Striving toward greater focusand coherence through

Content Standards and PracticeStandards

HowtoRead the Grade LevelContentStandards

Standards definewhatstudentsshouldunderstandandbeabletodo.

Clusters are groupsofrelatedstandards.Note thatstandardsfrom differentclustersmaysometimes becloselyrelated,because mathematicsisaconnectedsubject.

Domains are larger groups ofrelatedstandards.Standardsfrom differentdomainsmaysometimesbecloselyrelated.

StandardsforMathematicalPractice

The Common Core State Standards for Mathematical Practice are expected to be integrated into every mathematics lesson for all students Grades K-12. Below are a few examples of how these Practices may be integrated into tasks students complete.

1.Makesenseof problems and persevere in solving them.

MathematicallyproficientstudentsinFirstGradecontinuetodeveloptheabilitytofocusattention,testhypotheses,takereasonable risks,remainflexible,tryalternatives,exhibitself-regulation,andpersevere(Copley,2010).Astheteacherusesthoughtful questioningandprovidesopportunitiesforstudentstosharethinking,FirstGradestudentsbecomeconsciousofwhattheyknowandhowtheysolveproblems.Theymakesenseoftask-typeproblems,findanentrypointorawaytobeginthetask,andare willingtotryotherapproacheswhensolvingthetask.Theyaskthemselves,“Doesthismakesense?”FirstGradestudents’ conceptualunderstandingbuildsfromtheirexperiencesinKindergartenastheycontinuetorelyonconcretemanipulativesand pictorialrepresentationstosolveaproblem,eventuallybecomingfluentandflexiblewithmentalmathasaresultofthese experiences.

2. Reason abstractlyand quantitatively.

MathematicallyproficientstudentsinFirstGraderecognizethatanumberrepresentsaspecificquantity.Theyusenumbersand symbolstorepresentaproblem,explainthinking,andjustifyaresponse.Forexample,whensolvingtheproblem:“Thereare60 childrenontheplayground. Somechildrenlineup.Thereare20childrenstillontheplayground.Howmanychildrenlinedup?” firstgradestudentsmaywrite20+40=60toindicateaThink-Additionstrategy. Otherstudentsmayillustrateacounting-onby tensstrategybywriting20+10+10+10+10=60. Thenumbersandequationswrittenillustratethestudents’thinkingandthe strategiesused,ratherthanhowtosimplycompute,andhowthestoryisdecontextualizedasitisrepresentedabstractlywith symbols.

3. Constructviable arguments and critique thereasoning ofothers.

MathematicallyproficientstudentsinFirstGradecontinuetodeveloptheirabilitytoclearlyexpress,explain,organizeand consolidatetheirmaththinkingusingbothverbalandwrittenrepresentations. Theirunderstandingofgradeappropriatevocabulary helpsthemtoconstructviableargumentsaboutmathematics. Forexample,whenjustifyingwhyaparticularshapeisn’tasquare,a firstgradestudentmayholdupapictureofarectangle,pointingtothevariousparts,andreason,“Itcan’tbeasquarebecause,even thoughithas4sidesand4angles,thesidesaren’tallthesamesize.”Inaclassroomwhererisk-takingandvaryingperspectivesare encouraged,mathematicallyproficientstudentsarewillingandeagertosharetheirideaswithothers,considerotherideasproposed byclassmates,andquestionideasthatdon’tseemtomakesense.

4. Modelwith mathematics.

MathematicallyproficientstudentsinFirstGrademodelreal-lifemathematicalsituationswithanumbersentenceoranequation, andchecktomakesurethattheirequationaccuratelymatchestheproblemcontext.Theyalsousetools,suchastables,tohelp collectinformation,analyzeresults,makeconclusions,andreviewtheirconclusionstoseeiftheresultsmakesenseandrevisingas needed.

5. Use appropriate tools strategically.

MathematicallyproficientstudentsinFirstGradehaveaccesstoavarietyofconcrete(e.g.3-dimensionalsolids,tenframes,number balances,numberlines)andtechnologicaltools(e.g.,virtualmanipulatives,calculators,interactivewebsites)andusethemto investigatemathematicalconcepts. Theyselecttoolsthathelpthemsolveand/orillustratesolutionstoaproblem. Theyrecognize thatmultipletoolscanbeusedforthesameproblem-dependingonthestrategyused. Forexample,achildwhoisinthecounting stagemaychooseconnectingcubestosolveaproblem. While,astudentwhounderstandspartsofnumber,maysolvethesame problemusingten-framestodecomposenumbersratherthanusingindividualconnectingcubes. Astheteacherprovidesnumerous opportunitiesforstudentstouseeducationalmaterials,firstgradestudents’conceptualunderstandingandhigher-orderthinkingskillsaredeveloped.

6. Attend toprecision.

MathematicallyproficientstudentsinFirstGradeattendtoprecisionintheircommunication,calculations,andmeasurements.They areabletodescribetheiractionsandstrategiesclearly,usinggrade-levelappropriatevocabularyaccurately. Theirexplanationsand reasoningregardingtheirprocessoffindingasolutionbecomesmoreprecise.Invaryingtypesofmathematicaltasks,firstgrade studentspayattentiontodetailsastheywork. Forexample,asstudents’abilitytoattendtopositionanddirectiondevelops,they begintonoticereversalsofnumeralsandself-correctwhenappropriate.Whenmeasuringanobject,studentschecktomakesurethat therearenotanygapsoroverlapsastheycarefullyplaceeachunitendtoendtomeasuretheobject(iteratinglengthunits). Mathematicallyproficientfirstgradestudentsunderstandthesymbolstheyuse(=,,)anduseclearexplanationsindiscussionswithothers. Forexample,forthesentence43,aproficientstudentwhoisabletoattendtoprecisionstates,“Fourismorethan3”ratherthan“Thealligatoreatsthefour. It’sbigger.”

7. Look for and makeuseofstructure.

MathematicallyproficientstudentsinFirstGradecarefullylookforpatternsandstructuresinthenumbersystemandotherareasof mathematics.Forexample,whilesolvingadditionproblemsusinganumberbalance,studentsrecognizethatregardlesswhetheryou putthe7onapegfirstandthenthe4,orthe4onfirstandthenthe7,theybothequal11(commutativeproperty).When decomposingtwo-digitnumbers,studentsrealizethatthenumberoftenstheyhaveconstructed‘happens’tocoincidewiththedigit inthetensplace.Whenexploringgeometricproperties,firstgradersrecognizethatcertainattributesarecritical(numberofsides, angles),whileotherpropertiesarenot(size,color,orientation).

8. Look for and expressregularityin repeated reasoning.

MathematicallyproficientstudentsinFirstGradebegintolookforregularityinproblemstructureswhensolvingmathematicaltasks.Forexample,whenaddingthreeone-digitnumbersandbymakingtensorusingdoubles,studentsengageinfuturetaskslookingforopportunitiestoemploythosesamestrategies.Thus,whensolving8+7+2,astudentmaysay,“Iknowthat8and2equal10andthenIadd7more.Thatmakes17.IthelpstoseeifIcanmakea10outof2numberswhenIstart.” Further,studentsuse repeatedreasoningwhilesolvingataskwithmultiplecorrectanswers.Forexample,inthetask“Thereare12crayonsinthebox. Someareredandsomeareblue.Howmanyofeachcouldtherebe?”FirstGradestudentsrealizethatthe12crayonscouldinclude6 ofeachcolor(6+6=12),7ofonecolorand5ofanother(7+5=12),etc.Inessence,studentsrepeatedlyfindnumbersthataddupto12.

First Grade Mathematics CurriculumMap

Waterloo School DistrictScopeand Sequence Overview

Unit of Study / Everyday Math Alignment / Domain and Standards
1 / Section 1 / Domain:
Standards:
2
3
4
5
6
7
8
9
10
11
12

First Grade

Instruction andAssessmentSchedule

2013-2014

Itis expectedthattheunits will be taughtconsecutively. Thetablebelowreflectswhichunits are assessedoneach benchmark.Itis possibletobeginanewunit prior tothequarter in whichit is being assessed.

Approx. Numberof Daysof Instruction / Benchmark 1 / ?? / ?? / ?? / Common Assessment A / ?? / ?? / ?? / Common Assessment B / Benchmark 2 / ?? / ?? / ?? / Common Assessment C / ?? / ?? / ?? / Common Assessment D / Benchmark 3 / Endof
Year
Instructional
Content / Unit of
Study
1 / Unit of
Study
2 / Unit of
Study
3 / Unit of
Study
4 / Unit of
Study
5 / Unit of
Study
6 / Unit of
Study
7 / Unit of
Study
8 / Unit of
Study
9 / Unit of
Study
10 / Unit of
Study
11 / Unit of
Study
12 / Getting Ready forGr.
1 Unit
Assessment / Ch.1
Test / Ch.2
Test / Ch.3
Test / Ch.4
Test / Ch.5
Test / Ch.6
Test / Ch.7
Test / Ch.8
Test / Ch.9
Test / Ch.10
Test / Ch.11
Test / Ch.12
Test

First Grade Mathematics CurriculumMap - Overview

Waterloo School District policyrequires elementarymathematics instruction tobe60 minutes perday.

Unitof Study / Themathematical contentis sequencedinUnits ofStudythatwill take approximately2-3weekseachtoteach.
Thesequence ofUnitsofStudyprovides acoherentflowtomathematics instructionthroughouttheyear.
Everyday Math / The primarytextbook adoptedinWaterloo School Districtfor Grades K-6
Teacher’s
Resources and Notes / Teachersare encouraged tomakenotesoftheirownlessonideasandresourcesthat alignwith eachUnitof
Study.
Additional
Resources
Assessment / There aremanyformative andsummative assessmentoptions:
Unit of Study: 1
Routines / First Grade / Quarter1 / Approx.12 days
Domain: NBT
Cluster(s): 1, 3
MD
4
Domain: OA
Cluster(s): 1, 6
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
1.NBT.1
  • Count to 120.
  • Read numbers to 120.
  • Write numbers to 120.
1.NBT.3
  • Compare two digit numbers using symbols.
1.OA.1
  • Solve addition and subtraction word problems.
1.OA.6
Add and subtract numbers to 20, by beginning to
use mental strategies. / Number line
Tally mark
Tool kit
Pattern-block template
Slate/whiteboard
Calendar
Date
Exploration
More
Less
Pattern block
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
1.MD.4
  • Ask and answer questions about graphs and tables.
  • Collect data using tally marks.
/ Base-ten blocks
Geo-boards
Thermometer
Degree
Temperature
Fahrenheit
Number story
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Routine 1:
1-1
1.NBT.1
Routine 2:
1.NBT.1
Routine 3:
1.NBT.3
Routine 4:
1.NBT.1
Routine 5:
1.NBT.1
1.OA.1
1.OA.6
Routine 6:
1.NBT.3
Routine 7:
1.NBT.1
1.MD.4
Routine 8:
1.NBT.1
1.MD.4
Routine 9:
1.NBT.1
Routine 10:
1.OA.6
1.NBT.1
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Routine 11:
1.NBT.3
Routine 12:
1.NBT.1
1.MD.4
Routine 13:
1.OA.1
1.OA.6
1.NBT.1
Unit of Study 2 / First Grade / Quarter1 / Approx.??days
Domain: NBT
Cluster(s): 1, 4
Domain: OA
Cluster(s): 1,2,3,4,5,6,7
Domain: MD
Cluster(s): 1,3,4
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
1.NBT.1
  • Read and write numbers to 120.
  • Count to 120 starting at any number less than 120.
  • Count and write the number for a given amount of objects to 120.
  • Count to 120.
1.NBT.4
  • Add a 2-digit number and a 1-digit number.
  • Add a 2-digit number and a multiple of ten.
  • Explain what strategy I used to solve my problem.
  • Explain the steps I used to solve my problem.
/ Number grid
Ten frame
Add
Plus
Is equal to/same amount
Number model
Subtract
Minus
Addition
Subtraction
Equations
Counting on
Counting back
Unitof Study 2(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
1.OA.1
  • Solve addition and subtraction word problems.
1OA.2
  • Add three numbers to solve word problems using objects, drawings and equations.
1.OA.3
  • Add numbers in any order and get the same answer.
  • Group numbers together to find the answer.
1.OA.4
  • Use related facts to solve problems with missing values.
1.OA.5
  • Count on to add.
  • Count back to subtract.
  • Count up to subtract.
1.OA.6
  • Add and subtract numbers to 20 using strategies.
  • Fluently add and subtract numbers to 10.
1.OA.7
  • Determine if an addition or subtraction problem is true or false.
  • I know the meaning of the = sign.
/ Counting all
True
False
Everyday Math
Common Core
Alignment / Unitof Study 2 –AdditionalResources
Section:2-1:
1.OA.5
1.OA.6
1.NBT.1
1.NBT.4
Section 2-2:
1.OA.6
1.NBT.1
Section 2-3:
1.OA.6
1.NBT.1
Section 2-4:
1.NBT.1
Section 2-5:
1.NBT.1
1.MD.3
Section 2-6:
1.OA.1
1.NBT.1
1.MD.3
Section 2-7
1.OA.1
1.NBT.1
1.MD.1
Section 2-8
1.OA.1
1.OS.6
Section 2-9
1.MD.3
1.OA.5
1 NBT.3
Everyday Math
Common Core
Alignment / Unitof Study 2 –AdditionalResources
Section 2-10
1.OA.5
1.NBR.1
Section 2-11
1.OA.1
1.OA.5
1.OA.6
1.OA.7
1.NBT.1
1.MD.4
Section 2-12
1.OA.1
1.OA.6
Section 2-13
1.OA.1
1.OA.2
1.OA.3
1.OA.4
1.OA.5
1.OA.6
1.NBT.1
1.NBT.4
Unit of Study 3 / First Grade / Quarter?? / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study3(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study3–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study3–AdditionalResources
Unit of Study 4 / First Grade / Quarter?? / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study4(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study4–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study4–AdditionalResources
Unit of Study 5 / First Grade / Quarter?? / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study5(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study5–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study5–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Unit of Study 1 / Kindergarten / Quarter1 / Approx.?? days
Domain:
Cluster(s):
Domain:
Cluster(s):
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
I can:
Unitof Study1(continued)
MathContentObjectives / Vocabulary / Teacher’sResources and Notes
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources
Everyday Math
Common Core
Alignment / Unitof Study1–AdditionalResources