Ganado Unified School District Algebra 1
Ganado Unified School DistrictAlgebra 1PACING Guide SY 2019-20Timeline &ResourcesGlencoeAlgebra 1TextbookChapter 0:Preparing forAlgebraChapter 1:Expressions,Equations, andFunctionsALEKS onlineintegrationTriumphLearningCommon CoreCoachAlgebra IAZ CCRS - MathematicsStandards for Mathematical Practices-will be applied in all units of study1. Make sense of problems and persevere insolving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique thereasoning 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 repeatedreasoning.A1.N-Q.A.1 Use units as a way to understand problemsand to guide the solution of multi-step problems; chooseand interpret units consistently in formulas; choose andinterpret the scale and the origin in graphs and datadisplays.A1.N-Q.A.2 Define appropriate quantities for the purposeof descriptive modeling. Include problem-solvingopportunities utilizing real-world context.A1.N-Q.A.3 Choose a level of accuracy appropriate tolimitations on measurement when reporting quantitiesutilizing real-world context.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10)T. Ames, E. Yazzie, H. AndriamasyEssential QuestionsHESS Matrix How can I recognize andwrite rules for numberpatterns? How do you write anexpression to represent areal world situation?Learning Goal Write verbal expression foralgebraic expressionsWrite algebraic expressionsfor verbal expressionsEvaluate numericalexpression by using theorder of operationsEvaluate algebraicexpressions by using theorder of operationsRecognize the properties ofequality and identityRecognize the Commutativeand Associative PropertiesUse the DistributiveProperty to evaluateexpressionsUse the DistributiveProperty to simplifyexpressions.Solve equations with onevariableSolve equations with twovariablesRepresent relationsInterpret graphs of luateOrder of OperationsEquivalentExpressionsAdditive eReciprocalAccuracyLike TermsSimplest FormCoefficientOpen SentenceEquationSolvingSolutionsPage1
A1.A-SSE.A.1 Interpret expressions that represent aquantity in terms of its context.a. Interpret parts of an expression, such as terms,factors, and coefficients.b. Interpret complicated expressions by viewingone or more of their parts as a single entity. A1.A-SSE.A.2 Use the structure of an expression toidentify ways to rewrite it.A1.A-CED.A.1 Create equations and inequalities in onevariable and use them to solve problems. Includeproblem-solving opportunities utilizing real-world context.Focus on linear, quadratic, exponential and piecewisefunctions (limited to absolute value and step).A1.A-REI.B.3 Solve linear equations and inequalities inone variable, including equations with coefficientsrepresented by letters.A1.F-IF.A.1 Understand that a function from one set(called the domain) to another set (called the range)assigns to each element of the domain exactly oneelement of the range. If f is a function and x is an elementof its domain, then f(x) denotes the output of fcorresponding to the input x. The graph of f is the graphof the equation y f(x).A1.F-IF.B.4 For a function that models a relationshipbetween two quantities, interpret key features of graphsand tables in terms of the quantities, and sketch graphsshowing key features given a verbal description of therelationship. Key features include: intercepts; intervalswhere the function is increasing, decreasing, positive, ornegative; relative maximums and minimums. Focus onlinear, quadratic, exponential and piecewise-definedfunctions (limited to absolute value and step).Ganado USD-PACING GUIDE (Algebra/Grade 9, 10)Determine whether arelation is a functionFind function valuesInterpret intercepts, andsymmetry of graphs offunctionsInterpret positive, negative,increasing and decreasingbehavior, extrema, and endbehavior of graphs offunctions.Replacement SetSetElementSolution SetIdentifyCoordinate SystemCoordinate PlaneX- and Y- AxesOriginOrdered PairX- and ariableDependent VariableFunctionDiscrete FunctionContinuous FunctionVertical Line TestFunction NotationNonlinear itiveNegativeIncreasingDecreasingExtremaRelative MaximumRelative MinimumEnd BehaviorPage2
A1.F-IF.A.2 Evaluate functions for inputs in their domains,and interpret statements that use function notation interms of a context.A1.F-IF.B.5 Relate the domain of a function to its graphand, where applicable, to the quantitative relationship itdescribes.A1.A-REI-D.10 Understand that the graph of an equationin two variables is the set of all its solutions plotted in thecoordinate plane, often forming a curve, which could be aline.A1.S-ID.A.1 Represent real-value data with plots for thepurpose of comparing two or more data sets.GlencoeAlgebra 1TextbookChapter 2:LinearEquationsA1.A-CED.A.1 Create equations and inequalities in onevariable and use them to solve problems. Includeproblem-solving opportunities utilizing real-world context.Focus on linear, quadratic, exponential and piecewisefunctions (limited to absolute value and step). A1.A-REI.A.1 Explain each step in solving linear andquadratic equations as following from the equality ofnumbers asserted at the previous step, starting from theassumption that the original equation has a solution.Construct a viable argument to justify a solution method. A1.A-REI.B.3 Solve linear equations and inequalities inone variable, including equations with coefficientsrepresented by letters.How do we solve equationusing addition, subtraction,multiplication and division?How do we utilizeequations to solveproblems?How do you rearrangeformulas to highlightspoints of interest?How do you write equationand inequalities?How do solve equationwith variable in both sides? A1.A-CED.A.4 Rearrange formulas to highlight a quantityof interest, using the same reasoning as in solvingequations. For example, rearrange Ohm’s law V IR tohighlight resistance R.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) Translate sentences intoequationsTranslate equations intosentencesUse algebra tiles to solveaddition, subtraction, andmultiplication equationsSolve Equations by usingaddition or subtractionSolve equations by usingmultiplication or divisionUse algebra tiles to solvemulti-step equationsSolve equations involvingmore than one operation.Solve equations involvingconsecutive integersSolve equations with thevariables on each sideFormulaSolve an EquationEquivalentEquationsMulti-Step EquationConsecutiveIntegersNumber e RateScaleScale ModelPercent of ChangePercent of IncreasePercent of DecreasePage3
A1.N-Q.A.1 Use units as a way to understand problemsand to guide the solution of multi-step problems; chooseand interpret units consistently in formulas; choose andinterpret the scale and the origin in graphs and datadisplays. GlencoeAlgebra 1TextbookChapter 3:LinearFunctionsA1.F-IF.B.4 For a function that models a relationshipbetween two quantities, interpret key features of graphsand tables in terms of the quantities, and sketch graphsshowing key features given a verbal description of therelationship. Key features include: intercepts; intervalswhere the function is increasing, decreasing, positive, ornegative; relative maximums and minimums. Focus onlinear, quadratic, exponential and piecewise-definedfunctions (limited to absolute value and step).A1.F-IF.C.7 Graph functions expressed symbolically andshow key features of the graph, by hand in simple casesand using technology for more complicated cases. Focuson linear, quadratic, exponential and piecewise-definedfunctions (limited to absolute value and step).A1.A-REI.D.10 Understand that the graph of an equationin two variables is the set of all its solutions plotted in theGanado USD-PACING GUIDE (Algebra/Grade 9, 10) How do we graph linearequations in two variables?How do we representfunction as tables, rules andgraphs?How do we use graph of afunction to solve real-worldproblems?How do changes in linearequations and functionsaffects the graph?What types of relationshipscan be modeled by lineargraphs? Solve equations involvinggrouping symbolsEvaluate absolute valueexpressionsSolve absolute valueequationsCompare ratiosSolve proportionsFind the percent of changeSolve problems involvingpercent of changeSolve equations for givenvariablesUse formulas to solve realworld problemsSolve mixture problemsSolve uniform motionproblemsAnalyze the key features oflinear graphsIdentify linear equations,intercepts, and zerosGraph linear equationsSolve linear equations bygraphingEstimate solutions to anequation by graphingUse rate of change tosolve problemsFind the slope of a lineWrite and graph directvariation equationsSolve problems involvingdirect variationRecognize arithmeticsequencesLiteral EquationDimensionalAnalysisUnit AnalysisWeighted averageMixture problemUniform motionproblemRate problemLinear FunctionConstant FunctionLinear EquationStandard FormConstantX-InterceptY-InterceptLinear FunctionParent FunctionFamily of GraphsRootZerosRate of ChangeSlopeDirect VariationConstant ofVariationConstant ofProportionalityPage4
coordinate plane, often forming a curve, which could be aline. A1.F-IF.B.6 Calculate and interpret the average rate ofchange of a continuous function (presented symbolicallyor as a table) over a specified interval. Estimate the rateof change from a graph. Include problem-solvingopportunities utilizing real-world context. Focus on linear,quadratic, exponential and piecewise-defined functions(limited to absolute value and step). Relate arithmeticsequences to linearfunctionsWrite an equation for aproportional relationshipWrite an equation for icSequenceCommon DifferenceA1.F-LE.A.1 Distinguish between situations that can bemodeled with linear functions and with exponentialfunctions.a. Prove that linear functions grow by equaldifferences over equal intervals, and thatexponential functions grow by equal factors overequal intervals.b. Recognize situations in which one quantitychanges at a constant rate per unit interval relativeto another.c. Recognize situations in which a quantity growsor decays by a constant percent rate per unitinterval relative to another.A1.F-LE.A.2 Construct linear and exponential functions,including arithmetic and geometric sequences, given agraph, a description of a relationship, or input-outputpairs.A1.F-BF.A.1 Write a function that describes a relationshipbetween two quantities. Determine an explicit expression,a recursive process, or steps for calculation from realworld context. Focus on linear, quadratic, exponential andpiecewise-defined functions (limited to absolute value andstep).Ganado USD-PACING GUIDE (Algebra/Grade 9, 10)Page5
GlencoeAlgebra 1TextbookChapter 4:Equations ofLinearFunctionsA1.F-IF.A.2 Evaluate functions for inputs in their domains,and interpret statements that use function notation interms of a context.A1.F-IF.C.7 Graph functions expressed symbolically andshow key features of the graph, by hand in simple casesand using technology for more complicated cases.Focus on linear, quadratic, exponential and piecewisedefined functions (limited to absolute value and step).A1.F-BF.A.1 Write a function that describes a relationshipbetween two quantities. Determine an explicit expression,a recursive process, or steps for calculation from acontext. Focus on linear, quadratic, exponential andpiecewise-defined functions (limited to absolute value andstep).A1.F-BF.B.3 Identify the effect on the graph of replacingf(x) by f(x) k, k f(x), f(kx), and f(x k) for specific valuesof k (both positive and negative); find the value of k giventhe graphs. Experiment with cases and illustrate anexplanation of the effects on the graph. Focus on linear,quadratic, exponential and piecewise-defined functions(limited to absolute value and step).A1.F-LE.A.2 Construct linear and exponential functions,including arithmetic and geometric sequences, given agraph, a description of a relationship, or two input-outputpairs.A1.F-IF.A.2 Evaluate a function for inputs in the domain,and interpret statements that use function notation interms of context.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) How can you distinguishbetween real-worldsituation using linear,quadratic and exponentialfunction?How do equations relate tofunctions?When is a linear modelappropriate for describinga relationship between twoquantities? Write and graph linearequations in slope-interceptformModel real-world data withequations in slope-interceptformUse a graphing calculator tocollect data and investigateslope-intercept form.Use a graphing a calculatorto investigate families oflinear functionsWrite an equation of a line inslope-intercept form giventhe slope and one pointWrite an equation of a line inslope-intercept form giventwo points.Write an equation of lines inpoint-slope formWrite linear equations indifferent formsWrite an equation of the linethat passes through a givenpoint, parallel to a given lineWrite an equation of the linethat passes through a givenpoint, perpendicular to agiven lineInvestigate relationshipsbetween quantities by usingpoints on scatter plotsUse lines of fit to make andevaluate predictionsSlope-InterceptFormConstant FunctionIdentity FunctionConstraintLinear ExtrapolationPoint-Slope FormParallel LinesPerpendicular LinesBivariate DataScatter PlotLine of FitLinear InterpolationCausationBest-Fit LineLinear RegressionCorrelationCoefficientResidualMedian-Fit LineInverse RelationInverse FunctionPage6
A1.S-ID.C.7 Interpret the slope as a rate of change andthe constant term of a linear model in the context of thedata. A1.S-ID.B.6 Represent data on two quantitative variableson a scatter plot, and describe how the variables arerelated.a. Fit a function to the data; use functions fitted to data tosolve problems in the context of the data. Focus on linearmodels.b. Informally assess the fit of a functionbyplotting and analyzing residuals. A1.S-ID.C.9 Distinguish between correlation andcausation.Explore the differencebetween correlation andcausationWrite equations of best-fitlines using linear regressionWrite equations of median-fitlinesFind the inverse of a relationFind the inverse of a linearfunctionDraw the inverse of arelation and determinewhether the inverse is afunctionA1.S-ID.C.8 Compute and interpret the correlationcoefficient of a linear relationship.A1.A-CED.A.2 Create equations in two or more variablesto represent relationships between quantities; graphequations on coordinate axes with labels and scales.A1.F-LE.B.5 Interpret the parameters in a linear orexponential function with integer exponents utilizing realworld context.GlencoeAlgebra 1TextbookChapter 5:LinearInequalitiesA1.A-CED.A.1 Create equations and inequalities in onevariable and use them to solve problems. Includeproblem-solving opportunities utilizing real-world context.Focus on linear, quadratic, exponential and piecewisedefined functions (limited to absolute value and step).A1.A-REI.B.3 Solve linear equations and inequalities inone variable, including equations with coefficientsrepresented by letters.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) Why do we want tocompare rather than get anexact answer? Solve linear inequalities byusing Addition Subtraction Multiplication DivisionUse algebra tiles to modelsolving inequalitiesSet-builder yHalf-PaneClosed (Open) HalfPanePage7
A1.A-CED.A.3 Represent constraints by equations orinequalities, and by systems of equations and/orinequalities, and interpret solutions as viable or non-viableoptions in a modeling context. A1.A-REI.D.12 Graph the solutions to a linear inequalityin two variables as a half-plane, excluding the boundary inthe case of a strict inequality, and graph the solution setto a system of linear inequalities in two variables as theintersection of the corresponding half-planes. GlencoeAlgebra 1TextbookChapter 6:Systems ofLinearEquations andInequalitiesA1.A-CED.A.3 Represent constraints by equations orinequalities, and by systems of equations and/orinequalities, and interpret solutions as viable or non-viableoptions in a modeling context.A1.A-CED.A.2 Create equations in two or more variablesto represent relationships between quantities; graphequations on coordinate axes with labels and scales.A1.A-REI.C.5 Prove that, given a system of twoequations in two variables, replacing one equation by thesum of that equation and a multiple of the other producesa system with the same solutions.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) How can we utilizeequations to solveproblems? Solve linear inequalitiesinvolving more than oneoperationSolve linear inequalitiesinvolving the DistributivePropertyIdentify compoundstatements connected bythe word and or or as true orfalse.Solve compound inequalitiescontaining the word and andgraph their solution setSolve compound inequalitiescontaining the word or andgraph their solution setSolve and graph absolutevalue inequalitiesGraph linear inequalities onthe coordinate plane solveinequalities by graphingUse a graphing calculator toinvestigate the graphs ofinequalitiesDetermine the number ofsolutions a system of linearequations has, if anySolve systems of linearequations by graphingUse a graphing calculator tosolve a system of equationsSolve systems of equationsby using substitutionSolve real-world problemsinvolving systems ofequations by usingsubstitution.System of gmented MatrixRow ReductionPage8
A1.A-REI.C.6 Solve systems of linear equations exactlyand approximately, focusing on pairs of linear equationsin two variables. Include problem-solving opportunitiesutilizing real-world context. A1.A-REI.D.12 Graph the solutions to a linear inequalityin two variables as a half-plane, excluding the boundary inthe case of a strict inequality, and graph the solution setto a system of linear inequalities in two variables as theintersection of the corresponding half-planes. GlencoeAlgebra 1TextbookA1.A-SSE.A.2 Use the structure to identify ways torewrite numerical and polynomial expressions. Focus onpolynomial multiplication and factoring patterns.Chapter 7:Exponents andExponentialFunctionsA1.F-IF.C.7 Graph functions expressed symbolically andshow key features of the graph, by hand in simple casesand using technology for more complicated cases. Focuson linear, quadratic, exponential and piecewise-definedfunctions (limited to absolute value and step).A1.F-BF.B.3 Identify the effect on the graph of replacingf(x) by f(x) k, k f(x), f(kx), and f(x k) for specific valuesof k (both positive and negative); find the value of k giventhe graphs. Experiment with cases and illustrate anexplanation of the effects on the graph. Focus on linear,quadratic, exponential and piecewise-defined functions(limited to absolute value and step).A1.F-LE.A.2 Construct linear and exponential functions,including arithmetic and geometric sequences, given aGanado USD-PACING GUIDE (Algebra/Grade 9, 10) How can you distinguishbetween real-world situationusing linear, quadratic andexponential function ? Solve systems of equationsby using elimination withmultiplicationSolve real-world problemsinvolving systems ofequationsDetermine the best methodfor solving systems ofequationsApply systems of equationsUse matrices to solvesystems of equationsSolve systems of linearinequalities by graphingApply systems of linearinequalities.Identity MatrixSystem ofInequalitiesMultiply monomials usingthe properties of exponentsSimplify expressions usingthe multiplication propertiesof exponentsDivide monomials using theproperties of exponentsSimplify expressionscontaining negative andzero exponentsEvaluate and rewriteexpressions involvingrational exponentsSolve equations involvingexpressions with rationalexponentsExpress numbers inscientific notationMonomialConstantZero ExponentsNegative ExponentOrder of MagnitudeRational ExponentCube RootNth RootExponentialEquationScientific NotationExponentialFunctionExponential GrowthFunctionExponential DecayFunctionCompound InterestGeometricSequencePage9
graph, a description of a relationship, or input-outputpairs. A1.A-REI.D.11 Explain why the x-coordinates of thepoints where the graphs of the equations y f(x) and y g(x) intersect are the solutions of the equation f(x) g(x);find the solutions approximately (e.g., using technology tograph the functions, make tables of values, or findsuccessive approximations. Focus on cases where f(x)and/or g(x) are linear, quadratic, exponential andpiecewise-defined function (limited to absolute value andstep). A1.F-LE.A.1 Distinguish between situations that can bemodeled with linear functions and with exponentialfunctions.a. Prove that linear functions grow by equal differencesover equal intervals, and that exponential functions growby equal factors over equal intervals.b. Recognize situations in which one quantity changes ata constant rate per unit interval relative to another.c. Recognize situations in which a quantity grows ordecays by a constant percent rate per unit interval relativeto another. Find products and quotientof numbers expressed inscientific notationGraph exponential functionsIdentify data that displayexponential behaviorSolve problems involvingexponential growthSolve problems involvingexponential decayIdentify and generategeometric sequencesRelate geometric sequencesto exponential functionsUse a recursive formula tolist the terms in a sequenceWrite recursive formulas forarithmetic and geometricsequences.Common RatioRecursive FormulaA1.F-IF.A.3 Recognize that sequences are functions,sometimes defined recursively, whose domain is a subsetof the integers.GlencoeAlgebra 1TextbookChapter 8:QuadraticExpressionsand EquationsA1.A-APR.A.1 Understand that polynomials form asystem analogous to the integers, namely, they areclosed under the operations of addition, subtraction, andmultiplication; add, subtract, and multiply polynomials.A1.N-RN.B.3 Explain why the sum or product of tworational numbers is rational; that the sum of a rationalnumber and an irrational number is irrational; and that theGanado USD-PACING GUIDE (Algebra/Grade 9, 10) Why do we need to usequadratic functions tomodel situations? Whyshould we factor? Howdoes the graph of aquadratic function relate toits algebraic equation? Use algebra tiles tomodel using theDistributive Property tofactor binomialsUse the DistributiveProperty to factorpolynomialsFactoringFactoring byGroupingZero ProductPropertyQuadratic EquationPrime PolynomialPage10
product of a nonzero rational number and an irrationalnumber is irrational. A1.A-SSE.A.1 Understand expressions that represent aquantity in terms of its context.a.a. Interpret parts of an expression, such asterms, factors, and coefficients.b.b. Interpret expressions by viewing one or moreof their parts as a single entity. A1.A-SSE.A.2 Use the structure to identify ways torewrite numerical and polynomial expressions. Focus onpolynomial multiplication and factoring patterns. A1.A-SSE.B.3 Choose and produce an equivalent form ofan expression to reveal and explain properties of thequantity represented by the expression.a. Factor a quadratic expression to reveal the zeros of thefunction it defines.b. Complete the square in a quadratic expression toreveal the maximum or minimum value of the function itdefines.A1.A-REI.B.4 Solve quadratic equations in one variable.a.Use the method of completing the square to transformany quadratic equation in x into an equation of the form (x- k)2 q that has the same solutions. Derive the quadraticformula from this form.a. b. Solve quadratic equations by inspection (e.g., for x2 49), taking square roots, completing the square, thequadratic formula and factoring, as appropriate to theinitial form of the equation. Focus on solutions forquadratic equations that have real roots. Include casesthat recognize when a quadratic equation has no realsolutions.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) Solve quadraticequations of the formax2 bx 0Factor trinomials of theform x2 bx cSolve quadraticequations of the formx2 bx c 0Factor trinomials of theform ax2 bx cSolve quadraticequations of the formax2 bx c 0Factor binomials thatare the difference ofsquares.Use the difference ofsquares to solveequations.Factor perfect squaretrinomialsSolve equationsinvolving perfectsquaresDifference of TwoSquaresPerfect SquareTrinomialPage11
A1.A-REI.A.1 Explain each step in solving linear andquadratic equations as following from the equality ofnumbers asserted at the previous step, starting from theassumption that the original equation has a solution.Construct a viable argument to justify a solution method.A1.A-APR.B.3 Identify zeros of polynomials whensuitable factorizations are available, and use the zeros toconstruct a rough graph of the function defined by thepolynomial.Focus on quadratic and cubic polynomials in which linearand quadratic factors are available.A1.F-IF.C.9 Compare properties of two functions eachrepresented in a different way (algebraically, graphically,numerically in tables, or by verbal descriptions).Focus on linear, quadratic, exponential and piecewisedefined functions (limited to absolute value and step).GlencoeAlgebra 1TextbookChapter 9:QuadraticFunctions andEquationsA1.F-IF.B.4 For a function that models a relationshipbetween two quantities, interpret key features of graphsand tables in terms of the quantities, and sketch graphsshowing key features given a verbal description of therelationship.Include problem-solving opportunities utilizing real-worldcontext. Key features include: intercepts; intervals wherethe function is increasing, decreasing, positive, ornegative; relative maximums and minimums. Focus onlinear, quadratic, exponential and piecewise-definedfunctions (limited to absolute value and step).A1.F-IF.B.6 Calculate and interpret the average rate ofchange of a function (presented symbolically or as atable) on a closed interval. Estimate the rate of changefrom a graph. Focus on linear, quadratic, exponential andpiecewise-defined functions (limited to absolute value andstep).Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) Why do we need to useexponential notation tomodel situations? Analyze the characteristicsof the graphs of quadraticfunctionsGraph quadratic functionuse a given quadraticfunction to investigate therate of change of aquadratic functionsolve quadratic equationsby graphingestimate solutions ofquadratic equations bygraphingapply translations ofquadratic functionsapply dilations andreflections to quadraticfunctionsQuadratic FunctionStandard FormParabolaAxis of SymmetryVertexMinimumMaximumDouble tex FormCompleting theSquareQuadratic FormulaDiscriminantStep FunctionPage12
A1.F-IF.C.7 Graph functions expressed symbolically andshow key features of the graph, by hand in simple casesand using technology for more complicated cases.Focus on linear, quadratic, exponential and piecewisedefined functions (limited to absolute value and step).A1.F-IF.C.8 Write a function defined by an expression indifferent but equivalent forms to reveal and explaindifferent properties of the function.a. Use the process of factoring and completing the squarein a quadratic function to show zeros, extreme values,and symmetry of the graph, and interpret these in termsof a context.A1.F-BF.B.3 Identify the effect on the graph of replacingf(x) by f(x) k, k f(x), f(kx), and f(x k) for specific valuesof k (both positive and negative); find the value of k giventhe graphs. Experiment with cases and illustrate anexplanation of the effects on the graph. Focus on linear,quadratic, exponential and piecewise-defined functions(limited to absolute value and step).A1.A-REI.B.4 Solve quadratic equations in one variable.a.Use the method of completing the square to transformany quadratic equation in x into an equation of the form (x- k)2 q that has the same solutions. Derive the quadraticformula from this form.b.Solve quadratic equations by inspection (e.g., for x2 49), taking square roots, completing the square, thequadratic formula and factoring, as appropriate to theinitial form of the equation.Focus on solutions for quadratic equations that have realroots. Include cases that recognize when a quadraticequation has no real solutions.Ganado USD-PACING GUIDE (Algebra/Grade 9, 10) Use a graphing calculatorto solve a system of onelinear and one quadraticequationcomplete the square towrite perfect squaretrinomialssolve quadratic equationsby completing the squaresolve quadratic equationsby using the QuadraticFormula.use the discriminant todetermine the number ofsolutions to a quadraticequation.identify linear, quadratic,and exponential functionsfrom given datawrite equations that modeldataidentify and graph stepfunctionsidentify and graph stepfunctionsidentify and graph absolutevalue and piecewisedefined functionsPiecewise-LinearFunctionGreatest IntegerFunctionAbsolute ValueFunctionPiecewise-DefinedFunctionPage13
A1.A-SSE.B.3 Choose and produce an equivalent form ofan expression to reveal and explain properties of thequantity represented by the expression.a. Factor a quadratic expression to reveal the zeros of thefunction it defines.b. Complete the square in a quadratic expression toreveal the maximum or minimum value of the function itdefines.A1.F-LE.A.1 Distinguish between situations that can bemodeled with linear functions and
Use algebra tiles to solve addition, subtraction, and multiplication equations Solve Equations by using addition or subtraction Solve equations by using multiplication or division Use algebra tiles to solve multi
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