Missouri Department Of Elementary And Secondary Education .

K-5 Mathematics Grade-Level ExpectationsMissouri Department of Elementary and Secondary EducationSpring 2016

Number SenseNSKindergartenAKnow the number namesand the count sequence.Understand and usenumbers up to 120.Grade 1Count to 100 by ones andtens.Count to 120, starting atany number less than120.Count forward beginningfrom a given numberbetween 1 and 20.Read and write numeralsand represent a numberof objects with a writtennumeral.Count backward from agiven number between 10and 1.Count backward from agiven number between 20and 1.Read and write numeralsand represent a numberof objects from 0 to 20.Count by 5s to 100starting at any multiple offive.Grade 2Grade 3See the Excel document here for coding.Grade 4Grade 52

Number SenseNSBKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Understand therelationship betweennumbers and quantities;connect counting tocardinality.Say the number nameswhen counting objects, inthe standard order,pairing each object withone and only one numbername and each numbername with one and onlyone object.Demonstrate that the lastnumber name said tellsthe number of objectscounted and the numberof objects is the sameregardless of theirarrangement or the orderin which they werecounted.Demonstrate that eachsuccessive number namerefers to a quantity that isone larger than theprevious number.See the Excel document here for coding.3

Number SenseRecognize, withoutcounting, the quantity ofgroups up to 5 objectsarranged in commonpatterns.Demonstrate that anumber can be used torepresent “how many”are in a set.NSCKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Compare numbers.Compare two or moresets of objects andidentify which set is equalto, more than or less thanthe other.Compare two numerals,between 1 and 10, anddetermine which is morethan or less than theother.See the Excel document here for coding.4

Number Sense and Operations in Base TenNBTAKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Use place valueunderstanding andproperties of operationsto perform multi-digitarithmetic with numbersup to one million.Round multi-digit wholenumbers to any place.Use place value systemunderstanding toperform operations withmulti-digit wholenumbers to billions anddecimals to thousandths.Read, write and identifynumbers from billions tothousandths usingnumber names, base tennumerals and expandedform.Work with numbers 11 –19 to gain foundationsfor place value.Understand place valueof two-digit numbers.Understand place valueof three digit numbers.Use place valueunderstanding andproperties of operationsto perform multi-digitarithmetic.Compose and decomposenumbers from 11 to 19into sets of tens withadditional ones.Understand that 10 canbe thought of as a bundleof 10 ones – called a“ten”.Understand three-digitnumbers are composed ofhundreds, tens and ones.Round whole numbers tothe nearest 10 or 100.Understand two-digitnumbers are composed often(s) and one(s).Understand that 100 canbe thought of as 10 tens –called a “hundred”.Read, write and identifywhole numbers within100,000 using base tennumerals, number namesand expanded form.Read, write and identifymulti-digit wholenumbers up to onemillion using numbernames, base ten numeralsand expanded form.Compare two numbersfrom billions tothousandths using thesymbols , or , andjustify the solution.Compare two two-digitnumbers using thesymbols , or .Count within 1000 by 1s,10s and 100s starting withany number.Demonstrate fluency withaddition and subtractionwithin 1000.Compare two multi-digitnumbers using thesymbols , or , andjustify the solution.Understand that in amulti-digit number, a digitrepresents 1/10 timeswhat it would representsin the place to its left.Count by 10s to 120starting at any number.Read and write numbersto 1000 using numbernames, base-tennumerals and expandedform.Multiply whole numbersby multiples of 10 in therange 10-90.Understand that in amulti-digit whole number,a digit represents 10times what it wouldrepresent in the place toEvaluate the value ofpowers of 10 andunderstand therelationship to the placevalue system.See the Excel document here for coding.5

Number Sense and Operations in Base TenCompare two three-digitnumbers using thesymbols , or .its right.Demonstrate fluency withaddition and subtractionof whole numbers.Round numbers frombillions to thousandthsplace.Multiply a whole numberof up to four digits by aone-digit whole numberand multiply two twodigit numbers, and justifythe solution.Add and subtract multidigit whole numbers anddecimals to thethousandths place, andjustify the solution.Find whole-numberquotients and remainderswith up to four-digitdividends and one-digitdivisors, and justify thesolution.Multiply multi-digit wholenumbers and decimals tothe hundredths place, andjustify the solution.Divide multi-digit wholenumbers and decimals tothe hundredths placeusing up to two-digitdivisors and four-digitdividends, and justify thesolution.See the Excel document here for coding.6

Number Sense and Operations in Base TenNBTBKindergartenGrade 1Use place valueunderstanding to addand subtract.Add within 100.Grade 2Grade 3Grade 4Grade 5Use place valueunderstanding andproperties of operationsto add and subtract.Demonstrate fluency withaddition and subtractionwithin 100.Calculate 10 more or 10less than a given numbermentally without havingto count.Add up to four two-digitnumbers.Add or subtract a multipleof 10 from another twodigit number, and justifythe solution.Add or subtract within1000, and justify thesolution.Use the relationshipbetween addition andsubtraction to solveproblems.See the Excel document here for coding.7

Number Sense and Operations in Base TenAdd or subtract mentally10 or 100 to or from agiven number within1000.NBTCKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Represent and solveproblems involvingaddition and subtraction.Write and solve problemsinvolving addition andsubtraction within 100.See the Excel document here for coding.8

Number Sense and Operations in FractionsNFAKindergartenGrade 1Grade 2Grade 3Develop understandingof fractions as numbers.Understand a unitfraction as the quantityformed by one part whena whole is partitioned intoequal parts.Understand that when awhole is partitionedequally, a fraction can beused to represent aportion of the whole.a. Describe thenumerator asrepresenting thenumber of pieces beingconsidered.b. Describe thedenominator as thenumber of pieces thatmake the whole.See the Excel document here for coding.Grade 4Grade 5Extend understanding offraction equivalence andordering. (Limitdenominators to 2, 3, 4,5, 6, 8, 10, 12 and 100.)Explain and/or illustratewhy two fractions areequivalent.Understand therelationship betweenfractions and decimals(denominators that arefactors of 100).Understand that parts ofa whole can be expressedas fractions and/ordecimals.Recognize and generateequivalent fractions.Convert decimals tofractions and fractions todecimals.9

Number Sense and Operations in FractionsRepresent fractions on anumber line.a. Understand the wholeis the interval from 0 to1.b. Understand the wholeis partitioned intoequal parts.c. Understand a fractionrepresents theendpoint of the lengtha given number ofpartitions from 0.Compare two fractionsusing the symbols , or , and justify the solution.Compare and orderfractions and/or decimalsto the thousandths placeusing the symbols , or , and justify the solution.Demonstrate that twofractions are equivalent ifthey are the same size, orthe same point on anumber line.Recognize and generateequivalent fractions usingvisual models, and justifywhy the fractions areequivalent.Compare two fractionswith the same numeratoror denominator using thesymbols , or , andjustify the solution.See the Excel document here for coding.10

Number Sense and Operations in FractionsExplain why fractioncomparisons are onlyvalid when the twofractions refer to thesame whole.NFKindergartenGrade 1Grade 2Grade 3Grade 4Extend understanding ofoperations on wholenumbers to fractionoperations.Understand addition andsubtraction of fractions asjoining/composing andseparating/decomposingparts referring to thesame whole.BSee the Excel document here for coding.Grade 5Perform operations andsolve problems withfractions and decimals.Estimate results of sums,differences and productswith fractions anddecimals to thethousandths.11

Number Sense and Operations in FractionsSee the Excel document here for coding.Decompose a fractioninto a sum of fractionswith the samedenominator and recordeach decomposition withan equation andjustification.Justify the reasonablenessof a product whenmultiplying with fractions.a. Estimate the size of theproduct based on thesize of the two factors.b. Explain why multiplyinga given number by afraction greater than 1results in a productlarger than the givennumber.c. Explain why multiplyinga given number by afraction less than 1results in a productsmaller than the givennumber.d. Explain why multiplyingthe numerator anddenominator by thesame number isequivalent tomultiplying the fractionby 1.Solve problems involvingadding and subtractingfractions and mixednumbers with likedenominators.Solve problems involvingaddition and subtractionof fractions and mixednumbers with unlikedenominators, and justifythe solution.12

Number Sense and Operations in FractionsSee the Excel document here for coding.Apply and extendprevious understandingsof multiplication tomultiply a fraction by awhole number.Extend the concept ofmultiplication to multiplya fraction or wholenumber by a fraction.a. Recognize therelationship betweenmultiplying fractionsand finding the areas ofrectangles withfractional side lengths.b. Calculate and interpretthe product of afraction by a wholenumber and a wholenumber by a fraction.c. Calculate and interpretthe product of twofractions less than one.Solve problems involvingmultiplication of afraction by a wholenumber.Extend the concept ofdivision to divide unitfractions and wholenumbers by using visualfraction models andequations.a. Calculate and interpretthe quotient of a unitfraction by a non-zerowhole number.b. Calculate and interpretthe quotient of a wholenumber by a unitfraction.13

Number Sense and Operations in FractionsNFKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Understand decimalnotation for fractions,and compare decimalfractions. (Denominatorsof 10 or 100)Use decimal notation forfractions withdenominators of 10 or100.CUnderstand that fractionsand decimals areequivalentrepresentations of thesame quantity.Read, write and identifydecimals to thehundredths place usingnumber names, base tennumerals and expandedform.Compare two decimals tothe hundredths placeusing the symbols , or , and justify the solution.See the Excel document here for coding.14