Georgia Standards of Excellence Curriculum Map 6th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Mathematics Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Georgia Standards of Excellence Sixth Grade Curriculum Map 1stSemester2ndSemester Unit 1 (4 5 weeks) Unit 2 (3 4 weeks) Unit 3 (4 5 weeks) Unit 4 (4 5 weeks) Unit 5 (4 5 weeks) Unit 6 (4 5 weeks) Unit 7 (3 4 weeks) Unit 8 (3 4 weeks) Number System Fluency Rate, Ratio and Proportional Reasoning Using Equivalent Fractions Expressions One-Step Equations and Inequalities Area and VolumeStatistics Rational Explorations: Numbers and their Opposites Show What We Know MCC6.NS.1 MCC6.NS.2 MCC6.NS.3 MCC6.NS.4 MCC6.RP.1 MCC6.RP.2 MSGE6.RP.3 MCC6.RP.3a MCC6.RP.3b MCC6.RP.3c MCC6.RP.3d MCC6.EE.1 MCC6.EE.2a MCC6.EE.2b MCC6.EE.2c MCC6.EE.3 MCC6.EE.4 MCC6.NS.4 MCC6.EE.5 MCC6.EE.6 MCC6.EE.7 MCC6.EE.8 MCC6.EE.9 MCC6.RP.3a MCC6.RP.3b MCC6.RP.3c MCC6.RP.3d (equations) MCC6.G.1 MCC6.G.2 MCC6.G.4 MCC6.SP.1 MCC6.SP.2 MCC6.SP.3 MCC6.SP.4 MCC6.SP.5 MCC6.NS.5 MCC6.NS.6a MCC6.NS.6b MCC6.NS.6c MCC6.NS.7a MCC6.NS.7b MCC6.NS.7c MCC6.NS.7dMCC6.NS.8 MCC6.G.3 ALL Theseunits werewritten to build upon concepts fromprior units, so later units contain tasks that depend upon theconcepts addressed in earlier units. All units will includetheMathematical Practices and indicateskills to maintain. NOTE: Mathematical standards areinterwoven and should beaddressed throughout theyear in as many different units and tasks as possiblein order to stress thenatural connections that exist among mathematical topics. Grades 6-8 Key: NS =TheNumber System, RP =Ratios and Proportional Relationships, EE =Expressions and Equations, G =Geometry, SP =Statistics and Probability. *Revised standards indicated in bold red font.Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Georgia Standards of Excellence Sixth Grade Curriculum Map 1st Semester Standards for Mathematical Practice 1 Makesenseof problems and perseverein solving them. 2 Reason abstractly and quantitatively. 3 Construct viablearguments and critiquethereasoning of others. 4 Model with mathematics. 5 Useappropriatetools strategically. 6 Attend to precision. 7 Look for and makeuseof structure. 8 Look for and express regularity in repeated reasoning. 1st Semester Unit 1Unit 2Unit 3Unit 4 Number System FluencyRate, Ratio and Proportional Reasoning Using Equivalent ExpressionsOne-Step Equations and Inequalities Applyandextendpreviousunderstandings ofmultiplicationanddivisiontodivide fractions by fractions. MCC6.NS.1Interpretandcompute quotientsoffractions,andsolveword problems involvingdivisionof fractionsby fractions,includingreasoningstrategies suchasusingvisualfractionmodelsand equations to represent the problem. For example: Createastorycontextfor(2/3)(3/4)and useavisualfractionmodeltoshowthe quotient; Usetherelationshipbetween multiplication and division to explain that (2/3)(3/4)=8/9becaus33/4of8/9is2/3. (In general, (a/b)(c/d) =ad/bc.) How much chocolate will each person get if3peopleshare1/2lbofchocolate equally? How many3/4-cupservingsarein2/3of a cup of yogurt? Howwideisarectangularstripofland withlength3/4miandarea1/2square mi? Computefluentlywithmulti-digitnumbers andfindcommonfactorsandmultiples. MCC6.NS.2Fluentlydividemulti-digit numbers using thestandard algorithm. Understandratioconceptsanduse ratio reasoning to solve problems. MCC6.RP.1Understand the concept of a ratio and use ratio language to describe a ratiorelationshipbetweentwoquantities. For example, The ratio of wings to beaks inthebirdhouseatthezoowas2:1, becauseforevery2wingstherewas1 beak.ForeveryvotecandidateA received,candidateCreceivednearly three votes. MCC6.RP.2Understand the concept of a unit rate a / b associated with a ratio a: b withb0(bnotequaltozero),anduse ratelanguageinthecontextofaratio relationship.Forexample,"Thisrecipe hasaratioof3cupsofflourto4cupsof sugar, so there is 3/4 cup of flour for each cupofsugar.""Wepaid$75for15 hamburgers,whichisarateof$5per hamburger." MCC6.RP.3Useratioandrate reasoningtosolvereal-worldand mathematicalproblemsutilizing strategiessuchastablesofequivalent ratios,tapediagrams(barmodels), doublenumberlinediagrams,and/or equations.

Applyandextendpreviousunderstandings ofarithmetictoalgebraicexpressions. MCC6.EE.1Write andevaluate numerical expressionsinvolvingwhole-number exponents. MCC6.EE.2Write, read, and evaluateexpressionsinwhichlettersstandfor numbers. MCC6.EE.2aWriteexpressions that record operationswithnumbersandwithletters standing for numbers. MCC6.EE.2bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view oneor more partsofanexpressionasasingle entity. MCC6.EE.2c Evaluateexpressions at specific values for their variables. Include expressions thatarise from formulasinreal-world problems.Perform arithmeticoperations, includingthose involvingwhole-number exponents,inthe conventionalorderwhen thereareno parentheses to specify a particular order (Order of Operations). MCC6.EE.3Applythe propertiesof operations to generateequivalent expressions. MCC6.EE.4Identifywhentwoexpressions are equivalent (i.e., when the two expressions namethe same numberregardlessofwhich valueis substituted into them). Reasonaboutandsolveone-variable equations and inequalities. MCC6.EE.5Understandsolvinganequation orinequalityasaprocessofansweringa question: which values froma specified set, if any, makethe equation or inequality true? Use substitutiontodetermine whetheragiven number in a specified set makes an equation or inequality true. MCC6.EE.6Use variablestorepresent numbers and writeexpressions when solving a real-worldormathematicalproblem;understandthatavariable canrepresentan unknownnumber,or,dependingonthepurposeat hand, any number in a specified set. MCC6.EE.7Solvereal-worldand mathematical problems by writing and solving equations of theform + = and = for cases in which p, q and x areall nonnegative rational numbers. MCC6.EE.8Write aninequalityofthe form > or < torepresentaconstraintor conditioninareal-worldormathematical problem.Recognize thatinequalitiesoftheform > or < have infinitelymany solutions;representsolutionsofsuch inequalities on number linediagrams. Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved MCC6.NS.3Fluently add, subtract, multiply, anddivide multi-digitdecimalsusingthestandard algorithmfor each operation. MCC6.NS.4Findthecommonmultiplesof two whole numbers less than or equal to 12 andthecommonfactorsoftwowhole numbers less than or equal to 100. a.Findthegreatestcommonfactorof2 whole numbers and use the distributive property to express a sum of two whole numbers1-100withacommonfactor asamultipleofasumoftwowhole numberswithnocommonfactors.(GCF)Example:36 + 8 =4(9 + 2) b.Applytheleastcommonmultipleof twowholenumberslessthanorequal to 12 to solve real-world problems. MCC6.RP.3a Maketables of equivalent ratios relatingquantitieswithwhole-number measurements,findmissingvaluesinthetables,andplotthe pairsofvaluesonthecoordinateplane. Usetables to compareratios. MCC6.RP.3bSolve unitrate problems includingthose involvingunitpricingand constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what ratewerelawns being mowed? MCC6.RP.3cFindapercentofaquantity asarateper100(e.g.30%ofaquantity means30/100timesthequantity);givena percent,solveproblemsinvolvingfinding thewholegivenapartandthepartgiven the whole. MCC6.RP.3d Given a conversion factor, use ratioreasoningtoconvertmeasurement unitswithinonesystemofmeasurement andbetweentwosystemsofmeasurements (customaryandmetric);manipulateand transformunitsappropriatelywhen multiplyingordividingquantities.For example,given1in.=2.54cm,howmany centimeters are in 6 inches? MCC6.NS.4Findthecommonmultiplesof two whole numbers less than or equal to 12 andthecommonfactorsoftwowhole numbers less than or equal to 100. a.Findthegreatestcommonfactorof2 whole numbers and use the distributive property to express a sum of two whole numbers1-100withacommonfactor asamultipleofasumoftwowhole numberswithnocommonfactors.(GCF)Example:36 + 8 =4(9 + 2) b.Applytheleastcommonmultipleof twowholenumberslessthanorequal to 12 to solve real-world problems. Representandanalyzequantitative relationshipsbetweendependentand independent variables. MCC6.EE.9Usevariablestorepresenttwo quantitiesinareal-worldproblemthat change in relationship to one another. a.Writeanequationtoexpressone quantity,thedependentvariable,in termsoftheotherquantity,the independent variable. b.Analyzetherelationshipbetweenthe dependentandindependentvariables usinggraphsandtables,andrelate these to the equation.For example, in a probleminvolvingmotionatconstant speed,listandgraphorderedpairsof distancesandtimes,andwritethe equationd=65ttorepresentthe relationship between distance and time. Understandratioconceptsanduseratio reasoning to solve problems. MCC6.RP.3Use ratioandrate reasoningto solve real-worldandmathematicalproblems, e.g.,byreasoningabouttablesofequivalent ratios,tape diagrams,double numberlinediagrams, or equations. MCC6.RP.3a Maketables of equivalent ratios relatingquantitieswithwhole-number measurements,findmissingvaluesinthe tables,andplotthe pairsofvaluesonthecoordinateplane. Usetables to compareratios. MCC6.RP.3bSolve unitrate problems includingthose involvingunitpricingand constant speed. MCC6.RP.3c Find a percent of a quantity as a rate per100(e.g.,30%ofaquantitymeans 30/100timesthe quantity);solve problems involving finding the whole givena partand thepercent. MCC6.RP.3dUse ratioreasoning toconvert measurement units; manipulate andtransformunitsappropriatelywhenmultiplyingor dividing quantities. Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved Georgia Standards of Excellence Sixth Grade Curriculum Map 2nd Semester Standards for Mathematical Practice 1 Makesenseof problems and perseverein solving them. 2 Reason abstractly and quantitatively. 3 Construct viablearguments and critiquethereasoning of others. 4 Model with mathematics. 5 Useappropriatetools strategically. 6 Attend to precision. 7 Look for and makeuseof structure. 8 Look for and express regularity in repeated reasoning. 2nd Semester Unit 5Unit 6Unit 7Unit 8 Area and VolumeStatisticsRational Explorations: Numbers and their Opposites Show What We Know Solvereal-worldandmathematical problems involving area, surface area, and volume. MCC6.G.1Findareaofrighttriangles, othertriangles,quadrilaterals,and polygonsbycomposingintorectanglesor decomposingintotrianglesandother shapes;applythesetechniquesinthe contextofsolvingreal-worldand mathematical problems. MCC6.G.2Findthevolumeofaright rectangularprismwithfractionaledge lengths by packing it with unit cubes of the appropriateunitfractionedgelengths(1/2 u), and show that the volume is the same as wouldbefoundbymultiplyingtheedge lengths oftheprism.ApplytheformulasV = (length) x (width) x (height) and V= (area ofbase)x(height)tofindvolumesofright rectangularprismswithfractionaledge lengthsinthecontextofsolvingreal-world and mathematical problems. MCC6.G.4Representthree-dimensional figures using netsmadeup of rectangles and triangles, and use the nets to find the surface area of thesefigures. Apply these techniques in the contextofsolvingreal-worldand mathematical problems. Developunderstandingofstatistical variability. MCC6.SP.1Recognize astatisticalquestion asone thatanticipatesvariabilityinthe data relatedtothe questionandaccountsforitin theanswers. MCC6.SP.2Understandthatasetofdata collected to answer a statistical question has a distributionwhichcanbe describedbyits center, spread, and overall shape. MCC6.SP.3 Recognize thatameasure ofcenterfora numerical data set summarizes all of its values withasingle number,while ameasureof variation describes how its values vary with a singlenumber. Summarizeanddescribedistributions. MCC6.SP.4Displaynumericaldatainplots onanumberline,includingdotplots, histograms, and box plots. MCC6.SP.5 Summarize numerical data sets in relation to their context, such as by: a.Reporting the number of observations. b.Describingthenatureoftheattribute underinvestigation,includinghowit wasmeasuredanditsunitsof measurement. c.Givingquantitativemeasuresofcenter (medianand/ormean)andvariability (interquartile range). d.Relating the choice of measures of Applyandextendpreviousunderstandings ofnumberstothesystemofrational numbers. MCC6.NS.5Understandthatpositive and negativenumbers areused together to describequantities having oppositedirections or values (e.g., temperature above/below zero, elevation above/belowsealevel,debits/credits, positive/negative electric charge); use positiveand negativenumbers to represent quantities in real-world contexts, explaining themeaning of 0 in each situation. MCC6.NS.6Understand a rational number as a point on thenumber line. Extend number linediagramsandcoordinate axesfamiliarfromprevious grades to represent points on thelineandinthe plane withnegative number coordinates. MCC6.NS.6aRecognize opposite signsof numbersasindicatinglocationsonoppositesides of 0 on the number line; recognize that theoppositeof theoppositeof a number is the number itself, e.g., (3) =3, and that 0 is its own opposite. MCC6.NS.6b Understand signs of numbers in orderedpairsasindicatinglocationsin quadrantsofthe coordinate plane;recognizethatwhentwoorderedpairsdifferonlyby signs, thelocations of the points arerelated by reflections across oneor both axes. ALL Georgia Department of Education Richard Woods, StateSchool Superintendent J uly 2015 All Rights Reserved centerandvariabilitytotheshapeof thedatadistributionandthecontext in which the data was gathered. MCC6.NS.6cFindandpositionintegersand otherrationalnumbersonahorizontalor vertical number linediagram; find and position pairs of integers and other rational numbers on a coordinateplane. MCC6.NS.7Understandorderingand absolutevalueof rational numbers. MCC6.NS.7aInterpretstatementsof inequalityasstatementsaboutthe relativepositionoftwonumbersonanumberlinediagram. MCC6.NS.7bWrite,interpret,andexplain statementsoforderforrationalnumbersin real-world contexts. MCC6.NS.7cUnderstandthe absolute valueof a rational number as its distancefrom0 on the numberline;interpretabsolute value as magnitude fora positive ornegative quantity in a real-world situation. MCC6.NS.7dDistinguishcomparisonsof absolute value from statementsaboutorder. MCC6.NS.8Solve real-worldand mathematicalproblems by graphing points in allfourquadrantsofthe coordinate plane. Includeuse of coordinates and absolute valueto find distances between points with thesame first coordinateor thesamesecond coordinate. Solvereal-worldandmathematical problemsinvolvingarea,surfacearea,and volume. MCC6.G.3Draw polygonsinthe coordinateplane givencoordinatesforthe vertices;usecoordinates to find thelength of a sidejoining pointswiththe same firstcoordinate orthesame secondcoordinate.Applythese techniques in thecontext of solving real-world and mathematical problems.