Content Map of Unit - Lower Dauphin School District



CP Alg IIDecision One:Curriculum MapGrade:Topic:Unit 1: Equations and ExpressionsThe key learning is to be able to simplify expressions, solve multi-step linear equations, linear inequalities, and absolute value equations and inequalities.How do we solve linear equations, linear inequalities, and absolute value equations?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 1.1, 1.2, 1.3, 1.4, 1.5Approximately 8 daysConcept:Concept:Concept:Concept:Properties of Real Numbers and Simplifying Algebraic ExpressionsSolving Linear EquationsSolving Linear InequalitiesSolving Absolute Value Equations and InequalitiesLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we use the properties of real numbers to simplify algebraic expressions?What is the solution to a linear equation?How do we find the solution to a linear equation?What are the solutions to a linear inequality?How do we find the solutions to a linear inequality?What are the solutions to an absolute value equation or inequality?How do we find the solutions to an absolute value equation or inequality?Vocabulary:Vocabulary:Vocabulary:Vocabulary:OppositeReciprocalAbsolute ValueEvaluateCompound InequalitiesExtraneous SolutionUnit 2: Linear and Absolute Value FunctionsCP Alg IIDecision One:Curriculum MapGrade:Topic:The graph of an equation represents all ordered pairs that satisfy the equation. How do we graph and write linear equations and inequalities?How do we graph absolute value equations or inequalities?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 2.2, 2.4, 2.5, 2.6, 2.7Approximately 10-12 daysConcept:Concept:Concept:Concept:Graphing Linear EquationsWriting Linear EquationsGraphing Absolute Value EquationsGraphing Linear and Absolute Value InequalitiesLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we represent linear equations graphically?How do we find x and y intercepts?How do we write the equation of a line given points and/or slope?How do we write an equation of a line given a set of data points?How do we graph an absolute value equation?How do we graph linear and absolute value inequalities?Vocabulary:Vocabulary:Vocabulary:Vocabulary:Dependent VariableIndependent Variablex-intercepty-interceptSlopeZero SlopeUndefined SlopeStandard FormPoint-Slope FormSlope-Intercept FormScatter PlotLine of Best FitCorrelationVertexParent FunctionTranslationReflectionBoundary LineTest PointSolution RegionUnit 3: Systems of Linear EquationCP Alg IIDecision One:Curriculum MapGrade:Topic:Systems of equations can be used to solve problems with more than one variable.How do we solve a system of linear equations?How do we write a system of linear equations to solve real world problems?How do we solve a system of linear inequalities?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 3.1, 3.2, 3.3, 3.6Approximately 10 daysConcept:Concept:Concept:Concept:Solving Linear Systems of Equation by Graphing, Substitution, and EliminationApplications of Linear Systems of EquationsGraphing Systems of Linear InequalitiesSystems of Equations with Three VariablesLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we solve linear systems of equations using graphing, substitution, and elimination?How do we apply linear system of equations to solve real world problems?How do we represent solutions of systems of linear inequalities with a graph?How do we solve systems of equations that contain three variables?Vocabulary:Vocabulary:Vocabulary:Vocabulary:Linear SystemIndependent SystemDependent SystemInconsistent SystemSolution RegionBoundary LineOrdered TripleCoordinate SpaceZ-axisUnit 4: Quadratic Expressions and EquationsCP Alg IIDecision One:Curriculum MapGrade:Topic:A quadratic equation can be solved by factoring, by using the quadratic formula, and by using square roots. How do we solve quadratic equations?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 5.4, 5.5, 5.6, 5.8Approximately 15-18 daysConcept:Concept:Concept:Concept:Factoring Quadratic ExpressionsSolving Quadratic EquationsComplex NumbersQuadratic FormulaLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we factor quadratic expression using GCF?How do we factor a difference of two squares?How do we factor trinomials?How can factoring methods be combined to completely factor quadratic expressions?How do we solve quadratic equation by factoring or by using square roots without a calculator?What does the solution to a quadratic equation represent?What is an imaginary number?What is a complex number?How do we perform mathematical operations on complex numbers?How do we solve equations that have complex solutions?How do we solve equations using the Quadratic Formula without a calculator?How do we approximate solutions with the Quadratic Formula using a calculator?How do we solve equations that have complex solutions using the Quadratic Formula?Vocabulary:Vocabulary:Vocabulary:Vocabulary:FactorsGCFPerfect SquaresDifference of Two SquaresPrime PolynomialsCoefficientStandard Form or a QuadraticLinear CoefficientZerosRootsSolutionsImaginary NumberComplex NumberImaginary SolutionsQuadratic CoefficientLinear CoefficientConstant CoefficientDiscriminantUnit 5: Graphing Quadratic EquationsCP Alg IIDecision One:Curriculum MapGrade:Topic:The graph of a quadratic equation is a parabola with a vertex, an axis of symmetry, and a y-intercept.X-intercepts of a quadratic graph are solutions of the equation.How do we investigate and graph quadratic equations?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 5.1, 5.2, 5.3Approximately 15-18 daysConcept:Concept:Concept:Concept:Introduction to quadratic graphsProperties of ParabolasTransforming Parabola GraphsApplications of Quadratic EquationsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions: How do we graph quadratic equations using x-y tables?How do we identify direction of opening, vertex, and axis of symmetry of a parabola?How do we determine the maximum or minimum of a parabola?How do we construct the graph of a parabola using the vertex, intercepts, and symmetry?How do we construct the graph of a parabola using the vertex form of the quadratic equation?How do apply concepts of parabola graphs to real world problems?How do we use a graphing calculator to find the vertex and x-intercepts of a quadratic equation?Vocabulary:Vocabulary:Vocabulary:Vocabulary:ParabolaQuadratic CoefficientAxis of SymmetryVertexVertex FormulaMaximum ValueMinimum ValueX-interceptVertex FormTranslationRefectionUnit 6: Functions CP Alg IIDecision One:Curriculum MapGrade:Topic:A function is a relationship between variables with specialized notation and operations.Domain and Range of functions must be identified.What is a function?How do we use function notation?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 2.1, 6.1, 6.2, 7.6, 7.7Approximately 15-18 daysConcept:Concept:Concept:Concept:Definition of FunctionsGraphing Families of FunctionsPolynomial FunctionsFunction OperationsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:What is the difference between a function and a relation?What are the domain and range of a function?How do we evaluate functions?How do we graph linear, absolute value, and quadratic functions?How do we use function values to construct graphs?How do we classify polynomial functions?What does the degree of a polynomial function tell us about the graph?How do we perform mathematical operations on a function?How do we compose two functions?How do we find the inverse of a function?Vocabulary:Vocabulary:Vocabulary:Vocabulary:RelationFunctionDomainRangeVertical Line TestFunction NotationFunction MappingEvaluateFunction GraphsFunction ValuesDegreeTermStandard Form of a PolynomialCubic CoefficientQuartic Coefficient Polynomial FactorsZeros of a PolynomialRestricted DomainComposition of FunctionsInverse FunctionsInverse RelationsUnit 7: Rational Exponents and Radicals CP Alg IIDecision One:Curriculum MapGrade:Topic:Expressions with rational exponents can be written as radical expressions.Equations with radicals can be graphed as functions. How do we solve and graph radical equations?How do we simplify and evaluate radical expressions?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 7.1, 7.2, 7.3, 7.4, 7.5, 7.8Approximately 22-25 daysConcept:Concept:Concept:Concept:Exponent RulesRoots and Radical ExpressionsMultiplying and Dividing Radical ExpressionsRational ExponentsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:What are the rules for simplifying expressions containing rational exponents, including negative exponents?What is the nth root of a number?How do we simplify radical expressions?How do we multiply monomials and binomial containing radicals?How do we rationalize the denominator of a rational expression?What is the meaning of a rational exponent?How do we simplify expressions containing rational exponents?How do we write rational exponents as radicals?How do we write radicals using rational exponents?Vocabulary:Vocabulary:Vocabulary:Vocabulary:BasesExponentZero ExponentRadicalRadicandIndexRootPrinciple RootRationalizeConjugateRadical FormRational Exponent FormConcept:Concept:Concept:Concept:Solving Radical EquationsGraphing Square Root and Cube Root FunctionsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we solve equations containing radicals?How do we graph a square root function?How do we graph a cube root function?What are the domain and range of radical functions?Vocabulary:Vocabulary:Vocabulary:Vocabulary:Extraneous Solution“Isolate the Radical”Unit 8: Exponential and Logarithmic FunctionsCP Alg IIDecision One:Curriculum MapGrade:Topic:Exponential functions can be used to model growth and decay. Logarithms can be used to solve exponential equations.What is an exponential function?What are the properties of logarithms?How can logarithms be used to solve exponential equations?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6Approximately 20-25 daysConcept:Concept:Concept:Concept:Exponential FunctionsLogarithmic FunctionsProperties of Logarithms Exponential EquationsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How does an exponential function model growth or decay?How do we graph exponential functions?How do we solve problems using growth or decay factors?How do we write an exponential equation in logarithmic form using the definition of a log?How do we write a logarithmic equation in exponential form using the definition of a log?How do you evaluate a logarithm without a calculator?How do we use the properties of logarithms to expand or condense expressions?How do we solve equations with exponential expressions?How do we check solutions of exponential equations?Vocabulary:Vocabulary:Vocabulary:Vocabulary:Exponential FunctionBaseGrowth FactorDecay FactorDepreciationAppreciationSimple InterestCompound InterestBase eAsymptoteLogarithmDefinition of a LogarithmBaseCommon LogarithmExpandCondenseProduct PropertyQuotient PropertyPower PropertyExponential EquationConcept:Concept:Concept:Concept:Logarithmic EquationsNatural Logarithmic and Exponential FunctionsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we solve equations that contain logarithms?How do we check for extraneous solutions to logarithmic equations?How do we evaluate expression with natural logarithms or base e?How do we solve equations with natural logarithms or base e?Vocabulary:Vocabulary:Vocabulary:Vocabulary:Logarithmic EquationsChange of Base FormulaNatural BaseNatural LogarithmContinuously Compounding InterestHalf LifeUnit 9: Algebraic Fractions CP Alg IIDecision One:Curriculum MapGrade:Topic:Properties of fractions can be extended to algebraic expressions or equations.How do we simplify rational algebraic expressions?How do we solve rational algebraic equations?OptionalInstructional Tools:Unit Essential Question(s):Key Learning(s):Prentice Hall Algebra IISections: 2.3, 9.1, 9.2, 9.4, 9.5, 9.6Approximately 15-18 daysConcept:Concept:Concept:Concept:Models of VariationReciprocal Function GraphsMultiplying and Dividing Rational ExpressionsAdding Subtracting Rational ExpressionsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we solve problems using direct and inverse variation?How do we solve problems using joint and combined variation?What does the graph of the function f(x) = a/x look like?How do we graph reciprocal equations using an x-y table?How do we simplify an algebraic rational expression?How do we multiply two algebraic rational expressions?How do we divide and simplify two algebraic rational expressions?How do we add or subtract two algebraic rational expressions with common denominators?How do we add or subtract two algebraic rational expressions without common denominators?What is the least common denominator for two algebraic rational expressions?Vocabulary:Vocabulary:Vocabulary:Vocabulary:Constant of VariationDirect VariationInverse VariationJoint VariationCombined VariationAsymptoteRational ExpressionVariable RestrictionsReciprocalLeast Common MultipleLeast Common DenominatorConcept:Concept:Concept:Concept:Solving Rational EquationsLesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:Lesson Essential Questions:How do we solve rational equations by cross multiplying?How do we solve rational equations by multiplying by the least common denominator?How do we check for extraneous solutions of rational equations?Vocabulary:Vocabulary:Vocabulary:Vocabulary: ................
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