetandincheslistingthenumberpairs(1,12),(2,24),(3,36),...

4.MD.A.2

Usethefouroperationstosolvewordproblemsinvolvingdistances,intervalsoftime,liquidvolumes, massesofobjects,andmoney, includingproblemsinvolvingsimplefractionsordecimals,andproblemsthatrequireexpressingmeasurementsgiveninalargerunitin termsofasmallerunit.Representmeasurementquantitiesusingdiagramssuchasnumberlinediagramsthatfeatureameasurement scale.

Grade 4 Math Pacing—5th Six Weeks

Math Domains / Math Pacing / Math Standards / Resources
= Focus Standard / = Supporting Standard

= Additional Standard / Task Arc
To access tasks:
username: tneducation
password: fastestimproving / Additional Tasks
Additional Standards
Rationale
Students will apply understanding of major work of the grade level while learning additional standard content. / 6 weeks / Generalize and analyze patterns

4.OA.C.5

Generateanumberor shapepatternthatfollowsagivenrule.Identifyapparentfeaturesofthepatternthatwerenotexplicitintherule itself.Forexample,giventhe rule“Add3”andthestartingnumber1,generatetermsinthe resultingsequenceandobservethattheterms appeartoalternatebetweenoddandevennumbers.Explaininformallywhythenumberswillcontinuetoalternateinthisway.

Draw and ID lines/angles, and classify shapes by properties of lines/angles

4.G.A.1

Drawpoints,lines,linesegments,rays,angles(right,acute,obtuse),andperpendicularandparallellines.Identifytheseintwo- dimensionalfigures.

4.G.A.2

Classifytwo-dimensionalfiguresbasedonthepresenceorabsenceofparallelorperpendicularlines,orthepresenceorabsenceof anglesofaspecifiedsize.Recognizerighttrianglesasacategory,andidentifyrighttriangles.

4.G.A.3

Recognizealineofsymmetryforatwo-dimensionalfigureasalineacrossthefiguresuchthatthefigurecanbefoldedalongtheline intomatchingparts.Identifyline-symmetricfiguresanddrawlinesofsymmetry.

Geometric measurement: Understand concepts of angles & measure angles

4.MD.C.5/5a/5b

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

a.An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
b.An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6

Measureanglesinwhole-numberdegreesusingaprotractor.Sketchanglesofspecifiedmeasure.

4.MD.C.7

Recognizeanglemeasureasadditive.Whenanangleisdecomposedintonon-overlappingparts,theanglemeasureofthewholeisthe sumoftheanglemeasuresoftheparts.Solveadditionandsubtractionproblemstofindunknownanglesonadiagraminrealworldand mathematicalproblems,e.g.,byusingan equationwithasymbolfortheunknownanglemeasure.

Grade 4 Math Pacing—6th Six Weeks

Review and extend conceptual understanding ofgrade 4 standards based on student data

Connecting major 4th grade concepts with 5th grade concepts

Focus on extending understanding of adding and subtracting fractions to unlike denominators
Extend through multiplication of decimals