KINDERGARTEN MATHEMATICS COMMON CORE STATE STANDARDS K MATH
M A T H E M A T I C SCOMMON CORESTATE STANDARDSKMATHK I N D E R G A RT E NA Crosswalk to the Michigan Grade LevelContent ExpectationsIntroductionIn June 2010, the Michigan State Board of Education adopted the Common CoreState Standards (CCSS) as the state K-12 content standards for Mathematics andEnglish Language Arts.The complete CCSS standards document can be found at www.michigan.gov/k-12 .Districts are encouraged to begin this transition to instruction of the new standardsas soon as possible to prepare all students for career and college. New assessmentsbased on the Common Core State Standards will be implemented in 2014-2015. Moreinformation about Michigan’s involvement in the CCSS initiative and development ofcommon assessments can be found at www.michigan.gov/k-12 by clicking the CommonCore State Standards Initiative linkThe CCSS for Mathematics are divided into two sets of standards: the Standards forMathematical Practices and the Standards for Mathematical Content. This documentis intended to show the alignment of Michigan’s current mathematics Grade LevelContent Expectations (GLCE) to the Standards for Mathematical Content to assistwith the transition to instruction and assessment based on the CCSS.It is anticipated that this initial work will be supported by clarification documentsdeveloped at the local and state level, including documents from national organizationsand other groups. This document is intended as a conversation starter for educatorswithin and across grades. While curriculum revisions will be guided by local curriculumexperts, ultimately the alignment is implemented at the classroom level. Educators willneed to unfold these standards in order to compare them to current classroompractice and identify adjustments to instruction and materials that support the depthof understanding implicit in these new standards.The crosswalk between the Grade Level Content Expectations and the Standardsfor Mathematical Content is organized by Michigan Focal Points/CCSS Critical Areas.There is not an attempt to show one-to-one correspondence between expectationsand standards, because for the most part there is none at this level. The alignment occurswhen looking across focal points/critical areas and/or across GLCE topics/CCSS domains.(continued on next page)www.michigan.gov/mde
Mathematical PracticesThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators atall levels should seek to develop in their students. These standards appear in every grade level and are listedbelow:Mathematical Practices1. Make sense of problems, and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments, and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for, and make use of, structure.8. Look for, and express regularity in, repeated reasoning.Organization of the Common Core State StandardsEach CCSS grade level document begins with a description of the “critical areas.” These Critical Areas are parallelto the Michigan Focal Points. Below is a comparison of the Michigan Focal Points to the Critical Areas for thisgrade.MichiganKindergarten Focal PointsCommon Core State StandardsKindergarten Critical AreasRepresenting, comparing, and ordering wholenumbers and joining and separating setsRepresenting and comparing whole numbers, initiallywith sets of objectsDescribing shapes and spaceDescribing shapes and spaceOrdering objects by measurable attributesThe standards themselves are organized by Domains (large groups that progress across grades) and then byClusters (groups of related standards, similar to the Topics in the Grade Level Content Expectations).Cluster statement2K I N D E R GA RT E NM AT H E M AT I C S MICHIGAN DEPARTMENT OF EDUCATION
The table below shows the progression of the CCSS domains and clusters across the grade before, the target grade, and the followinggrade.PREKINDERGARTEN (MI)1KINDERGARTEN1ST GRADECOUNTING AND CARDINALITY (CC)ELE. 7. Develop an understanding ofnumbers and explore simplemathematical processes (operations)using concrete materials. Know number names and the countsequence. Count to tell the number of objects. Compare numbers.OPERATIONS AND ALGEBRAIC THINKING (OA) Understand addition as putting together andadding to, and understand subtraction astaking apart and taking from. Represent and solve problems involvingaddition and subtraction. Understand and apply properties ofoperations and the relationship betweenaddition and subtraction. Add and subtract within 20. Work with addition and subtractionequations.NUMBER AND OPERATIONS IN BASE TEN (NBT) Work with numbers 11–19 to gainfoundations for place value. Extend the counting sequence. Understand place value. Use place value understanding andproperties of operations to add andsubtract.ELE.2. Develop skills of comparing andclassifying objects, relationships, and eventsin their environment.MEASUREMENT AND DATA (MD) Describe and compare measurableattributes. Measure lengths indirectly and by iteratinglength units.ELE. 5. Discover simple ways to measure. Classify objects and count the number ofobjects in categories. Tell and write time. Represent and interpret data.GEOMETRY (G)ELE. 8. Build visual thinking skills throughexplorations with shape and the spaces intheir classrooms and neighborhoods. Identify and describe shapes. Reason with shapes and their attributes. Analyze, compare, create, and rly Childhood Standards of Quality 160470 7.PDF. It should be noted that the MathematicsEarly Learning Expectations not listed in this chart map to the Standards for Mathematical Practices.1M AT H E M AT I C S MICHIGAN DEPARTMENT OF EDUCATIONK I N D E R GA RT E N3
4K I N D E R GA RT E NM AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
Alignment of Michigan Content Expectations to Common CoreStandards by Michigan Focal PointMichigan Content ExpectationsCommon Core State StandardsFocal PointCritical AreaRepresenting, comparing, and ordering wholenumbers and joining and separating setsRepresenting and comparing whole numbers,initially with sets of objectsCOMMON CONTENTMathematicalPractices1. Make sense ofproblems, andpersevere insolving them.2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.Count, write, and order numbersN.ME.00.01 Count objects in sets up to 30.N.ME.00.02 Use one-to-one correspondence tocompare and order sets of objects to 30 usingphrases such as “same number”, “more than”, or “lessthan”; use counting and matching.N.ME.00.03 Compare and order numbers to 30using phrases such as “more than” or “less than.”N.ME.00.04 Read and write numbers to 30 andconnect them to the quantities they represent.N.ME.00.05 Count orally to 100 by ones. Count to30 by 2’s, 5’s and10’s using grouped objects asneeded.4. Model withmathematics.5. Use appropriatetools strategically.Know number names and the count sequenceMathematicalK.CC.1 Count to 100 by ones and by tens.PracticesK.CC.2 Count forward beginning from a given1. Make sense ofnumber within the known sequence (instead ofproblems, andhaving to begin at 1).persevere inK.CC.3 Write numbers from 0 to 20. Representasolving them.number of objects with a written numeral 0-20 (with2. Reason abstractly0 representing a count of no objects).and quantitatively.Count to tell the number of objects3. Construct viableK.CC.4 Count to tell the number of objects.arguments, andUnderstand the relationship between numbersandcritique thequantities; connect counting to cardinality.reasoning ofothers. namesa. When counting objects, say the numberin the standard order, pairing each object with4. Model withone and only one number name and eachmathematics.number name with one and only one object.6. Attend toprecision.5. Useappropriateb. Understand that the last numbernamesaidtoolstells the number of objects counted.Thestrategically.numberof objects is the same regardless of their6. Attendtoarrangement or the order in whichthey wereprecision.counted.7. Look for, and makeuse of, structure7. Lookfor, andmakec. Understand that each successivenumbernameuse of, structurerefers to a quantity that is one larger.K.CC.5 Count to answer “how many?”questions8. Lookfor, andabout as many as 20 things arranged inexpressa line, aregularityrectangular array, or a circle, or as manyin,asrepeated10 thingsin a scattered configuration; given a numberfromreasoning.1-20, count out that many objects.8. Look for, andexpress regularityin, repeatedreasoning.Compare numbersK.CC.6 Identify whether the number of objects inone group is greater than, less than, or equal to thenumber of objects in another group, e.g., by usingmatching and counting strategies. (Include groupswith up to ten objects.)K.CC.7 Compare two numbers between 1 and 10presented as written numerals.M AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010K I N D E R GA RT E N5
Michigan Content ExpectationsCommon Core State StandardsCompose and decompose numbersWork with numbers 11-19 to gain foundations forplace valueN.ME.00.06 Understand the numbers 1 to 30 ashaving one, or two, or three groups of ten and someones. Also count by tens with objects in ten-groupsto 100.K.NBT.1 Compose and decompose numbers from11 to 19 into ten ones and some further ones, e.g.,by using objects or drawings, and record eachcomposition or decomposition by a drawing orequation (such as 18 10 8); understand thatthese numbers are composed of ten ones and one,two, three, four, five, six, seven, eight, or nine ones.N.MR.00.07 Compose and decompose numbersfrom 2 to 10, e.g., 5 4 1 2 3, with attentionto the additive structure of number systems, e.g., 6 isone more than 5, 7 is one more than 6.MathematicalN.MR.00.08Practices Describe and make drawings torepresent situations/stories involving putting1. Makesenseandof taking apart for totals up to 10; usetogetherproblems,andfinger and object counting.persevere inAdd andsubtract numberssolvingthem.N.MR.00.09 Record mathematical thinking by2. Reason abstractlywriting simple addition and subtraction sentences,and quantitatively.e.g., 7 2 9, 10 - 8 2.Understand addition as putting together and addingto, and understand subtraction as taking apart andtaking fromK.OA.1 Represent addition and subtraction withobjects, fingers, mental images, drawings (drawingsneed not show details, but should show themathematics in the problem), sounds (e.g., claps),acting out situations, verbal explanations, expressions,or equations.3. Constructviable patternsExplore numberarguments, andN.MR.00.10Create, describe, and extend simplecritiquethenumber patterns.reasoningofothers.K.OA.2 Solve addition and subtraction wordproblems, and add and subtract within 10, e.g., byusing objects or drawings to represent the problem.K.OA.3 Decompose numbers less than or equal to10 into pairs in more than one way, e.g., by usingobjects or drawings, and record each decompositionby a drawing or equation (e.g., 5 2 3 and 5 4 1).4. Model withmathematics.5. Use appropriatetools strategically.K.OA.4 For any number from 1 to 9, find thenumber that makes 10 when added to the givennumber, e.g., by using objects or drawings, andrecord the answer with a drawing or equation.6. Attend toprecision.7. Look for, and makeuse of, structure8. Look for, andexpress regularityin, repeatedreasoning.1stGradeAdd and subtract whole numbersCONTENT THAT IS DIFFERENTContent moving into KindergartenUnderstand addition as putting together and addingto, and understand subtraction as taking apart andtaking fromN.FL.01.12 Know all the addition facts up to 10 10, and solve the related subtraction problemsfluently.6K I N D E R GA RT E NM AT H E M AT I C SMathematicalPractices1. Make sense ofproblems, andpersevere insolving them.2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.4. Model withmathematics.5. Use appropriatetools strategically.6. Attend toprecision.7. Look for, and makeuse of, structure.8. Look for, andexpress regularityin, repeatedreasoning.K.OA.5 Fluently add and subtract within 5. M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
Michigan Content ExpectationsCommon Core State StandardsFocal PointCritical AreaDescribing shapes and spaceDescribing shapes and spaceCOMMON CONTENTCreate, explore, and describe shapesMathematicalPractices1. Make sense ofproblems, andpersevere insolving them.G.GS.00.01 Relate familiar three-dimensionalobjects inside and outside the classroom to theirgeometric name, e.g., ball/sphere, box/cube, soupcan/cylinder, ice cream cone/cone, refrigerator/prism.G.GS.00.02 Identify, sort, and classify objects byattribute and identify objects that do not belong in aparticular group.2. Reason abstractlyand quantitatively.4. Model withmathematics.5. Use appropriatetools strategically.7. Look for, and makeuse of, structure.8. Look for, andexpress regularityin, repeatedreasoning.K.MD.3 Classify objects into given categories; countthe numbers of objects in each category and sortthe categories by count. (Limit category counts to beMathematicalless than or equal to 10.)PracticesIdentify and describe shapes (such as squares, circles,1. cones,Make senseoftriangles, rectangles, hexagons, cubes,cylinders,problems,andand spheres)persevere inK.G.1 Describe objects in the environment usingsolving them.names of shapes, and describe the relative positionsReasonabstractlyof these objects using terms such as2. above,below,andquantitatively.beside, in front of, behind, and next to.K.G.3 Identify shapes as two-dimensional(lying ina3. Constructviableplane, “flat”) or three-dimensional (“solid”).arguments, andAnalyze, compare, create, and composecritiqueshapesthereasoning ofK.G.4 Analyze and compare two- andothers.threedimensional shapes, in different sizes and orientations,Modelwithusing informal language to describe4.theirsimilarities,differences, parts (e.g., number of sidesmathematics.andvertices/“corners”) and other attributes(e.g.,having5. Useappropriatesides of equal length).tools strategically.3. Construct viablearguments, andcritique thereasoning ofothers.6. Attend toprecision.Classify objects and count the number of objects ineach categoryK.G.5 Model shapes in the world by building shapes6. Attend tofrom components (e.g., sticks and clay balls) andprecision.drawing shapes.7. Look for, and makeuse of, structureCONTENT THAT IS DIFFERENT8. Look for, andContent moving out of Kindergartenexpress regularityin, repeatedExplore geometric patterns[Not in the Common Core State Standards]reasoning.G.GS.00.03 Create, describe, and extend simplegeometric patterns.M AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010K I N D E R GA RT E N7
Michigan Content ExpectationsCommon Core State StandardsContent moving into Kindergarten2nd GradeIdentify and describe shapesAnalyze, compare, create, and compose shapesG.GS.02.02 Explore and predict the results ofputting together and taking apart two-dimensionaland three-dimensional shapes.G.TR.02.06 Recognize that shapes that have beenslid, turned, or flipped are the same shape, e.g., asquare rotated 45 is still a square.MathematicalPracticesK.G.6 Compose simple shapes to form larger shapes.For example, “can you join these two triangles with fullsides touching to make a rectangle?”Identify and describe shapes (such as squares, circles,triangles, rectangles, hexagons, cubes, cones, cylinders,and spheres)K.G.2. Correctly name shapes regardless of theirorientations or overall size.1. Make sense ofproblems, andpersevere inFocal PointCritical Areasolving them.Ordering objects by measurable attributes2. Reason abstractlyCOMMON CONTENTand quantitatively.Explore other measurement attributes3. Construct viableM.UN.00.04arguments,and Compare two or more objects bylength, weightand capacity, e.g., which is shorter,critiquethereasoningoflonger, taller?others.4. Model withmathematics.5. Use appropriatetools strategically.Describe and compare measurable attributesK.MD.1 Describe measurable attributes of objects,such as length or weight. Describe several measurableattributes of a single object.K.MD.2 Directly compare two objects with ameasurable attribute in common, to see which objecthas “more of ”/“less of ” the attribute, and describe thedifference. For example, directly compare the heightsof two children and describe one child as taller/shorter.6. Attend toprecision.CONTENT THAT IS DIFFERENT7. Look for, and makeContentmoving out of Kindergartenuse of, structure8. ExploreLook for,otherand measurement attributesexpress regularityM.PS.00.05Compare length and weight of objectsin, repeatedbycomparing to reference objects, and use termsreasoning.suchas shorter, longer, taller, lighter, heavier.8K I N D E R GA RT E NM AT H E M AT I C S1st GradeMeasure lengths indirectly and by iterating length units1. MD.1 Order three objects by length; compare thelengths of two objects indirectly by using a third object. MathematicalPractices1. Make sense ofproblems, andpersevere insolving them.2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.4. Model withmathematics.5. Use appropriatetools strategically.6. Attend toprecision.7. Look for, and makeuse of, structure.8. Look for, andexpress regularityin, repeatedreasoning.M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010
Michigan Content ExpectationsExplore concepts of time2Common Core State Standards[Not in the Common Core State Standards]M.UN.00.01 Know and use the common words forthe parts of the day (morning, afternoon, evening,night) and relative time (yesterday, today, tomorrow,last week, next year).M.TE.00.02 Identify tools that measure time (clocksmeasure hours and minutes; calendars measure days,weeks, and months).M.UN.00.03 Identify daily landmark times to thenearest hour (lunchtime is 12 o’clock; bedtime is ices1. Make sense ofproblems, andpersevere insolving them.1. Make sense ofproblems, andpersevere insolving them.2. Reason abstractlyand quantitatively.2. Reason abstractlyand quantitatively.3. Construct viablearguments, andcritique thereasoning ofothers.3. Construct viablearguments, andcritique thereasoning ofothers.4. Model withmathematics.4. Model withmathematics.5. Use appropriatetools strategically.5. Use appropriatetools strategically.6. Attend toprecision.6. Attend toprecision.7. Look for, and makeuse of, structure.7. Look for, and makeuse of, structure8. Look for, andexpress regularityin, repeatedreasoning.8. Look for, andexpress regularityin, repeatedreasoning.2Not previously linked to a focal pointM AT H E M AT I C S M I C H I G A N D E P A R T M E N T O F E D U C A T I O N 12 -2 010K I N D E R GA RT E N9
Michigan State Board of EducationJohn C. Austin, PresidentAnn ArborCasandra E. Ulbrich, Vice PresidentRochester HillsNancy Danhof, SecretaryEast LansingMarianne Yared McGuire, TreasurerDetroitKathleen N. StrausBloomfield TownshipDr. Richard ZeileDetroitEileen WeiserAnn ArborDaniel VarnerDetroitGovernor Rick SnyderEx OfficioMichael P. Flanagan, ChairmanSuperintendent of Public InstructionEx OfficioMDE StaffSally Vaughn, Ph.D.Deputy Superintendent and Chief Academic OfficerLinda Forward, DirectorOffice of Education Improvement and Innovation
4 KINDERGARTEN MATHEMATICS MICHIGAN DEPARTMENT OF EDUCATION 12-2010 MATHEMATICS MICHIGAN DEPARTMENT OF EDUCATION 12-2010 KINDERGARTEN 5 Mathematical Practices 1. Make sense of problems, and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments, and critique the reasoning of others. 4.
A Correlation of enVisionmath2.0, 2016 to the Common Core State Standards for Mathematics 1 SE Student Edition TE Teacher’s Edition Common Core State Standards for Mathematics Kindergarten enVisionmath2.0, 2016 Kindergarten Mathematical Practices
The Mathematics Kindergarten to Grade 9 Program of Studies has been derived from The Common Curriculum Framework for K–9 Mathematics: Western and Northern Canadian Protocol, May 2006 (the Common Curriculum Framework). The program of studies incorporates the conceptual framework for Kindergarten to Grade 9 Mathematics and the
benefit from starting a kindergarten program later. Where can I get advice on the best time to start kindergarten? If you are unsure about the best time for your child to start a kindergarten program, ask a kindergarten educator for advice. Find out how the kindergarten program can support your child. Meet with the principal or a teacher at the
The Common Core State Standards for Mathematics Murat Akkus* Adnan Menderes University, Turkey Abstract The Common Core State Standards for Mathematics (CCSSM) was published in 2010 and includes a complete collection of standards that are published and reviewed as a ‘common core’ in which math skills have been extensively adopted.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 4Problem Set 3 cm Name Date 1. Determine the perimeter and area of rectangles A and B. . NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 Exit Ticket 4 Lesson 2 : . NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 Homework 4 Lesson 2 : .
The Bottom Line New York has completed the fourth year of a 12-year Common Core phase-in. The Class of 2022: Had just completed kindergarten when the Common Core was adopted by the Board in summer 2010; Was enrolled in third grade when student progress on the Common Core was first measured in spring 2013; Will generally take the Common Core Algebra I Regents Exam in
The Common Core State Standards Initiative 4 Beginning in the spring of 2009, Governors and state commissioners of education from 48 states, 2 territories and the District of Columbia committed to developing a common core of state K-12 English-language arts (ELA) and mathematics standards. The Common Core State Standards Initiative (CCSSI)
TUTORIAL 1 - BASIC DIFFERENTIATION This tutorial is essential pre-requisite material for anyone studying mechanical engineering. This tutorial uses the principle of learning by example. The approach is practical rather than purely mathematical and may be too simple for those who prefer pure maths. Calculus is usually divided up into two parts, integration and differentiation. Each is the .
