envision 2.0 grade 1 unit 1 - mrs. finney - about 2.0 topics 1-2 overarching understandings:...

SDUSD First Grade Unit 1 Overview

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FIRST GRADE Unit 1

Addition and Subtraction within 10 35 days

enVision 2.0 Topics 1-2

Overarching Understandings: Mathematical problem situations can be solved and interpreted by using multiple representations such as models, drawings, equations, and words. Addition and subtraction problems can be solved using strategies based on place value, properties of operations, and the relationship between the two operations Essential Questions:

• How can we solve problems in different ways? • How can we solve addition and subtraction problems using different strategies? • How can problem situations and problem-solving strategies be represented? • How can we show that addition and subtraction are related? • How can we use different combinations of numbers and operations to represent the same quantity?

Common Core State Standards: 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.3 Apply properties of operations as strategies to add and subtract. 1.OA.4 Understand subtraction as an unknown-addend problem. 1.OA.5 Relate counting to addition and subtraction. 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums. 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false Key Vocabulary: whole / part / unknown sum difference related facts addition sentence / subtraction sentence minus ( - ) plus ( + ) equals / the same quantity as ( = )

Sentence Frames:

The whole is ____ and the parts are ____ and _____.

The sum of ____ and ____ is _____.

The difference between ______ and _____ is _______.

The related facts for this addition/subtraction sentence are…

I solved the problem by…. This makes sense because…

Suggested Materials: Connecting Cubes Ten-Frames Two-Color Counters Number Cubes (Labeled 1-5) Dominoes Cups Numeral Cards (End of Unit) Number Cubes (Labeled 1-3 twice)

SDUSD First Grade Unit 1 Overview

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Number Talks: Number Talks are used to build number sense and to develop fluency: • Dot Cards • Ten Frames (recognition) • Snap It

SDUSD First Grade Unit 1

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FIRST GRADE

Unit 1 Addition and Subtraction within 10

35 days

31 lessons 1 Assessment Day

2 Re-teaching/Enrichment Days

Suggested Order of Lessons Objective 1: Students will solve problems involving composing and decomposing numbers to 10 by using objects, drawings, number bonds, and equations. (1.OA.1) Lesson Source Title Page Number Notes

1 Engage NY Decompose Numbers to 10 Unit p. 10 2 Engage NY Decompose Numbers to 10 Unit p. 17 3 enVision 2.0 1-2 Solve Problems: Put Together ENV TE p. 15

4 enVision 2.0 1-3 Solve Problems: Both Addends Unknown

ENV TE p. 21

5 Engage NY Ways to Make 6 Unit p. 25 6 Engage NY Ways to Make 7 Unit p. 31 7 SDUSD Ways to Make 8 Unit p. 39 8 SDUSD Ways to Make 9 Unit p. 40 9 enVision 2.0 2-10 Look For and Use Structure ENV TE p. 133

10 SDUSD Represent and Solve Addition Problems

Unit p. 41

Objective 2: Students will solve addition and subtraction story problems by modeling the situations and by using drawings, number bonds, and equations to represent the problem. (1.OA.1, 1.OA.4, 1.OA.6) Lesson Source Title Page Number Notes

11 enVision 2.0 1-4 Solve Problems: Take From ENV TE p. 27

12 enVision 2.0 1-5 Solve Problems: Compare Situations

ENV TE p. 33

13 enVision 2.0 1-6 Continue to Solve Problems:

Compare Situations ENV TE p. 39

14 enVision 2.0 1-7 Practice Solving Problems:

Add To ENV TE p. 45

15 enVision 2.0 1-8 Solve Problems: Put

Together/Take Apart ENV TE p. 51

16 enVision 2.0 1-9 Construct Arguments ENV TE p. 57


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Objective 3: Students will solve problems by using strategies such as counting on or counting back, doubles, and/or the relationship between addition and subtraction. (1.OA.1, 1.OA.3, 1.OA.4, 1.OA.5, 1.OA.6) Lesson Source Title Page Number Notes

17 enVision 2.0 2-1 Count On to Add ENV TE p. 79 18 SDUSD* Counting On to Add Unit p. 43 19 SDUSD* Use a Number Line to Count On Unit p. 45 20 enVision 2.0 2-6 Count Back to Subtract ENV TE p. 109 21 SDUSD* Use a Number Line to Count Back Unit p. 50 22 SDUSD* Use a Number Line to Count Back Unit p. 53 23 enVision 2.0 2-2 Doubles ENV TE p. 85 24 SDUSD Doubles Unit p. 54 25 enVision 2.0 2-7 Think Addition to Subtract ENV TE p. 115

26 enVision 2.0 2-8 Continue to Think Addition to Subtract

ENV TE p. 121

Objective 4: Students will understand the meaning of the equal sign by pairing equivalent expressions and constructing true number sentences (1.OA.3 and 1.OA.7)

Lesson Source Title Page Number Notes 27 enVision 2.0 2-5 Add In Any Order ENV TE p. 103

28 Engage NY Understand the Meaning of the Equal Sign

Unit p. 55

29 SDUSD Concepts of Equality Unit p. 58 Objective 5: Students will solve problems by using various strategies and multiple representations. (1.OA.1, 1.OA.3, 1.OA.4, 1.OA.6) Lesson Source Title Page Number Notes

30 SDUSD* Addition and Subtraction Problem Solving

Unit p. 61

31 SDUSD* Addition and Subtraction Problem Solving

Unit p. 62

32 Assessment 33-35 Re-teaching/Enrichment

Notes: enVision 2.0 Lesson 1-1, 2-3, 2-4,and 2-9 were not included in the suggested order of lessons in an effort to ensure that students have access to a variety of high-cognitive demand tasks that also provide opportunities for students to learn through collaboration. Some of the lessons in Topic 2 are suggested in a different order, as to group lessons of similar focus together. *Unit 1 Lessons 18-19, 21-22, 24,and 30-31 were used with permission of Perry and Associates, Inc. by San Diego Unified School District solely, and Perry and Associates, Inc. retains the copyright on these lessons.


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SDUSD Math Lesson Map

The structure of math lessons should follow the Launch, Explore, Summarize format. This structure allows students to explore mathematical concepts with rigor (fluency, concept development, and application) to develop understanding in ways that make sense. Some rich tasks may take multiple days for students to explore. In these cases, each day should still follow the Launch, Explore, Summarize format.

EXPLORE (15–20 minutes)

The teacher provides opportunities and support for students to develop conceptual understanding by providing meaningful explorations and tasks that promote active student engagement. The teacher monitors the development of student understanding by conferring with students and asking students questions in order to understand and stimulate their thinking. The teacher uses this information to plan for the Summarize and, if needed, to call the students together for a mid-Explore scaffold to focus or propel student thinking. The students are actively engaged in constructing meaning of the mathematical concept being taught. Students engage in private reasoning time before working with partners or groups. Students use multiple representations to solve rich tasks and communicate their mathematical understanding.

INDIVIDUAL, PAIRS, OR SMALL GROUP

SUMMARIZE (15–20 minutes)

The teacher provides opportunities to make public the learning that was accomplished by the students by sharing evidence of what was learned, and providing opportunities for students to analyze, compare, discuss, extend, connect, consolidate, and record thinking strategies. A summary of the learning is articulated and connected to the purpose of the lesson. The students are actively engaged as a community of learners, discussing, justifying, and challenging various solutions to the Explore task. The students are able to articulate the learning/understanding of the mathematical concept being taught either orally or in writing. Students can engage in this discussion whether or not they have completed the task.

WHOLE GROUP

PRACTICE, REFLECT, and APPLY (10–15 minutes) This time is saved for after the Summarize so students can use what they have learned to access additional tasks. The opportunities that teachers provide are responsive to student needs. The students may have the opportunity to: revise their work, reflect on their learning, show what they know with an exit slip, extend their learning with a similar or extension problem, or practice with centers or games. The teacher confers with individual students or small groups.

INDIVIDUAL, PAIRS, OR SMALL GROUP

Number Talks 15 minutes

Number Talks are a chance

for students to come together to practice fluency and share their mathematical thinking by

engaging in conversations and discussions around

problem solving and number sense activities.

LAUNCH (5–10 minutes) The teacher sets the stage for learning by ensuring the purpose and the rationale of the lesson are clear by connecting the purpose to prior learning, posing the problem(s), and introducing the Explore task for students. During this time the teacher is identifying the tools and materials available, reviewing academic vocabulary, and setting the expectations for the lesson. The students are actively engaged in a short task or discussion to activate prior knowledge in preparation of the Explore task. Students may be using tools and/or manipulatives to make sense of the mathematical concept.

WHOLE GROUP

FO

RM

ATIVE A

SSESSMEN

T

The teacher determines w

hat students are learning and are struggling with by conferring w

ith students and by examining student w

ork throughout the lesson. This form

ative assessment inform

s ongoing adjustments in the lesson and next steps for the class and each student.

The students are actively engaged in showing their learning accom

plishments related to the m

athematical concept of the lesson.


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SDUSDMathematicsUnitsWeunderstandthatfordeepandsustainablechangeinmathematicstotakeplace,teachers,students,andleadersmustgrapplewithwhattherichmathematicsaskedforbyCommonCoreStateStandards-Mathematicslookslikeintheclassroom,inpedagogicalpractice,instudentwork,incurriculum,andinassessments.ItisourgoalthatteachersandsiteleadersworkcollaborativelytowardasharedvisionofmathinstructionthatdevelopsmathematicallyproficientstudentsasdefinedbytheCCSS-Mathematics.Itisourhopethattheseunitsprovideacommoninstructionalfoundationforthiscollaboration.TheSDUSDMathematicsUnitsaredesignedtosupportteachersandstudentsasweshiftfromamoredirectivestyleofteachingmathematicstowardamoreinquiry-basedstyle.Inproblem-basedlearning,studentsdevelopthehabitsofmindandinteractionofmathematiciansthroughengaginginmathematicaldiscourse,connectingrepresentations,askinggenuinequestions,andjustifyingandgeneralizingideas.ThesemathematicalhabitsreflecttheshiftsinpedagogyrequiredtosupporttheCommonCoreStandardsforMathematicalPractice.TheSDUSDmathunitsarecompiledwithmultiplesourcestoensurestudentshaveavarietyofmathematicalexperiencesalignedtotheCCSS.AlllessonsshouldfollowthestructureofLaunch,Explore,andSummarize.Thefollowingdocumentwillguideteachersinplanningfordailylessons,byhelpingthemunderstandthestructuresofeachofthesources.

StructureforenVision2.0Lessons

UseStep1Develop:Problem-BasedLearningistheLaunch,Explore,andSummarizeforeveryenVision2.0Lesson.

Launch:(Before)StartwiththeSolve-and-Shareproblem.Posetheproblemtothestudentsmakingsuretheproblemisunderstood.Thisdoesnotmeanyouexplainhowtodotheproblem,ratheryouensurethatstudentsunderstandwhattheproblemisabout.Establishclearexpectationsastowhetherstudentswillworkindividually,inpairs,orinsmallgroups.Thisincludesmakingsurestudentsknowwhichrepresentationsandtoolstheymightbeusingoriftheywillhaveachoiceofmaterials.Explore:(During)Studentsengageinsolvingtheproblemusingavarietyofstrategiesandtools.Usethesuggestedguidingquestionstocheckinbrieflywithstudentsasneeded,inordertounderstandandpushstudentthinking.Youmaywanttousethe“ExtensionforEarlyFinishers”asneeded.Summarize:(After)Selectstudentworkfortheclasstoanalyzeanddiscuss.Ifneeded,usetheSampleStudentWorkprovidedforeachlessoninenVision2.0.Practice,Reflect,Apply:(SelectProblemsfromWorkbookPages,Reteach,Games,InterventionActivity)Duringthistime,studentsmayrevisetheirworkfromtheExploretimeoryoumayusepiecesofStep2Develop:VisualLearningandStep3AssessandDifferentiate.Note:TheQuick-CheckcomponentisnowafewselectproblemsthatarehighlightedwithapinkcheckmarkintheTeacher’sEdition.Thistimeprovidesanexcellentopportunitytopullsmallgroupsofstudentsthatmayneedadditionalsupport.


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StructureforEngageNYLessons

Launch/Explore:(ConceptDevelopment)TheConceptDevelopmentconstitutesthemajorportionofinstructionaltimewhennewlearningisintroduced.Duringthistime,thelessonsmovethroughadeliberateprogressiononmaterial,fromconcretetopictorialtoabstract.Yourwordchoicemaybeslightlydifferentfromthatinthevignettes,andyoushouldusewhatworksfromthesuggestedtalkingpointstomeetyourstudents’needs.Summarize:(StudentDebrief)Thestudentdebriefpiecehelpsdevelopstudents’metacognitionbyhelpingthemmakeconnectionsbetweenpartsofthelesson,concepts,strategies,andtoolsontheirown.Thegoalisforstudentstoseeandhearmultipleperspectivesfromtheirclassmatesandmentallyconstructamultifacetedimageoftheconceptsbeinglearned.Throughquestionsthathelpmaketheseconnectionsexplicit,anddialoguethatdirectlyengagesstudentsintheStandardsforMathematicalPractice,theyarticulatethoseobservationssothelesson’sobjectivebecomeseminentlycleartothem.Practice,Reflect,Apply:(ProblemSet/ExitTicket)TheProblemSetoftenincludesfluencypertainingtotheConceptDevelopment,aswellasconceptualandapplicationwordproblems.TheprimarygoaloftheProblemSetisforstudentstoapplytheconceptualunderstandingslearnedduringthelesson.ExitTicketsarequickassessmentsthatcontainspecificquestionstoprovideaquickglimpseoftheday’smajorlearning.ThepurposeoftheExitTicketistwofold:toteachstudentstogrowaccustomedtobeingindividuallyaccountablefortheworktheyhavedone,andtoprovideyouwithvaluableevidenceoftheefficacyofthatday’sworkwhichisindispensibleforplanningpurposes.Thistimeprovidesanexcellentopportunitytopullsmallgroupsofstudentsthatmayneedadditionalsupport.


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StructureforGeorgiaStandardsLessonsTheGeorgiaStandardstaskshavebeenincludedintheunitstoprovidestudentsopportunitiesforrich,engaging,real-worldmathematicalexperiences.Thesetasksallowstudentstodevelopconceptualunderstandingovertimeandmaytakemorethanonemathlessontocomplete.Theextratimefortheselessonshasbeenallottedforintheunits.WhenplanningforaGeorgiaTask,itissuggestedthatyoustartbydoingthemathematicsthestudentswillbeengaginginbeforepresentingittothestudents.Launch:Youmayneedtoactivatepriorknowledgeforsomeofthetasksthatwillbepresentedbyshowingimages,lettingstudentsengageinpartnertalkaboutreal-lifesituations,orusingthesuggestedactivityfromthebackgroundknowledgecomponent.Posethetasktothestudentsmakingsurethetaskisunderstood.Thisdoesnotmeanthatyouexplainhowtodotheproblem,ratheryouensurethatstudentsunderstandwhattheproblemisabout.Youestablishclearexpectationsastowhetherstudentswillworkindividually,inpairs,orinsmallgroups.Thisincludesmakingsurestudentsknowwhichrepresentationsandtoolstheymightbeusingoriftheywillhaveachoiceofmaterials.Explore:Studentswillengageinworkingonthetaskusingavarietyofstrategiesandtools.YoumayusetheEssentialQuestionsorFormativeAssessmentquestionsprovidedinthelessonasneededinordertounderstandandpromptstudentthinking.Summarize:Selectstudentworkfortheclasstoanalyzeanddiscuss.Usepartnershipsandwhole-classcollaborativeconversationstohelpstudentsmakesenseofeachothers’work.TheFormativeAssessmentquestionsmayalsobeusedduringthistimetofacilitatetheconversation.Practice,Reflect,Apply:Atthistime,providestudentstimetoreflectandrevisetheirworkfromtheExploreafterthey have engaged in the conversationintheSummarizeportionofthelesson.Thistimeprovidesanexcellentopportunitytopullsmallgroupsofstudentsthatmayneedadditionalsupport.


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CommonCoreApproachtoAssessmentAssessmentsprovideongoingopportunitiesforstudentstoshowtheirlearningaccomplishmentsinadditiontoofferingstudentsapathwaytomonitortheirprogress,celebratesuccesses,examinemistakes,uncovermisconceptions,andengageinself-reflectionandanalysis.Acentralgoalofassessmentsistomakestudentsawareoftheirstrengthsandweaknessesandtogivethemopportunitiestotryagain,dobetterand,indoingso,enjoytheexperienceofseeingtheirhardworkpayoffastheirskillandunderstandingincreases.Furthermore,thedatacollectedasaresultofassessmentsrepresentinvaluabletoolsinthehandsofteachersandprovidesspecificdataaboutstudentunderstandingthatcaninforminstructionaldecisions.ForeachTopicinenVision2.0thefollowingassessmentsareavailable: IntheStudentWorkbook: -TopicAssessment -PerformanceAssessment OnlineTeacher’sEdition: -AdditionaltopicassessmentBlack-lineMaster -AdditionalperformanceassessmentBlack-lineMaster OnlineStudentAssessment -Teachercanmodifythenumberofitemsonanassessment -Teachercanrearrangeorderofproblems AlloftheassessmentitemsforenVision2.0arealignedtothetypesofproblemsstudentsmayencounteronstatetesting.WehavefoundenVision2.0hasanexcessiveamountofitemssuggestedforeachtopic.Toavoidover-assessing,werecommendthatschoolsitesworkcollaborativelyingrade-levelteamstodeterminehowtobestusealltheassessmentresourcesavailabletoevaluatestudentunderstandingandreducetheamountofitemsassessed.TheSDUSDmathunitshavegroupedrelatedtopicstogetherwithinaunit.Sitesmaychoosetoonlygiveanassessmentattheendofeachunit,consistingofitemsfrommultipletopics,ratherthanusingmultipledaystoassesseachtopicindividually.

SDUSD First Grade Unit 1 Lesson 1

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NYSCOMMONCOREMATHEMATICSCURRICULUM 1

Objective:Analyzeanddescribeembeddednumbers(to10)using5-groupsandnumberbonds.

ConceptDevelopment(30minutes)

Materials:(T)TenFrame(S)TenFrameforeachstudent,10counters,personalwhiteboardwithnumberbondtemplate

T: Pulloutyourtenframe.Counttofindouthowmanyframesthereare.Waitforthesignaltotellme.

S: (Pause.Whenallareready,givethesignal.)10!T: Howmanyframesareinthetoprow?:5!T: Howmanyframesareinthebottomrow?S: 5!T: Takeoutthecountersinyourbag.Place5counters

intothetoprow.(Pause.)Howmanycountersdoyouhaveinyourtoprow?

S: 5!T: Nowwearegoingtobenumberdetectives.Let’ssee

whatnumbersarehidinginsideof5!T: Isee2hidinginside.Look.(Showthe2objectsyou

found.)Whatothernumbersdoyouseehidinginside5?Talktoyourpartner.

T: (Circulateandlisten.Encouragethosewhoaretouchingandcountingratherthanseeingtheembeddednumberswithin5torecognizequantitiesofatleast2or3.)

T: (ShowtheNumberBond)ThisiscalledaNumberBond.Writethe5inthetotalboxofanumberbond.)That’sourtotal,orwhole.

T: Yousaidtherewasa2hidinginsideof5.That’sapart.(Writethe2inthenumberbond.)

T: Let’scoverthose2counters.Whatistheotherpart?S: 3!T: Let’swritethatintheotherpartofthenumberbond.(Write3.)T: What2partsdidwefindmake5,detectives?S: 2and3!T: Let’sseeifwecanfinddifferentnumbersinsideof5.(Write5inthetotalboxinsideanew

numberbond.)T: (Continuetofindtheothernumbersinsideof5andgeneratethecorrespondingnumberbonds

usingthesameprocess.)T: Let’stakeout2morecountersandputtheminthe

total

part part

5

2 3

NumberBond


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bottomrowofthetenframe.T: Howmanycountersaretherenow?S: 7.T: Turnandtalktoyourpartneraboutwhatnumbersyou

seeinside7.S: (Studentssharetheirobservationsasyoucirculate.T: Iheardastudentsaythattheysaw5counters.Are

there5counters?S: Yes!T: Let’sdraw5dotsasapartinournumberbondinsteadofthenumber

5.T: Wheredidyouseethe5?S: Inthetoprow.T: Let’scoverthe5.Whatistheotherparttomake7?S: 2!T: Let’sdrawin2dotsastheotherpartinthenumberbond.T: Let’scountonfrom5tofindourtotal.Countwithme.Let’sstartwith

5.(Pointtothefifthdot.)T/S:Fiiiiiive,6,7.(Pointtoeachofthedotsasyoucountthem.Drawin7

dotsinthetotalboxthe5-groupway.)T: Let’snowrepresentthisnumberbondwithnumbersinsteadofdots.(Leadthe

studentstomakethenumberbondnumericallyontheirpersonalwhiteboards.)

Continuetofindfiveanditspartnerwithin6,7,8,and9.OthercombinationswillbeexploredinLesson2.Releasethestudentstoworkindependentlyasyoudetermineisbest.

ProblemSet(10minutes)

StudentsshoulddotheirpersonalbesttocompletetheProblemSet.Someproblemsdonotspecifyamethodforsolving.ThisisanintentionalreductionofscaffoldingthatinvokesMP.5,UseAppropriateToolsStrategically.

MP.7Numberbondwithpartsdrawnthe5-

groupsway.


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StudentDebrief(7minutes)

LessonObjective:Analyzeanddescribeembeddednumbers(to10)using5-groupsandnumberbonds.

TheStudentDebriefisintendedtoinvitereflectionandactiveprocessingofthetotallessonexperience.

InvitestudentstoreviewtheirsolutionsfortheProblemSet.Havethemworkinpairstocheckovertheirworkanddiscusshowtheysawthe5andtheotherparttomaketheirnumberbondsandfindthetotals.Thengooveranswersasaclass.LookformisconceptionsormisunderstandingsthatcanbeaddressedintheDebrief.GuidestudentsinaconversationtodebrieftheProblemSetandprocessthelesson.Youmaychoosetouseanycombinationofthequestionsbelowtoleadthediscussion.

§ Arethere5butterflies?Strawberries?(Wewantstudentstoseethatthereare5soccerballs,etc.,embeddedwithinthelargernumbers.Thereare6butterfliesinall.Havethemidentifytheotherpartoncetheyhaveseenthefivewithinthenumber.)

§ Lookatthesoccerballsandthepencils.Whatisthesameaboutthem?Whatisdifferentaboutthem?(Guidestudentstoseethatboth8and9have5embeddedinthem.Iftheynoticetheotherembeddednumberssuchas1to8,thatisgreat!)

§ Canyoushowmefivefingers?Showmefivewithtwohands(i.e.,4and1,or3and2).Nowshowmefivewithonehand.

ExitTicket(3minutes)

AftertheStudentDebrief,instructstudentstocompletetheExitTicket.Areviewoftheirworkwillhelpyouassessthestudents’understandingoftheconceptsthatwerepresentedinthelessontodayandplanmoreeffectivelyforfuturelessons.Youmayreadthequestionsaloudtothestudents.


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NYSCOMMONCOREMATHEMATICSCURRICULUM 1 ProblemSet

Name Date

Circle5andmakeanumberbond.1.

2.

3.

4.

5 5

5

5


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ProblemSetNYSCOMMONCOREMATHEMATICSCURRICULUM 1

Makeanumberbondthatshows5asonepart.7. 8. 9. 10.


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ExitTicketNYSCOMMONCOREMATHEMATICSCURRICULUM 1

Name Date

Makeanumberbondforthepicturesthatshows5asonepart.1. 2.


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NYSCOMMONCOREMATHEMATICSCURRICULUM 1•1

Objective:Reasonaboutembeddednumbersinvariedconfigurationsusingnumberbonds.

ApplicationProblem

Bellaspilledsomepencilsonthecarpet.Genocameovertohelpherpickthemup.Genofound5pencilsunderthedeskandBellafound4bythedoor.Howmanypencilsdidtheyfindtogether?Drawamathpictureandwriteanumberbondandanumbersentence,orequation,thattellsaboutthestory.

(Bonus:Haveearlyfinishersdrawthe9pencilsinadifferentarrangementtoshowtwoparts.)

Note:Usethetermsnumbersentenceandequationinterchangeably.Thisapplicationproblemisdesignedasabridgefromthepreviouslesson,whichfocusedonseeingandcountingonfrom5.Studentsagainworkwith5andanothernumbertoencouragethiscountingon.

ConceptDevelopment

Materials:(T)Dotcardsof6–9(S)Dotcardsof6–9,personalwhiteboards

T: (Pointtothe7apples.)Howmanyapplesarethere?S: (Pause.Whenallareready,givethesignal.)7!T: Talktoyourpartneraboutthedifferentgroupsofapplesyousee

hidinginsideof7.(Circulateandlistentostudentdiscussion.)Whattwodifferentgroupsornumberpartnersdoyousee?

S: (Answersmayvary.)Isaw4and3.T: (Group4and3applesbydrawingacirclearoundthem.)T: Countontofindthetotal.Startwith4.(Pointtoeachapplein

the3group.)T/S:Foooouuuur,5,6,7.Whatisthetotal?S: 7.T: Whataretheparts?S: 4and3.T: Let’smakeanumberbondtomatchthispicture.(Drawthebond.Askstudentstonamethepartsandthewhole.)T: Whatothernumberpartnersdoyousee?(Elicitotherwaysthatstudentsseetwoembeddednumbers

within7andmakecorrespondingnumberbonds.)T: (Continuemodeling,decomposing6,8,or9andfillinginthetwo-partnumberbondbycountingon

tofindthetotal.)

Configurationof7toshowordraw:


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NYSCOMMONCOREMATHEMATICSCURRICULUM 1•1


StudentsshoulddotheirpersonalbesttocompletetheProblemSetwithintheallotted10minutes.Forsomeclasses,itmaybeappropriatetomodifytheassignmentbyspecifyingwhichproblemstheyworkonfirst.Someproblemsdonotspecifyamethodforsolving.StudentssolvetheseproblemsusingtheRDWapproachusedforApplicationProblems.

Note:Oncestudentshavecircledtheparts,encouragethemtocountonfromonequantitytodeterminethetotal(atthispointitdoesn’tmatterifit’sthelargerorsmallerquantity).Ifastudentisreluctant,hideonepartwithapaperoryourhand.Ask,“Howmanyareundermyhand?”Letthestudentrecountifnecessaryandhidethepartagain.Thenhavethemcountonfromthehiddenpartoncetheyareconfident.


LessonObjective:Reasonaboutembeddednumbersinvariedconfigurationsusingnumberbonds.


InvitestudentstoreviewtheirsolutionsfortheProblemSet.Theyshouldcheckworkbycomparinganswerswithapartner,discussinghowtheyfoundembeddednumbersandcountedontodeterminethetotal,beforegoingoveranswersasaclass.LookformisconceptionsormisunderstandingsthatcanbeaddressedintheDebrief.

GuidestudentsinaconversationtodebrieftheProblemSetandprocessthelesson.Youmaychoosetouseanycombinationofthequestionsbelowtoleadthediscussion.

§ TalktoyourpartnerabouthowyoufoundthetotalinProblem6.Didyoucountallofthedotsordidyoucountonfromapartyousaw?

§ Pickonequestionwhereyouandyourpartnercameupwithadifferentwaytomakethetotal.Howisthetotalthesamewhenyoucameupwithdifferentparts?

§ Istherealwaysmorethanonewaytomakethetotal?§ LookatProblem9.Howwereyoursolutionsdifferentorsimilartoyourpartner’ssolutions?§ (Showexamplesofstudentworkfromtheapplicationproblem.)Whatwerethetwopartsinour

storyproblem?Whatdoesthathaveincommonwithtoday’slesson?Canyouseeanotherwaytoarrangethesepencils?

§ Turntoyourpartnerandsharewhatyoulearnedintoday’slesson.Whatdidyougetbetteratdoingtoday?


AftertheStudentDebrief,instructstudentstocompletetheExitTicket.Areviewoftheirworkwillhelpyouassessthestudents’understandingoftheconceptsthatwerepresentedinthelessontodayandplanmoreeffectivelyforfuturelessons.Youmayreadthequestionsaloudtothestudents.


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ProblemSetNYSCOMMONCOREMATHEMATICSCURRICULUM 1•1

Name Date

Circle 2 parts you see. Make a number bond to match.

1. 2.

3. 4. 5. 6.


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ProblemSetNYSCOMMONCOREMATHEMATICSCURRICULUM 1•1

9. How many pieces of fruit do you see? Write at least 2 different number bonds to show different ways to break apart the total.


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ExitTicketNYSCOMMONCOREMATHEMATICSCURRICULUM 1•1

Name Date

Circle 2 parts you see. Make a number bond to match.

1. 2.


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DotCardsTemplateNYSCOMMONCOREMATHEMATICSCURRICULUM 1•1


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24



25

2

22


Objective:Representputtogethersituationswithnumberbonds.Countonfromoneembeddednumberorparttototalsof6and7andgeneratealladditionexpressionsforeachtotal.


Materials:(T)Charttorecorddecompositionsof6(S)Bagof10two-colorcounters,picturecardwith6apples

Chooseagroupofstudentswhohavedifferentattributestorepresentdecompositionsof6(e.g.,4boys,2girls;5withshoelaces,1without;3withshortsleeves,3withlongsleeves).Besuretoencouragetheactorsthemselvestoparticipateinthemathematicsofthelesson.

T: Howmanystudentsdoyousee?S: 6!T: Howmanyboysarethere?S: 4!T: Howmanygirlsarethere?S: 2!T: Talktoyourpartneraboutwhatwouldbeagoodstrategytoseehowmanystudentsthereare

altogether.(Circulateandlistentostudentdiscussion.)S: Wecancountonfrom4.T: Pointwithmetokeeptrackaswecountonfrom4.(Gesturearoundthegroupof4,andthentouch

the2studentsontheheadasyoucountonwiththeclass.)S: Fouuuur,5,6!T: Whatpartsdidweputtogethertomake6?T: Let’swritethosepartsinanumbersentence.(Callonstudentstohelpyouwritetheequation 6=4+2ontheboard.)T: (Askthe2girlstomovetotheleft,andthe4boystomovetotheright.)Whatwouldournumber

sentencelooklikeifwestartedwiththegirlsfirst?Talktoyourpartneraboutwhatthenumbersentencewouldbe.

T: (Circulateandlistentostudentdiscussion.Callonstudentstohelpyouwritetheequation6=2+4ontheboard.)

T: Now,lookattheshoesonthesestudents.Inoticeshoesthathave…S: (Answersmayvary.)Shoelaces!


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2

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Repeattheearlierprocesswithdecomposingaccordingtohavingshoelacesandnot,andagainwithshortsleevesandnot,inordertocompletedecomposing6.

Bringupthetopicofzeroandthetotalasapossibledecomposition:

T: Howmanystudentsdoyouseeuphere?S: 6!T: Howmanytigersdoyouseeuphere?S: 0!T: Howmanylivingthingsdoyouseeuphere?S: 6!T: Howcanwewritethatstoryinanumbersentence?S: 6+0=6!T: Thinkofadifferentstorythatshows6+0=6.(Ifnecessaryask,“Thinkofwhatwecanmakethe

zerorepresent.”)Callonstudentstoshare.T: Whenweaddzero,weaddnothingtotheotherpart.Andthisisanotherwaywecanmake6!Six

andzeromakes6!


Distributethepicturecardfor6,theProblemSet,andabagof10two-colorcounterstoeachstudent.

T: Let’slookatthepictureof6applesanduseourcounterstofinddifferentwaystomake6.T: Howmanyapplesdoyousee?S: 6.T: Let’sseehowmanyappleswithstemsarethere.Putaredcounteroneachappleaswecount.S: 1,2,3,4.T: Howmanyapplesdonothavestems?Let’sputayellow/whitecounteroneachstem-lessappleand

count.S: 1,2.T: Let’sseehowmanyapplestherearebycountingonfromtheredcounters.Asyoucount,touch

eachcounter.S: Foooour,5,6.T: (Havestudentswritetheexpressionstomatchtheseparts.)Whenwewritethepartslikethis,4

+2,wecallitanexpression.It’snotafullnumbersentence.Itshowsthetwopartswithoutshowingwhatitisequalto.

Repeatthisprocesstoexploretherestoftheapplecombinationsinthepictureandtocompletetheremainderoftheproblemset.Helpstudentssetupaportfoliotosavetheirworkwithdecompositionsof6.Intheupcominglessonstheywillsavedecompositionsof7,8,9,and10.Youdonotneedtofocusonthecommutativepropertyinthislesson.


27

2

22



LessonObjective:Representputtogethersituationswithnumberbonds.Countonfromoneembeddednumberorparttototalsof6and7andgeneratealladditionexpressionsforeachtotal.


InvitestudentstoreviewtheirsolutionsfortheProblemSet.Theyshouldcheckworkbycomparinganswerswithapartnerbeforegoingoveranswersasaclass.LookformisconceptionsormisunderstandingsthatcanbeaddressedintheDebrief.GuidestudentsinaconversationtodebrieftheProblemSetandprocessthelesson.Youmaychoosetouseanycombinationofthequestionsbelowtoleadthediscussion.

T: Whydidwekeeptrackoftheapplesaswecounted?S: Sowewouldn’tcountanytwiceormissany!T: Talkwithyourpartneraboutallofthedifferentwaysyou

made6!S: (Studentsworktogethertochecktheirworkandthe

numbers’referentsinthepicture.)T: Wewillwritenumberbondstoshowallthedifferentways

youmade6.Whatwasthebiggestpartyoufoundinyournumberbond,andwhatwasitspartner?

S: 6!And0!T: (Recordthisnumberbondonachart,andcallonstudentsto

helpyouwritetheexpressions.)

Repeatthisprocessinordertorecordallofthedecompositionsof6(5+1,4+2,3+3).Askthefollowingquestiontoclosethelesson:

§ Whatdoyounoticeaboutthetwopartsintheexpressionsthatmake6aswelookattheminorderfromlefttoright?

§ Turntoyourpartnerandtalkaboutwhatwelearnedaboutintoday’slesson.Whatdidyougetreallygoodattoday?


AftertheStudentDebrief,instructstudentstocompletetheExitTicket.Areviewoftheirworkwillhelpyouassessthestudents’understandingoftheconceptsthatwerepresentedinthelessontodayandplanmoreeffectivelyforfuturelessons.Youmayreadthequestionsaloudtothestudents


28

ProblemSet


Name Date Ways to Make 6

Use the apple picture to help you write all of the different ways to make 6.

+

+

+

+

+

+

+

+


29

ExitTicket


Name Date

Show different ways to make 6. In each set, shade some circles and leave the others blank.

Write a number bond to match this picture.

Write a number sentence to match this picture.

+ =


30

Lesson2DotCardsTemplate


31


Objective:Representputtogethersituationswithnumberbonds.Countonfromoneembeddednumberorparttototalsof6and7andgeneratealladditionexpressionsforeachtotal.


Materials:(T)Numberbondonthewhiteboard,markers,charttorecorddecompositionsof7(S)5-groupcards,picturecardwithsevenchildreninaclassroom,scissors,gluestick,asheetofblankpaperfordebrief

Havestudentssitinabigsemi-circlefacingthegiantnumberbondinthemiddle.Distribute5-groupcardstoeachpairofstudents.Tellthemtheywillbeusingthemtoshowdifferentwaystomake7.Instructstudentstoputtheircardsinorderfromsmallesttolargest.

Usingyourstudentsasactors,chooseagroupofstudentswhohavedifferentattributesthatrepresentdecompositionsof7,andhavethemlineupattheboard(e.g.,6withshorthair,1withlonghair).

Note:Besuretoencouragetheactorsthemselvestoparticipateinthemathematicsofthelesson.

T: Howmanystudentsarehere?S: 7!T: Write7inthetotalboxofthenumberbond.)T: Whatdoesthis7represent?(Pointtothe7.)S: (Responsesmayvary.)Thekids.T The7inourwholerepresentsthenumberofstudents.(Labelthewholewiththewordstudents.)T: There’s1studentupherewhohassomethingdifferentfromtherest!Whatisit?S: 1haslonghair!T: (Write1inthenumberbond.)T: Whatdoesthis1represent?(Pointtothe1.)S: Longhair.T: The1representsthepartofourstudentswithlonghair,soIamgoingtolabelthispartlonghair.

(Writelonghairnexttothepartwiththenumber1.)T: Show1withyour5-groupcardusingthedotside,andputitinfrontofyou.T: If[Student1withlonghair]haslonghair,whatabouttherestofthesestudents?S: TheyhaveshorthairT: Howmanystudentshaveshorthair?S: 6!T: (Write6inthenumberbond.)T: HowshouldIlabelthispart?S: Shorthair.T: Yes.6representsthenumberofstudentswithshorthair.(Teacherwritesshorthairnexttothepart

withthenumber6.)


32


1

T: Nowshow6withyour5-groupcardusingthedotside,rightnexttoyourfirstcard.T: What’sthebeststrategytofindouthowmanystudentstherearealtogether?S: (Responsesmayvary.)Countonfrom1!T: Pointwithmetokeeptrackaswecountonfrom1.(Gesturearoundthegroup

of1,andthentouchthe6studentsontheheadasyoucountonwiththeclass;havethemsitdownasyoucountthem.)

T: Nowit’syourturntocounton.Flipoveryour1dotcardtoshowthenumber1.Thencountonfrom1.Besuretotouchandcount!

S: (Countonfrom1to7,pointingtoeachdot.)T: Whatarethe2partsthatmake7?S: 1and6.T: Saythenumbersentencethatmakes7.(Pointtoeach

boxasstudentsrespond.)S: 1+6=7.T: (Recordthisonthechartbeneaththenumberbond.)T: Saythenumbersentencestartingwiththestudents

withshorthair.S: 6+1=7.T: Saythenumbersentencestartingwiththetotal.S: 7=1+6.T: Saythenumbersentencestartingwiththetotalbutflip

thepartsthistime.S: 7=6+1.

Continuethisprocesswiththeotherdecompositionsof7.Keepthesameactorsbutrearrangethemtoshowdifferentdecompositionsof7(e.g.,2sit,5stand;3smiling,4frowning).Reviewzeroifnecessary.ProblemSet(10minutes)Distributethepicturecardwithsevenstudentsinaclassroom,theworksheet,and5-groupcardsforeachstudent.SimilartoLesson4,studentsrecordallofthedecompositionsof7(innumberbondsandasexpressions)ontheirworksheetastheyusethe5-groupcardstocountonjustastheydidduringtheConceptDevelopmentlesson.Useyourjudgmenttodeterminewhetherstudentsshouldcompletethiswhole-group,insmallgroups,orindependently.

StudentsshoulddotheirpersonalbesttocompletetheProblemSet.Forsomeclasses,itmaybeappropriatetomodifytheassignmentbyspecifyingwhichproblemstheyworkonfirst.Someproblemsdonotspecifyamethodforsolving.StudentssolvetheseproblemsusingtheRDWapproachusedforApplicationProblems.


33



LessonObjective:Representputtogethersituationswithnumberbonds.Countonfromoneembeddednumberorparttototalsof6and7andgeneratealladditionexpressionsforeachtotal.

HavestudentsbringtheirProblemSettothemeetingarea.Askthemtocutouttheirnumberbondsfromthesheet,andplacetheminanorderthatisnumerical(studentsmaybeginwith7+0,then6+1,5+2,etc.,or0+7,1+6,2+5,etc.).

T: Talkwithyourpartnerabouthowyouputyournumberbondsof7inanorderbasedonthenumbers.Doesyourwayoforderinglookthesameasordifferentfromyourpartners?

S: (Responsesmayvary.)T: Let’swriteallofthenumberbondsof7.(Recordallof

thenumberbondsof7onachartbeginningwith7and0,andcallonstudentstohelpyouwritetheexpressions.)

Havethestudentsgluetheirnumberbondsinanorder,startingwith7and0,onablanksheetofpaper.Studentswillrefertothissheetastheyworktowardsmasteringalldecompositionsof7.Askthefollowingquestionstoclosethelesson:

§ Lookatallthewayswemade7inthisposter.Whatpatternsdoyousee?

§ Let’srevisitourposterfor6.Whatdoyouseeisthesameanddifferentaboutourpostershowingwaystomake6,andourpostershowingwaystomake7?Talktoyoupartner.


34



35

ProblemSetNYSCOMMONCOREMATHEMATICSCURRICULUM 1

+

+

Name Date Ways to Make 7! Use the classroom picture to help you write the expressions and number bonds to show all of the different ways to make 7.

+

+

+

+

+

+


36

ExitTicketNYSCOMMONCOREMATHEMATICSCURRICULUM 1

Name Date Color in two dice that make 7 together. Then fill in the number bond and number sentences to match the dice you colored.

7

7

7

7

7


37

TemplateNYSCOMMONCOREMATHEMATICSCURRICULUM 1

5-groupcards.Copydouble-sidedoncardstocktomake5-groupcardsandsingle-sidedformatchinggames.

0 1 2 3

4 5 6 7

8 9 10 10

10 10 5 5


38

TemplateNYSCOMMONCOREMATHEMATICSCURRICULUM 1


39

First Grade Unit 1 Lesson 7

LESSON FOCUS

Ways to Make 8

MATERIALS Two-Color Counters, Cup, White Board LAUNCH Model Ketchup and Mustard Game

1. Put 8 Two-Color Counters in a cup 2. Shake cup and spill the counters to show on document camera. 3. Have students describe what they notice about the counters to a

partner. 4. Students share ideas to the group. 5. Teacher names the red counters as “ketchup” and the yellow

counters as “mustard.” 6. Have students record a number bond and equation to represent the

situation. 7. Repeat

EXPLORE Ketchup and Mustard Game

1. Students play Ketchup and Mustard with a partner and record a number

bond and equation to match.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display one of their arrangements on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: How many different ways can you show eight? Have students turn and talk to a partner, then facilitate a whole class discussion. Teacher records equations on a chart. Ask, “How do you know we have all the ways?”


40


LESSON FOCUS Ways to Make 9 MATERIALS Two-Color Counters, Cup, White Board LAUNCH Model Ketchup and Mustard Game

1. Put 9 Two-Color Counters in a cup 2. Shake cup and spill the counters to show on document camera. 3. Have students describe what they notice about the counters to a

partner. 4. Students share ideas to the group. 5. Teacher names the red counters as “ketchup” and the yellow

counters as “mustard.” 6. Have students record a number bond and equation to represent

the situation. 7. Repeat

EXPLORE Ketchup and Mustard Game

1. Students play “Ketchup and Mustard” with a partner and record a number

bond and equation to match.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display one of their arrangements on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: How many different ways can you show nine? Have students turn and talk to a partner, then facilitate a whole class discussion. Teacher records equations on a chart. Ask, “How do you know we have all the ways?”


41

First Grade Concept 1 Lesson 10

LESSON FOCUS

Students will represent and solve problems involving addition to 10

MATERIALS

Number Cubes (labeled 1-5), Two-Colored Counters, Recording Sheet (See master at end of lesson)

LAUNCH

Joining Groups of Apples

1. Draw a Number Bond on the board 2. Tell students that you have 4 red apples and 3 yellow apples. 3. Ask students, “How can we find out how many apples in all using our number

bond?” 4. Have students help fill in the parts of the number bond with 4 and 3 and 7 as

the whole. 5. Repeat with other combinations to 10.

EXPLORE

Bushels of Apples Students work with partners. Use red and yellow counters or tiles to represent “apples” for this task. 1. Partner one rolls a number cube and places that many red “apples” in the barrel. 2. Partner two then rolls a number cube and places that many yellow “apples” in the second barrel. 3. Students write the two numbers on the recording sheet, find the sum, and write an addition sentence. 4. Students should trade recording sheets and check each other’s addition. 5. Ask students to discuss the following questions with their partner (display these questions using a chart or computer):

1. How did you find out how many apples there were in the two barrels? 2. Which number sentence shows the most apples? 3. Which number sentence shows the least apples?

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Pose the following question: How did you find out how many apples there were in the two barrels?

Have students turn and talk to a partner, then facilitate a whole class discussion.


42

Name: _________________________ Directions: One partner rolls the number cube and places that many red “apples” in the barrel. The second partner rolls the number cube and places that many yellow “apples” in the other barrel. Record the number of apples and write an addition sentence in the table below.

Red (1st Roll)

Yellow (2nd Roll)

In all

Addition Sentence

#1

_______ + _______ = _______

#2

_______ + _______ = _______

#3

_______ + _______ = _______

#4

_______ + _______ = _______

Red(1stRoll)

Yellow(2ndRoll)


43

ProblemSolvingAddition

ToolsYouCanUse2-ColorCounters

StrategiesForSolvingCountOn4+2(think4,5,6)


LESSON FOCUS

Count On 1 and 2

MATERIALS Cups, 2-Color Counters, Number Cube (1-6), Numeral Cards (1-2), Recording Sheet LAUNCH:

Counting On 1. Tell students to start with the number 4 and count on one more. 2. Have students say 4 softly or in their minds and then say 7. 3. Tell students to start with the number 6 and count on two more. 4. Have students say 6 softly or in their minds and then say 7,8. 5. Repeat with different numbers counting on one and two more. Give each student a cup and ten 2-color counters. 6. Have students put 4 counters in their cup. 7. Have students place two more counters in front of their cup. 8. Guide students as they add one counter at a time to the cup. 9. Have them say 4 and count on as they drop each counter in. 10. Have students dump out all their counters out of their cup. 11. Repeat with different numbers counting on 1 and 2 more. 12. Tell students that one strategy for adding two numbers together is to begin with

one number and count on. 13. Begin the following chart that you will add to during the next few lessons:

EXPLORE:

Count On 1 and 2 Students work with partners. Give each partnership a Count On Recording Sheet, a cup, 2-color counters, a number cube, and numeral cards 1-2. 1. One student rolls a number cube and places that amount of 2-color counters in

the cup. 2. The other student picks a numeral card and counts on while adding that amount

of 2-color counters in the cup. 3. Students draw a picture to model the situation and addition sentences on their

recording sheet. 4. Students dump the counters out. 5. Partners switch roles and repeat with different numbers.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Pose the following question: How can you find the sum without counting all?



44

Name _________________________________ Date _________________

567

_______ + _______ = _______ ______ + ______ = _______

_______ + _______ = _______ ______ + ______ = _______

___5____ + ___2____ = ___7____ ______ + ______ = _______


45


LESSON FOCUS

Use a Number Line to Count On

MATERIALS Large Number Line (See master at end of lesson), Number Line Recording Sheet (See master at end of lesson), Addition Expression Slips (See master at end of lesson), 2-Color Counters

LAUNCH

Number Lines Draw a number line on the board that spans 0-10. 1. Tell students that a number line can help us count on. 2. Write 5 + 2 on the board. 3. Ask students, “How can we use the number line to solve this problem?”

(Students should say find the 5 and count on 2 more. If not, guide them in this direction continuing from yesterday’s lesson)

4. Have a student come up and circle the 5 on the number line. [0d1d2d3d4d5d6d7d8d9d0!d] 5. Ask, “Now what do you do?” 6. Have students count on 2 aloud with you as you draw the hops on the

number line. Encourage students to count aloud 5, 6, 7. [00d1d2d3d4d5dD6DdF7d8d9d0!d] 7. Ask students, “How does this help you find the sum for 5 + 2?” 8. Write 2 + 7 on the board. 9. Ask students, “How do you know what number to count on from?” 10. Repeat the process above for this expression starting at 7 and counting on

2 more. 11. Tell students that they can use the count on strategy by using a number

line as a tool. 12. Add to Number Lines to Problem Solving Chart. Note: Counting on is more efficient if students say the larger number first, then count on 1, 2, or 3 as required.

Problem Solving Addition

Tools You Can Use 2-Color Counters Number Lines

Strategies For Solving Count On 4 + 2 (think 4, 5, 6)

EXPLORE Adding on a Number Line Give each student a Large Number Line, a Number Line Recording Sheet, some Addition Expression Slips and 2-color counters. 1. Students choose an Addition Expression Slip. 2. Students place a 2-color counter on the number line for one addend and

then count on to find the sum. 3. Students record their work on the Number Line Recording Sheet and write

the sum. Students repeat with a different Addition Expression Slip.


46

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display one of their number lines on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: How can a number line help you to count on? Have students turn and talk to a partner, then facilitate a whole class discussion. Teacher records equations on a chart.

Ask, “How do you know we have all the ways?”


47

[0d1d2d3d4d5d6d7d8d9d0!d]




[0d1d2d3d4d5d6d7d8d9d0! d]


48

Name_____________________________________Date_______________

4+2=6


[0d1d2d3d4dD5dD6dF7d8d9d0! d]







________+________=________

________+________=________

________+________=________

________+________=________

________+________=________

________+________=________ ________+________=________


49

1+4 6+1 2+85+2 2+4 1+51+8 9+1 3+47+3 2+6 2+77+1 3+6 5+31+6 8+2 4+38+1 6+3 5+14+1 3+7 7+2


50


LESSON FOCUS

Use a Number Line to Count Back 1 and 2

MATERIALS Counters, Large Number Line (See master for Lesson 25), Number Line Recording Sheet (See master at end of lesson),, Subtraction Expression Slips (See master at end of lesson), 2-Color Counters

LAUNCH Counting Back from 10 1. Review counting to 10 forward and backward aloud with the class. 2. Show students a number line with endpoints 0 and 10. 3. Have students count aloud with you as you point to each number on the

number line. 4. Place a counter on the 10 on the number line. 5. Have the students count back 1 aloud as you move the counter. 6. Have students say the subtraction sentence (10 - 1 = 9). Write it on the

board. 7. Continue to count back 1 and 2, moving the counter and saying the

subtraction sentences aloud. 8. Start a new chart for subtraction strategies that you will add to in the next

few lessons. 9. Tell students that one strategy for solving subtraction problems that involve

1, 2, and 3 is to count back.

EXPLORE

Number Line Subtraction Give each student a Large Number Line, a Number Line Recording Sheet, some Subtraction Expression Slips and 2-color counters. 1. Students choose a Subtraction Expression Slip. 2. Students place a 2-color counter on the number line for the first number and

then count back to find the difference. 3. Students record their work on the Number Line Recording Sheet and write

the difference. 4. Students repeat with a different Subtraction Expression Slip.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display one of their number lines on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: How can a number line help you to count back? Have students turn and talk to a partner, then facilitate a whole class discussion.

ProblemSolvingSubtraction

ToolsYouCanUseNumberLine

StrategiesForSolvingCountBack5-2(think5,4,3)


51

Name _____________________________________ Date _______________

4+2=6








________+________=________

________+________=________

________+________=________

________+________=________

________+________=________

________+________=________ ________+________=________

[0d1d2d3dK4d5d6d7d8d9d0!d]


52

4-2 3-2 10-28-1 2-1 10-17-2 5-2 6-23-1 7-1 5-19-2 8-2 2-21-1 6-1 9-14-1


53


LESSON FOCUS

Use a Number Line to Count Back 3

MATERIALS Connecting Cubes, Number Cubes (labeled 1-3 twice), Numeral Cards 4-10, Number Line 0-10 (See master at end of lesson 26), Number Line Recording Sheet

LAUNCH More Counting Back Give each student some connecting cubes. 1. Have students practice counting backward from 10, first as if counting down

to a rocket launch and then in groups of 3 (9-8-7, 6-5-4, 3-2-1). 2. Write 10 - 3 = ____ on the board. 3. Have students use the connecting cubes to model the problem. 4. Remind them to say 10 before they count back 3. (9, 8, 7) 5. Repeat with different subtraction sentences. 6. Add Connecting Cubes under Tools on the chart.

EXPLORE

More Number Line Subtraction Give partners a number cube, a set of numeral cards, a number line, and a Number Line Recording Sheet. 1. One student rolls the number cube and the other student picks a numeral

card. 2. Have students use the number on the card and the number on the number

cube to begin a subtraction sentence. 3. Partners work together to use the number line to solve the problem and

write the difference. 4. Partners repeat with different numbers.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display one of their number lines on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: How can a number line help you to count back? Have students turn and talk to a partner, then facilitate a whole class discussion.

ProblemSolvingSubtraction

ToolsYouCanUseNumberLineConnectingCubes

StrategiesForSolvingCountBack5-2(think5,4,3)


54


LESSON FOCUS

Doubles

MATERIALS Cups, 2-Color Counters, Number Cube (1-6), Numeral Cards (1-2)

LAUNCH

Doubles 1. Pose the following problem: Jan and Fran are twins. They have the same

number of toys. If they each have four toys, how many toys do they have in all? 2. Have students use connecting cubes to model the problem, draw a number

bond and write an equation to match. 3. Add doubles to the strategy chart.

EXPLORE

Doubles Students work with partners. Give each partnership a one number cube labeled 1-6, connecting cubes in two colors, and paper 1. One student rolls a number cube and both partners build a tower that

represents that number in different colored cubes. 2. Partners determine how many cubes they have in all, draw a number bond, and

write an equation to match. 3. Partners switch roles and repeat with different numbers.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Pose the following question: Is 6 + 4 a double? How do you know?



55

Lesson17NYSCOMMONCOREMATHEMATICSCURRICULUM 1

Lesson17Objective:Understandthemeaningoftheequalsignbypairingequivalentexpressionsandconstructingtruenumbersentences.


Materials:(S)Bagof20linkingcubes,10redand10yellow,expressiontemplate,personalwhiteboards

Havestudentssitnexttotheirmathpartnersattheirtables.

T: Let’splayagamecalledMakeitEqual.PartnerB,closeyoureyes.PartnerA,makeyourlinkingcubeslookexactlylikemine.(Show4redand1yellowcubesasastick.)Hideyourstickbehindyouandcloseyoureyes.

T: PartnerB,openyoureyes.Makeyourlinkingcubeslookexactlylikemine.(Show3redand2yellowcubesasastick.)

T: PartnerA,openyoureyes.Everyone,writetheexpressionthatshowshowmanycubesyouhave.S: (PartnerAwrites4+1;PartnerBwrites3+2.)T: Showeachotheryourlinkercubestick.Howaretheythesame?Howaretheydifferent?S: (Discussasteachercirculates.)T: Howaretheydifferent?S: Ihad4redand1yellowcubes,butmypartnerhad3redand2yellowcubes.T: Howaretheythesame?S: Webothhave5cubes.T: Eventhoughyouhavedifferentparts,doyouhavethesametotal?S: Yes.T: Putyourexpressionsnexttoeachother.Now,putyoursticksinbetweentheexpressionsbyputting

themoneabovetheother.Whatdothe2stickslooklikenow?S: Anequalsign!T: Hmmm….doesthismakesense?Howmanycubesdoyouhaveontheleftsideoftheequalsign?S: 5.T: Howmanycubesdoyouhaveontherightsideoftheequalsign?S: 5.T: Does5equal5?(Write5=5onboard)S: Yes!T: Does4+1equal3+2?(Write4+1=3+2onboard)S: Yes!T: Let’ssaythenumbersentence.T/S:4+1=3+2.T: Thisiscalledatruenumbersentence.


56

Lesson17NYSCOMMONCOREMATHEMATICSCURRICULUM 1

Repeatthisprocess.Youmightusethefollowingsuggestedsequence:5+2and6+1;7+2and6+3.

Next,project3redand3yellowlinkingcubesandhavepartnersuseoneboardtowritetheexpression.Thenproject1redand5yellowlinkingcubes.Partnerswritetheexpressiononthesecondboard.Askstudentstogivethumbsupiftheseexpressionsareequal.Ifyes,havethemdrawanimaginaryequalsignbetweenthetwoboardsandsaythetruenumbersentence.Repeatthisprocessbutbesuretoincludesomeexpressionsthatarenotequivalent(suchas3+5and4+2).

T: (Projectastickof6redand2yellowcubes.)Writeanexpressiontomatchthesecubesononeofyourwhiteboards.

S: (Write6+2.)T: Withyourpartner,useyourlinkingcubestomakeanothersticktoshowthesametotalinadifferent

way.Writetheexpressiontomatchyourstick.Thenuseyourstickstomaketheequalsigntohelpyousaythetruenumbersentence.

Ifstudentsfinishearly,encouragethemtomakeupasmanyequivalentexpressionsastheycan.Repeatthisprocess.Youmayusethefollowingsuggestedsequence:3+4,4+5,and3+7.


DistributeProblemSettostudents,andallowthemtoworkindependentlyorinsmallgroups.

StudentsshoulddotheirpersonalbesttocompletetheProblemSetwithintheallotted10minutes.Forsomeclasses,itmaybeappropriatetomodifytheassignmentbyspecifyingwhichproblemstheyworkonfirst.Someproblemsdonotspecifyamethodforsolving.StudentssolvetheseproblemsusingtheRDWapproachusedforApplicationProblems.


LessonObjective:Understandthemeaningoftheequalsignbypairingequivalentexpressionsandconstructingtruenumbersentences.


InvitestudentstoreviewtheirsolutionsfortheProblemSet.Theyshouldcheckworkbycomparinganswerswithapartnerbeforegoingoveranswersasaclass.LookformisconceptionsormisunderstandingsthatcanbeaddressedintheDebrief.GuidestudentsinaconversationtodebrieftheProblemSetandprocessthelesson.Youmaychoosetouseanycombinationofthequestionsbelowtoleadthediscussion.

§ LookatProblems1–4.InProblem1,wehaveapplesplusoranges,andthatequalsfruit.WhataboutProblem2?WhataboutProblem3?WhataboutProblem4?HowisProblem3differentfromtheothers?(Theyarelikeunits.)


57

Lesson17ProblemSetNYSCOMMONCOREMATHEMATICSCURRICULUM 1

Name Date

Write an expression that matches the groups on each plate. If the plates have the same amount of fruit, write the equal sign between the expressions.

+ +

+ +

+ +

+ +

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LESSON FOCUS

Students will pair equivalent expressions and construct true number sentences.

MATERIALS

Dominoes, White boards, Engage NY Lesson 17

LAUNCH

Domino Equality

1. Give every student one domino (dots sum 10 or less) 2. Have students record the addition sentence that represents their domino. 3. Choose several dominoes to draw up on the board and record the students’

number sentences. 4. Have students talk to their partners and discuss which dominoes have the

same sum. 5. Have students come up and model their dominoes with an equal sign in

between and ask, “How do we know these two expressions have the same value?”

6. Ask, “What is the same about the two expressions?” and “What is different about the two expressions?”

7. Write the entire equation on board (ex: 4 + 3 = 6 + 1) and ask, “Is this a true number sentence?”

8. Ask, “How do you know? Note: Continue to find expressions that are equal to each other and use them to write true number sentences, having the students explain why the number sentence is true.

EXPLORE

EngageNY Lesson 17 (Problems 5-6) Or Continue work from Launch giving each student a domino and having them try to find a match to match a true number sentence.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display one of their true number sentences on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: How can you tell if your number sentence is true or false? Have students turn and talk to a partner, then facilitate a whole class discussion.


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5. Write an expression to match each domino.

Find two sets of expressions that are equal. Connect them below with = to make true number sentences.

Find two sets of expressions that are equal. Connect them below with = to make true number sentence

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Name Date

Shade the equal dominoes. Write a true number sentence.


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LESSON FOCUS

Addition and Subtraction Strategies

LAUNCH

Solving Story Problems 1. Write the following problem on the board: Jared collects rocks. He has 4

rocks in his collection. How many more rocks does he need to have 8 altogether?

2. Ask, “What do we need to find out?” 3. Have students use connecting cubes to solve the problem. 4. Ask, “What strategy did you use to solve the problem?” 5. Ask, “Did someone use a different strategy?” 6. Have several students share their thinking on the board or overhead. 7. Have students share an equation that matches this problem. (There may be

more than one) 8. Repeat the process with the following problem: Bob has $3. How many

more dollars will he need to earn to have $8 altogether EXPLORE Solving Story Problems

1. Write the following problem on the board: Sue has _____ marbles in her

collection. Sarah has _______ marbles in her collection. How many more marbles does Sue need to have the same amount as Sarah?

2. Give students three different number choices to use when solving the problem: (2, 3), (4, 7), (13, 18)

3. Students may work with partners or small groups to solve the problem using any strategy they want.

4. Students use words, pictures and/or numbers to explain how they got their answer.

5. Students choose another set of numbers to use in the problem as time allows.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display a few different strategies used by students on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: Which strategy was used to solve the problem? Have students turn and talk to a partner, then facilitate a whole class discussion.


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LESSON FOCUS

Addition and Subtraction Strategies

LAUNCH

Solving Story Problems 1. Write the following problem on the board: There are some kids playing in

the park. 5 more come and join them in the park. Now there are 9 kids playing in the park. How many kids were there to start?

2. Ask, “What do we need to find out?” 3. Have students use connecting cubes to solve the problem. 4. Ask, “What strategy did you use to solve the problem?” 5. Ask, “Did someone use a different strategy?” 6. Have several students share their thinking on the board or overhead. 7. Have students share an equation that matches this problem. (There may be

more than one)

EXPLORE: Solving Story Problems Write the following problem on the board: Michael has some toy cars. His brother has _____ toy cars. Altogether they have ______ toy cars. How many does Michael have? 1. Give students three different number choices to use when solving the

problem: (3, 5), (2, 7), (8, 13) 2. Students may work with partners or small groups to solve the problem using

any strategy they want. 3. Students use words, pictures and/or numbers to explain how they got their

answer. 4. Students choose another set of numbers to use in the problem as time

allows.

SUMMARIZE Refocus the class by sitting in a large circle for a whole class discussion. Select a student to display a few different strategies used by students on the document camera or in the center of the circle. Ask students, “What do you notice about _______’s work? Pose the following question: Which strategy was used to solve the problem? Have students turn and talk to a partner, then facilitate a whole class discussion.

envision 2.0 grade 1 unit 1 - mrs. finney - about 2.0 topics 1-2 overarching understandings:...

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