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c. Understand the absolutevalue of a rational number asits distance from 0 on thenumber line; interpretabsolute value as magnitudefor a positive or negativequantity in real-world context.d. Distinguish comparisons ofabsolute value fromstatements about order inmathematical problems andproblems in real-worldcontext. McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)6.NS.C.8Solve mathematical problems andproblems in real-world context bygraphing points in all fourquadrants of the coordinateplane. Include use of coordinatesand absolute value to finddistances between points with thesame first coordinate or the samesecond coordinate.Bloom’s Taxonomy: ApplicationMcGraw-Hill MathTextbook6.EE.A.1Bloom’s Taxonomy: ApplicationGanado USD – PACING GUIDE (MATH/6TH GRADE)HESS Matrix: DOK Level 2Essential Question(s): How are integers related towhole numbers?write statements of orderfor rational numbers in realworld context explain statements of orderfor rational numbers in realworld context understand the absolutevalue of a rational numberas its distance from 0 on anumber line interpret absolute value asmagnitude for a /- quantityin a real-world situation distinguish comparisons ofabsolute value fromstatements about orderI will be able to: solve real-world problemsby graphing points in all fourquadrants of the coordinateplane solve mathematicalproblems by graphing pointsin all four quadrants of thecoordinate plane include use of coordinates tofind distances betweenpoints with the same firstcoordinate or the samesecond coordinate include use of absolutevalue to find distancesbetween points with thesame first coordinate or thesame second coordinateI will be able to: coordinate planex-axisy-axisquadrant(s)ordered pairsorigin standard formexpanded formPage 7

PowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)Write and evaluate numericalexpressions involving wholenumber exponents. EvaluationHESS Matrix: DOK Level 2 DOK Level 3Essential Question(s): What are whole numbersplace values? How can whole numbers bewritten, compared, andordered?6.EE.A.2Write, read, and evaluatealgebraic expressions.a. Write expressions that recordoperations with numbers andvariables.b. Identify parts of an expressionusing mathematical terms(sum, term, product, factor,quotient, and coefficient);view one or more parts of anexpression as a single entity.c. Evaluate expressions givenspecific values of theirvariables. Include expressionsthat arise from formulas usedto solve mathematicalproblems and problems inreal-world context. Performarithmetic operations,including those involvingwhole-number exponents, inthe conventional order whenthere are no parentheses toBloom’s Taxonomy: Application Comprehension EvaluationHESS Matrix: DOK Level 1 DOK Level 2 DOK Level 3Essential Question(s): What are algebraicexpressions and how canthey be written andevaluated? What arithmetic numberrelationships, calledproperties, are always true? read and write numbers totrillions in standard,expanded, and word formand give the values ofspecific digitswrite numerical expressionsinvolving whole-numberexponentsevaluate numericalexpressions involving wholenumber exponents word formtrillionperiodbaseexponentpowerexponential formsquaredcubedrootI will be able to: write expressions in whichletters stand for numbers read expressions in whichletters stand for numbers evaluate expressions inwhich letters stand fornumbers write expressions thatrecord operations withnumbers and with lettersstanding for numbers identify parts of anexpression usingmathematical terms view one or more parts of anexpression as a single entity evaluate expressions at theirspecific values of theirvariables include expressions thatarise from formulas used inreal-world problems variabletermvariable termconstant tioninput/outputtablefactor Page 8Ganado USD – PACING GUIDE (MATH/6TH GRADE)

specify a particular order(Order of Operations). McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)6.EE.A.3Apply the properties of operationsto generate equivalentexpressions. For example, applythe distributive property to theexpression 3 (2 x) to produce theequivalent expression 6 3x.Bloom’s Taxonomy: ApplicationHESS Matrix: DOK Level 2perform arithmeticoperations, including thoseinvolving whole-numberexponents, in theconventional order whenthere are no parenthesesorder (Order of Operations)I will be able to: apply the properties ofoperations to generateequivalent expressions Essential Question(s): What are algebraicexpressions and how canthey be written andevaluated? What arithmetic numberrelationships, calledproperties, are always true? McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART Board6.EE.A.4Identify when two expressions areequivalent. For example, theexpressions y y y and 3y areequivalent because they name thesame number regardless of whichnumber y stands for.Bloom’s Taxonomy: ComprehensionHESS Matrix: DOK Level 2I will be able to: identify when twoexpression are equivalent commutativeproperty ofadditioncommutativeproperty ofmultiplicationassociativeproperty ofadditionassociativeproperty ofmultiplicationidentity propertyof additionidentity propertyof multiplicationorder onequationequationaddition propertyof equalitysubtractionproperty ofequalityEssential Question(s):Page 9Ganado USD – PACING GUIDE (MATH/6TH GRADE)

ALEKSconnected.mcgrawhill (Online)McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online) What procedures can beused to solve equations? 3rd Quarter6.EE.B.5Bloom’s Taxonomy:Understand solving an equation or Applicationinequality as a process of Comprehensionreasoning to find value(s) of thevariables that make that equation HESS Matrix:or inequality true. Use DOK Level 2substitution to determinewhether a given number in aEssential Question(s):specified set makes an equation How are sums, differences,or inequality true.products, and quotientsinvolving decimals estimatedand found? What procedures can beused to solve equations? How can equations begraphed? What patterns can be foundin the graph of equations?6.EE.B.6Use variables to representnumbers and write expressionswhen solving mathematicalproblems and problems in realworld context; understand that avariable can represent anunknown number or any numberin a specified set.Bloom’s Taxonomy: Application ComprehensionHESS Matrix: DOK Level 2Essential Question(s): What are algebraicexpressions and how canmultiplicationproperty ofequalitydivision propertyof equalityI will be able to: understand solving anequation or inequality as aprocess of answering aquestion use substitution todetermine whether a givennumber in a specified setmakes an equation orinequality true inequalityinverserelationshipI will be able to: use variables to representnumbers write expressions whensolving real-world problem write expressions whensolving mathematicalproblems understand that a variablecan represent an unknown verserelationship Page 10Ganado USD – PACING GUIDE (MATH/6TH GRADE)

McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART Board6.EE.B.7Solve mathematical problems andproblems in real-world context bywriting and solving equations ofthe form x p q, x – p q, px q, and x/p q for cases in which p,q, and x are all non-negativerational numbers.6.EE.B.8Write an inequality of the form x c, x c, x c, or x c to representa constraint or condition to solvemathematical problems andproblems in real-world context.they be written andevaluated?What arithmetic numberrelationships, calledproperties, are always true?How are sums, differences,products, and quotientsinvolving decimals estimatedand found?What procedures can beused to solve equations?Bloom’s Taxonomy: ApplicationHESS Matrix: DOK Level 2Essential Question(s): What procedures can beused to solve equations? What are standardprocedures for estimatingand finding quotients offractions and mixednumbers? How can equations begraphed? What patterns can be foundin the graphs of equations?Bloom’s Taxonomy: Application ComprehensionHESS Matrix: DOK Level 2number, or depending onthe purpose at hand, anynumber in a specific setI will be able to: solve real-world problemsby writing equations of theform x p q and px q forcases in which p, q and x areall nonnegative rationalnumbers solve mathematicalproblems by solvingequations of the forms x p q and px q for caseswhich p, q, and x arenonnegative rationalnumbers I will be able to: write an inequality of theform x c or x c torepresent a constraint orcondition in a real-world ormathematical problem equationaddition propertyof equalitysubtractionproperty ofequalitymultiplicationproperty ofequalitydivision propertyof equalityinverserelationshipinequalityPage 11Ganado USD – PACING GUIDE (MATH/6TH GRADE)

ALEKSconnected.mcgrawhill (Online)Recognize that inequalities haveinfinitely many solutions;represent solutions of suchinequalities on number lines. McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)6.EE.C.9Use variables to represent twoquantities that change inrelationship to one another tosolve mathematical problems andproblems in real-world context.Write an equation to express onequantity (the dependent variable)in terms of the other quantity (theindependent variable). Analyzethe relationship between thedependent and independentvariables using graphs and tables,and relate these to the equation.Bloom’s Taxonomy: Application AnalysisMcGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)6.G.A.1Find the area of right triangles,other triangles, specialquadrilaterals, and polygons bycomposing into rectangles ordecomposing into triangles andother shapes; apply thesetechniques to solve mathematicalproblems and problems in realworld context.Bloom’s Taxonomy: Application Essential Question(s): How can equations begraphed? What patterns can be foundin the graphs of equations?HESS Matrix: DOK Level 3Essential Question(s): How can equations begraphed? What patterns can be foundin the graph of equations?HESS Matrix: DOK Level 2Essential Question(s): What are standardprocedures for estimatingand finding products offractions and mixednumbers?recognize that inequalitiesof the x c or x c haveinfinitely many solutions;represent solutions of suchinequalities on number linediagramsI will be able to: use variables to representtwo quantities in a realworld problem that changein relationship to oneanother write an equation to expressone quantity, thought of asthe dependent variable, interms of the other quantity,thought of as theindependent variable analyze the relationshipbetween the dependent andindependent variables usinggraphs and tables, andrelate these to the questionI will be able to: find the area of righttriangles find the area of othertriangles find the area of specialquadrilaterals find the area of polygons bycomposing into rectangles find the area of polygons bydecomposing into trianglesand other shapes formulaT-tablelinear acute angleright angleobtuse anglestraight angleacute triangleright triangleobtuse triangleequilateraltriangleisosceles trianglescalene trianglePage 12Ganado USD – PACING GUIDE (MATH/6TH GRADE)

McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)McGraw-Hill MathTextbookPowerPointPresentations6.G.A.2Find the volume of a rightrectangular prism with fractionaledge lengths by packing it withunit cubes of the appropriate unitfraction edge lengths, and showthat the volume is the same aswould be found by multiplying theedge lengths of the prism.Understand and use the formula V B · h, where in this case, B is thearea of the base (B l x w) to findvolumes of right rectangularprisms with fractional edgelengths in mathematical problemsand problems in real-worldcontext.6.G.A.3Draw polygons in the coordinateplane given coordinates for thevertices; use coordinates to findHow can angles bemeasured, drawn, andclassified?What are special shapes andhow can they be describedand compared?What are the meanings ofperimeter and area?How can the perimeter andarea of certain shapes befound?Bloom’s Taxonomy: ApplicationHESS Matrix: DOK Level 2Essential Question(s): What is the meaning ofvolume and how can volumebe found? What is the meaning ofsurface area and how cansurface area be found? How can the volume ofcertain figures be found?4th QuarterBloom’s Taxonomy: ApplicationHESS Matrix: ngthwidth2-dimensionalfiguresI will be able to: find the volume of a rightrectangular prism withfractional edge lengths bypacking it with unit cubes ofthe appropriate unit fractionedge lengths show that the volume is thesame as would be found bymultiplying the edge lengthsof the prism apply the formulas V l w hand V b h to find thevolumes of right rectangularprisms with fractional edgelengths in the context ofsolving real-world andmathematical problems formulavolumecubeI will be able to: draw polygons in thecoordinate plane givencoordinates for the vertices pointlinerayline segment apply these techniques inthe context of solving realworld problemsapply these techniques inthe context of solvingmathematical problemsPage 13Ganado USD – PACING GUIDE (MATH/6TH GRADE)

WorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)the length of a side joining pointswith the same first coordinate orthe same second coordinate.Apply these techniques to solvemathematical problems andproblems in a real-world context. McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)6.G.A.4Represent three-dimensionalfigures using nets made up ofrectangles and triangles, and usethe nets to find the surface areaof these figures. Apply thesetechniques to solve mathematicalproblems and problems in realworld context.Bloom’s Taxonomy: ApplicationMcGraw-Hill A.1Recognize a statistical question asone that anticipates variability inthe data related to the questionand accounts for variability in theBloom’s Taxonomy: ComprehensionDOK Level 2Essential Question(s): How are integers related towhole numbers? How can angles bemeasured, drawn, andclassified? What are special shapes andhow can they be describedand compared?HESS Matrix: DOK Level 2Essential Question(s): What is the meaning ofarea? How can the area of certainshapes be found? What is the meaning ofvolume and how can volumebe found? What is the meaning ofsurface area and how cansurface area be found? How can the volume ofcertain figures be found?HESS Matrix: DOK Level 1 use coordinates to find thelength of a side joiningpoints with the same firstcoordinate or the samesecond coordinateapply these techniques inthe context of solving realworld and mathematicalproblems congruent linesegmentsmidpointintersecting linesplaneparallel linesperpendicularlinesI will be able to: represent three-dimensionalfigures using nets made upof rectangles and triangles using the nets to find thesurface area of these figures apply these techniques inthe context of solving realworld and mathematicalproblems revertexsurface arealengthwidthheight3-dimensionalfiguresI will be able to: recognize a statisticalquestion as one thatanticipates variability in thedata related to the question statisticalquestionPage 14Ganado USD – PACING GUIDE (MATH/6TH GRADE)

SMART BoardALEKSconnected.mcgrawhill (Online) McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online) answers. For example, "How oldam I?" is not a statisticalquestion, but "How old are thestudents in my school?" is astatistical question because oneanticipates variability in students'ages6.SP.A.2Understand that a set of datacollected to answer a statisticalquestion has a distribution whosegeneral characteristics can bedescribed by its center, spread,and overall shape.Essential Question(s): How can graphs be used torepresent data and answerquestions?Bloom’s Taxonomy: ComprehensionHESS Matrix: DOK Level 1Essential Question(s): How can graphs be used torepresent data and answerquestions?McGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKSconnected.mcgrawhill (Online)6.SP.A.3Recognize that a measure ofcenter for a numerical data setsummarizes all of its values with asingle number, while a measure ofvariation uses a single number todescribe the spread of the dataset.Bloom’s Taxonomy: ComprehensionMcGraw-Hill MathTextbookPowerPointPresentationsWorksheetsSMART BoardALEKS6.SP.B.4Display and interpret numericaldata by creating plots on anumber line including histograms,dot plots, and box plots.Bloom’s Taxonomy: ApplicationHESS Matrix: DOK Level 2Essential Question(s): How can graphs be used torepresent data and answerquestions?HESS Matrix: DOK Level 2Essential Question(s):and accounts for it in theanswersI will be able to: understand that a set ofdata collected to answer astatistical question has adistribution, which can bedescribed by its center,s

6th Grade Math PACING Guide SY 2021-2022 Resources AZ College and Career Readiness Standard Essential Question (HESS Matrix) Learning Goal Vocabulary (Content/Academic) 1st Quarter 6.RP.A.1McGraw-Hill Math Textb