Download Math Common Core Admin Snapshot

California Common Core State Standards
Introduction to the Mathematics Administrator Snapshot
OVERVIEW
The Common Core State Standards (CCSS) define what students should understand and be able to do in the study of mathematics. Students who master the CCSS
for mathematics will be prepared for college-level courses and possess the skills necessary for success in today’s workforce.
There are two types of Mathematical Standards
 Mathematical Practices - describe a set of skills and processes that all students should develop as part of their study of mathematics
 Content Standards - the mathematics students are expected to learn
The Mathematical Practices are the same for every grade level and high school conceptual cluster. The Content Standards differ from year to year.
The Mathematical Practices are similar to California’s idea of Balanced Mathematics for developing mathematics proficiency in students. In California there are three
components: Computational and Procedural Skills, Conceptual Understanding and Problem Solving. There are eight Mathematical Practices. These are listed
below with short, bulleted descriptions.
1 Make sense of problems and persevere in solving them
 Find meaning in problems
 Analyze, conjecture and plan solution pathways
 Verify answers
 Ask themselves the question: “Does this make sense?”
2
Reason abstractly and quantitatively
 Make sense of quantities and their relationships in problems
 Create coherent representations of problems
3
Construct viable arguments and critique the reasoning of
others
 Understand and use information to construct arguments
 Make and explore the truth of conjectures
 Justify conclusions and respond to arguments of others.
4
Model with mathematics
 Apply mathematics to problems in everyday life
 Identify quantities in a practical situation
 Interpret results in the context of the situation and reflect on
whether the results make sense
5
Use appropriate tools strategically
 Consider the available tools when solving problems
 Are familiar with tools appropriate for grade or course (pencil
and paper, concrete models, ruler, protractor, calculator,
spreadsheet, computer programs, digital content located on a
website, and other technological tools)
6
Attend to precision
 Communicate precisely to others
 Use clear definitions, state the meaning of symbols and are
careful about specifying units of measure and labeling axes
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 Calculate accurately and efficiently
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Look for and make use of structure
 Discern patterns and structures
 Can step back for an overview and shift perspective
 See complicated things as single objects or as being composed
of several objects
Look for and express regularity in repeated reasoning
 Notice if calculations are repeated and look both for general
methods and shortcuts
 In solving problems, maintain oversight of the process while
attending to detail
 Evaluate the reasonableness of their immediate results
The Content Standards are organized by domain. Under each domain is a set of clusters that are groups of related standards. Each grade K-8 has either four or
five domains. Following is a chart of the K-8 domains.
Domains K-8
Counting
&
Cardinality
Ratios & Proportional
Relationships
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations - Fractions
Measurement and Data
Geometry
K
1
2
3
4
5
The Number System
Expressions and Equations
Functions
6
Geometry
Statistics and Probability
7
8
The following section is a summary snapshot of the changes highlighted in the Common Core State Standards (CCSS). The left column represents topics new or
highlighted in the CCSS and the right column represents topics that have been moved to another grade level or eliminated.
While not an exhaustive list, this chart should help familiarize you with many of the CCSS and allow you to communicate with teachers about their grade level
content.
Common Core Standards for California
Mathematics Snapshot for Administrators
Grade
K
What standards are new or highlighted at this grade level?
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Countto100byonesandtens(CountingandCardinality:1)
Writenumbersfrom0‐20(CountingandCardinality:3)
California State Standards that have been moved or
are no longer included?
Moved to Grade 1
 Time (telling and writing)
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Explicitstandardforone‐to‐onecorrespondence(CountingandCardinality:4a)
Knowingthatthelastnumbercountedisthetotal(CountingandCardinality:4b)
Composeanddecomposenumbersfrom11‐19intotenonesandsomefurtherones
(NumberandOperationsinBaseTen:1)
Decomposenumberslessthanorequalto10intopairs(OperationsandAlgebraic
Thinking:3)
Fluentlyaddandsubtractwithin5(OperationsandAlgebraicThinking:5)
Arrangeanddescribeobjectsinspace(Geometry:1)
Identifyshapesaseithertwo‐orthree‐dimensional(Geometry:3)
CountingandCardinalitydomainuniquetoKindergarten
Countto120startingatanynumberlessthan120(NumberandOperationsinBase
Ten:1)
Applypropertiesofoperationsasstrategiestoaddandsubtract(Operationsand
AlgebraicThinking:3)
Partitioningcirclesandrectanglesintotwoandfourequalsharesanddescribing
thosesharesusingfractionallanguage(Geometry:3)
Telltimetothenearesthour,half‐hourusinganaloganddigitalclocks(Measurement
andData:3)
Organize,representandinterpretdatawithuptothreecategories(Measurementand
Data:4)
Skipcountby5s,10sand100swithin1000(NumberandOperationsinBaseTen:2)
Committomemoryallsumsoftwoone‐digitnumbers(OperationsandAlgebraic
Thinking:2)
Writeanequationtoexpressanevennumberasasumoftwoequaladdends
(OperationsandAlgebraicThinking:3)
Estimatinglengthsusinginches,feet,centimetersandmeters(MeasurementandData:
3)
Measuretodeterminehowmuchlongeroneobjectisthananother(Measurementand
Data:4)
Representwhole‐numbersumsanddifferenceswithin100onanumberlinediagram
(MeasurementandData:6)
Knowthevalueofcoinsandsolvewordproblemsinvolvingcombinationsofcoinsand
dollarbills(MeasurementandData:8)
Generalizeplacevalueunderstandingformulti‐digitwholenumbers(Numberand
OperationsinBaseTen:1.1)
Modelingandsolvingmultiplicationanddivisionproblems(OperationsandAlgebraic
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Data Collection and basic graphing
Statistics and Probability standards
MovedtoKindergarten
 Identificationoftwo‐andthree‐dimensionalshapes
 Arrangeanddescribeobjectsinspace
 Countingby10sto100
 MovedtoGrade2
 Knowingthevalueofcoins
 Commitadditionandsubtractionfacts(to20)to
memory
 Countingby5s
 MovedtoGrade3
 Measuringandestimatingliquidvolume
StatisticsandProbabilitystandards
MovedtoGrade3
 Committhemultiplicationtablesof2s,5s,and10sto
memory
 Modelingandsolvingsimplemultiplicationand
divisionproblems
 Basicfractionconcepts
 Measurementconceptsofelapsedtime
StatisticsandProbabilitystandards
MovedtoGrade4
 Multi‐digitmultiplicationanddivisionbeyond100
 Addingandsubtractingfractionswithlike
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Thinking:3)
Understandmultiplicationanddivisionandtherelationshipbetweenthetwo
(OperationsandAlgebraicThinking:5)
Applypropertiesincludingthedistributivepropertyasstrategiestomultiplyand
divide(OperationsandAlgebraicThinking:5)
Fluentlymultiplyanddividewithnumberswithin100(OperationsandAlgebraic
Thinking:7)
Knowfrommemoryallproductsoftwoone‐digitnumbers(OperationsandAlgebraic
Thinking7)
Developinganunderstandingoffractionsasnumbers(NumberandOperations‐
Fractions:1)
Locatingfractionsonanumberline:knowingthatonanumberline1/8andanother
1/8endataspotidentifiedas2/8(NumberandOperations‐Fractions:2)
Understandelapsedtime(MeasurementandData:1)
Measuringandestimatingliquidvolume(MeasurementandData:2)
Understandconceptsofareameasurement(MeasurementandData:5)
denominators
 Usingdecimalnotationforfractions
 Workwithanglesasgeometricshapes
MovedtoGrade5
 Unitconversions
MovedtoGrade7
 Probabilitystandards
Generalizeplacevalueunderstandingbyknowingthatadigitinoneplacerepresents
tentimeswhatitrepresentsintheplacetoitsright(NumberandOperationsinBase
Ten:1)
Multi‐digitmultiplicationanddivisionbeyond100(NumberandOperationsinBase
Ten:5)
Generatenumberorshapepatternsthatfollowagivenrule(OperationsandAlgebraic
Thinking:5)
Understandingadditionandsubtractionoffractionswithlikedenominators(Number
andOperations‐Fractions:3b)
Multiplyfractionsbyawholenumber(NumberandOperations‐Fractions:4b)
Usingdecimalnotationforfractionswithdenominatorsof10or100(Numberand
Operations‐Fractions:6)
Knowrelativesizesofmeasurementunitswithinonesystemincludingkm,m,cm;kg,
g;l,ml;hr,min,sec.(MeasurementandData:1)
Recognizeanglesasgeometricshapes(MeasurementandData:5)
MovedtoGrade5
 Addition,subtractionandroundingofdecimals
 Usingthestandardalgorithmformultiplication
 Useofparenthesesinnumericexpressions
 Coordinategraphing
MovedtoGrade6
 Conceptofnegativenumbers
 Evaluatingalgebraicexpressionsandgraphinglinear
functions
 Knowingmode,medianandoutliers
 Identifyingtheradiusanddiameterofacircle
StatisticsandProbabilitystandards
Visualizing,describingandmakingmodelsofgeometric
solids
StatisticsandProbabilitystandards
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Read,write,compareandrounddecimalstothethousandths(NumberandOperations
inBaseTen:3)
Fluentlymultiplymulti‐digitwholenumbersusingthestandardalgorithm(Number
andOperationsinBaseTen:5)
Add,subtract,multiplyanddividedecimalstohundredthsusingmodels,drawings,
strategies,properties(NumberandOperationsinBaseTen:7)
MovedtoGrade6
 Findingdecimalandpercentequivalentsand
computingagivenpercentofawholenumber
 Understandingandcomputingpositiveinteger
powersofnonnegativeintegers
 Usealettertorepresentanunknownnumber
 Deriveandusetheformulaforareaofatriangle
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Useequivalentfractionsasastrategytoaddandsubtractfractionswithunlike
denominators(NumberandOperations‐Fractions:1)
Interpretmultiplicationasscaling(NumberandOperations‐Fractions:5)
Solverealworldproblemsinvolvingmultiplicationanddivisionoffractionsandmixed
numbers(NumberandOperations‐Fractions:6)
Useparenthesesinnumericexpressions(OperationsandAlgebraicThinking:1)
Writeandinterpretsimpleexpressionswithoutevaluatingthem(Operationsand
AlgebraicThinking:2)
Graphpointsonthecoordinateplanetosolvereal‐worldandmathematicalproblems
(OperationsandAlgebraicThinking:3)
Convertamongdifferent‐sizedstandardsmeasurementunitswithagiven
measurementsystem(MeasurementandData:1)
Identifypropertiesoftwo‐dimensionalfigures(Geometry:3)
 Useratiosandratesto:
o Comparequantitieswithinandbetweenmeasurementsystems(Ratiosand
ProportionalRelationships:3)
o Relatethechangeofscaleinmeasurementswiththechangeofscaletounits
used(RatiosandProportionalRelationships:3)
 Solveproblemsinvolvingpercent;findingthewhole,whengivenapartandthe
percent(RatiosandProportionalRelationships:3c)
 Understandpositiveandnegativenumbers(TheNumberSystem:5)
 Workwithallfourquadrantsisincludedingraphingconcepts(TheNumberSystem:6)
 Absolutevalueconceptsaredevelopedandapplied(TheNumberSystem:7)
 Addandsubtractnegativeintegers(TheNumberSystem:7.1)
 Writeandevaluateexpressionsinvolvingwhole‐numberexponents(Expressionsand
Equations:1)
 Usealettertorepresentanunknownnumber(ExpressionsandEquations:2a)
 Representsolutionsofinequalitiesonnumberlinediagrams(Expressionsand
Equations:8)
 Analyzetherelationshipbetweendependentandindependentvariables(Expressions
andEquations:9)
 Useofcompositionanddecompositiontofindareaofgeometricshapes(Geometry:1)
 Drawpolygonsinthecoordinateplane(Geometry:3)
 Computesurfacearea(Geometry:4)
 Knowvariousformsofdisplayfordatasets(StatisticsandProbability:4)
 Understandthemeaningofandbeabletocompute,theminimum,thelowerquartile,
themediantheupperquartileandthemaximumofadataset(Statisticsand
Probability:5c)
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Computesurfacearea
StatisticsandProbabilitystandards
MovedtoGrade5
 Identifyingpropertiesoftwo‐dimensionalfigures
MovedtoGrade7
 Useproportionstosolveproblems
 Identifyanglesasvertical,adjacent,complementary
orsupplementaryandprovidedescriptionsofthese
terms
 Usepropertiesaboutsupplementaryand
complementaryanglesandthesumoftheanglesofa
triangletosolveproblems
 Drawtrianglesandquadrilateralsfromgiven
information
 Samplingtechniques
 Theoreticalandexperimentalprobability
 Understandthedifferencebetweenindependentand
compoundevents
 Determinetheprobabilityofcompoundevents
 Determinethelikelihoodofaneventoccurring
 Usedatatoestimatetheprobabilityoffutureevents
MovedtoGrade8
 Understandhowtheinclusionorexclusionofoutliers
affectsmeasuresofcentraltendency
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 Recognizeandrepresentproportionalrelationshipsbetweenquantities(Ratiosand
ProportionalRelationships:2a)
 Identifyunitrateintables,graphs,equations,diagrams,andverbaldescriptionsof
proportionalrelationships(RatiosandProportionalRelationships:2b)
 Representproportionalrelationshipsbyequations(RatiosandProportional
Relationships:2c)
 Explainwhatapoint(x,y)onagraphoftheproportionalrelationshipmeansinterms
ofthesituation(RatiosandProportionalRelationships:2d)
 Drawgeometricshapesfromgiveninformation(Geometry:2)
 Usefactsaboutsupplementary,complementary,verticalanglestosolvesimple
equationsforanunknownangleinafigure(Geometry:5)
 Findsurfaceareaandvolumeofconesandspheres(Geometry:6)
 Usesamplingtechniquestodrawinferencesaboutapopulation(Statisticsand
Probability:2)
 Determinethelikelihoodofaneventoccurring(StatisticsandProbability:6)
 Usedatatoestimatetheprobabilityoffutureevents(StatisticsandProbability:6)
 Findtheoreticalandexperimentalprobabilities(StatisticsandProbability:7)
 Understandthedifferencebetweenindependentandcompoundevents(Statisticsand
Probability:8)
 Determinetheprobabilityofcompoundevents(StatisticsandProbability:8)
MovedtoGrade6
 Solveproblemsusingpercents
 Absolutevalueconceptsaredevelopedandapplied
 Representsolutionsofinequalitiesonnumberline
diagrams
 Writeandevaluateexpressionsusingwhole‐number
exponents
 Usealettertorepresentanunknownnumber
 Workwithallfourquadrantsisincludedingraphing
concepts
 Analyzetherelationshipbetweendependentand
independentvariables
 Useratiosandratestocomparequantitieswithin
andbetweenmeasurementsystems
 Userationsandratestorelatethechangeofscalein
measurementswithachangeofscaletotheunits
used
 Useofcompositionanddecompositiontofindareaof
geometricshapes
 Computesurfacearea
 Drawpolygonsinthecoordinateplane
 Knowvariousformsofdisplayfordatasets
 Understandthemeaningofandbeabletocompute
theminimum,thelowerquartile,themedian,the
upperquartileandthemaximumofadataset
MovedtoGrade8
 Graphandinterpretlinearandnonlinearfunctions
 Plotthevaluesofquantitieswhoseratiosarealways
thesame.Fitalinetotheplotandunderstandthat
theslopeofthelineequalsthequantities.
 Slopeofaline
 Radicalsandintegerexponents,includingrulesfor
workingwithexponents
 PythagoreanTheorem
 Congruencyofgeometricfigures
 Transformationalgeometry
 Scientificnotation
MovedtoAlgebra1
 Graphfunctionsoftheformy=nx2andy=nx3
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Plotthevaluesfromthevolumesofthree‐dimensional
shapesforvariousvaluesofedgelengths
Identifyandconstructbasicelementsofgeometric
figuresbyusingcompassandstraightedge
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