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CC ALGEBRA IIQuarter: 1Unit 1: Algebraic EssentialsTimeframe: 8 days CCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentA-CED.4A-SSE.1A-SSE.2A-APR.1Mathematical SkillsSolve linear equations and inequalities in one variableInterpret ExpressionsOperations of PolynomialsKnowledgeSolving EquationsExpressions and FormulasMultiplying PolynomialsProperties of ExponentsDoes order matter?How can a linear function be used to interpret data and find solutions?Why is it advantageous to use and solve equations algebraically for real-world problems?EngageNYKuta Math BitsEmathinstructionGraphing Calculator Teacher generatedCC ALGEBRA IIQuarter: 1 Unit 2: Functions Timeframe: 9 daysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources / Materials Unit AssessmentF-BF.1F-IF.1F-IF.2F.IF.5Mathematical SkillsFunction NotationDomain and RangeOne to One FunctionsInverse FunctionsKnowledgeIdentify the domain and range of relations and functionsUnderstanding the composition of functions. Write functions using function notationUse interval notation to describe the function as increasing or decreasing How do you determine whether a relation is a function, both algebraically and graphically? EngageNYKuta Math BitsEmathinstructionGraphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 1 Unit 3: Linear Functions and EquationsTimeframe: 9 daysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentA-CED.1A-CED.2A-CED.3A-REI.3A-REI.5A-REI.10F.IF.7Mathematical SkillsDirect VariationFinding the Average Rate of ChangeLinear ModelsPiecewise FunctionsSystems of Linear FunctionsKnowledgeFind the direct variation given the valuesFind the average rate of change given an intervalUnderstanding the forms of a line; point-slope form and slope-intercept formModeling linear functionsUnderstanding the inverse of linear functionsGraphing and evaluating piecewise functionsSolving systems of equations; 3 equations in 3 variablesHow do we solve multi-step problems?How do we find the smallest or largest solution to a problem?What are the similarities and differences of solving a linear equation and solving a linear inequality? EngageNYKuta Math BitsEmathinstructionGraphing Calculator Teacher generatedCC ALGEBRA IIQuarter: 1-2Unit 4: Exponential and Logarithmic FunctionsTimeframe: 17 daysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentF-BF.1F-BF.5F-LE.1F-LE.3F-LE.4F.LE.5F.IF.7eF-IF.8bN-Q.1N-Q.2N-Q.3A-SSE.1A-CED.1A-CED.2Mathematical SkillsProperties of ExponentsRational ExpressionsGraphing Exponential FunctionsWriting Exponential EquationsExponential Growth and DecayGraphing Logarithmic FunctionsSolving Exponential EquationsNatural Log and eCompound InterestKnowledgeWrite the exponential equation based on a table of values or a graphDetermine if an exponential function is growth or decayUnderstanding the laws of Logarithmic functionsSolving exponential equations using properties and laws of exponentsUsing the natural log and e to solve exponential equationsSolving exponential equations using compound interestHow can you simplify the equation using properties of exponents?What characterizes exponential growth of decay?How are expressions with exponents and logarithms related?EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 2Unit 5: Sequences and SeriesTimeframe: 8 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentF-BF.1F-BF.2F.IF.3A-SSE.3A-SSE.4F-LE.1F-LE.2Mathematical SkillsArithmetic SequencesGeometric SequencesSummation Natation SeriesKnowledgeIdentifying PatternsRecognizing sequences are functionsWrite an explicit sequence for both arithmetic and geometric functionsWrite a recursive sequence for both arithmetic and geometric functionsConstruct linear and exponential functionsDistinguish between linear and exponential functionsUsing summation notation to fine the sun of a sequenceFind the sum of an arithmetic/geometric seriesHow are sequences used to model real life situations?In real life situations what is the difference between arithmetic and geometric?EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 2Unit 6: Quadratic FunctionsTimeframe: 13 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentA-SSE.1A-SSE.2A-SSE.3A-CED.2A-REI.2A-REI.4F-IF.7Mathematical SkillsFactoring Quadratic FunctionsSolving Quadratic FunctionsSolving Quadratic InequalitiesGraphing Quadratic FunctionsGraphing CirclesLocus and DirectrixKnowledgeFactoring quadratic expressions in different formsSolve a quadratic function using different methodsUse Completing the square to write the equation of a circleModeling real life situations with quadratic functionsDetermining the locus, driectrix, or vertex of a parabolaWhy is it important to supply a zero for a coefficient of any missing term, when you are dividing polynomials? How do you find real roots of a polynomial equation? How is multiplying two polynomials just an expansion of the distribution property? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 2-3Unit 7: Transformations of FunctionsTimeframe: 7 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentF-BF.3Mathematical SkillsIdentify the effects of a transformation of a functionKnowledgeUnderstanding the vertical and horizontal shiftsUnderstanding the cause of a reflection over the axesUnderstanding what causes a vertical stretch or compressionUnderstanding what causes a function to be even or oddWhat effects does k have on the parent function? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 3Unit 8: Radicals and the Quadratic FormulaTimeframe: 9 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentA-REI.1A-REI.2A-REI.4A-SSE.3A-APR.3 Mathematical SkillsSolving Square Root FunctionsProperties of ExponentsSolving Quadratic FunctionsKnowledgeSolving and graphing square root function over a specific intervalSimplifying expressions using the properties of exponentsSolving Quadratic Equations using the quadratic formula How do you find real roots of a polynomial equation? How do square root functions differ from other functions? What makes them unique?Are the properties of exponents the same for whole numbers as they are for fractions? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 3Unit 9: Complex Numbers Timeframe: 6 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentN-CN 1N-CN 2N-CN 3N-CN 4N-CN 5N-CN 7N-CN 8N-CN 9 Mathematical SkillsPerform arithmetic operations with complex numberRepresent complex numbers and their operations on the complex number planeUse complex numbers in polynomial identities and equationsKnowledgeKnow that complex numbers existUse i with all the properties to add, subtract, and multiply complex numbersFind the conjugate of complex numbersRepresent complex numbers on the complex plane in rectangular polar formSolve quadratic equations with real coefficients that have complex solutions Use the discriminant to find the root(s) of the quadratic functionWhy are complex numbers essential?How are operations and properties of complex numbers related to those of real numbers? How do polynomial functions model real-world problems and their solutions?EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 3Unit 10: Polynomial and Rational FunctionsTimeframe: 17 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentA-APR 1A-APR 2A-APR 3A-APR 5A-APR 6A-APR 7A-CED 1A-CED 3 Mathematical SkillsPerform arithmetic operations of polynomialsUnderstand the relationship between zeros and factors of a polynomial functionUse polynomial identities to solve problemsRewrite rational expressionsCreate equations that describe number or relationshipsKnowledgeUnderstand that polynomials are close under the addition, subtraction, multiplication and division.Know and apply the remainder theoremIdentify the zeros of a polynomialKnow and apply the binomial theorem for expanding polynomialsRewrite simple rational expressions in different formsUnderstand that rational expressions for a system of analogous to the rational numbers closed under addition, subtraction, multiplication and division. Create equations and inequalities in one variable and use them to solve problemsRepresent constraints by equations or inequalities and by systems of equations or inequalities. Are rational expressions and their simplified form equivalent? What kind of asymptotes are created from rational expressions? How can rational expressions be related to real world problems? What does the remainder of a polynomial tell you about the factors? Why are there two (or more) ways to divide polynomials functions? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 3-4Unit 11: The Circular FunctionsTimeframe: 13 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentF-TF 1F-TF 2F-TF 3F-TF 4F-TF 5F-TF 6F-TF 7F-TF 8F-TF 9 Mathematical SkillsExtend the domain of trigonometric functions using the unit circleModel periodic phenomena using trigonometric functionsProve and apply trigonometric identitiesKnowledgeUnderstand radian measure of an angle of the length of the arc on the unit circleExplain how the unit circle in the coordinate plane enables the extension of trigonometric functionsUse special right triangles to determine the trigonometric valuesUse the unit circle to explain symmetry of functionsUse trigonometric functions to model frequency, amplitude, and periodUse inverse functions to solve trigonometric functionsUse the Pythagorean Identities to solve for a quadrant angleProve the addition and subtraction formulas for trigonometric functions How do you determine the reference angle of a given angle?Why is it necessary to memorize the unit circle? How do you derive the coordinates of the points of special angles on the unit circle? How do you find conterminal angles? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 4 Unit 12: ProbabilityTimeframe: 8 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentS-CP 1S-CP 2S-CP 3S-CP 4S-CP 5S-CP 6S-CP 7S-CP 8S-CP 9S-MD 1S-MD 2S-MD 3S-MD 4 Mathematical SkillsUnderstand independence and conditional probability and use them to interpret dataUse the rules of probability to compute probabilities of compound events in a uniform probability modelCalculate expected outcomes and use them solve problemsKnowledgeDescribe events as subsets of a sample space using characteristics of the outcomes of other eventsUnderstand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilitiesUnderstand conditional probabilityConstruct and interpret two-way frequency tablesRecognize and explain the concepts of conditional probability Find the conditional probability of given eventsApply the addition rule and interpret the answersApply the general multiplication rule and interpret the answersUse permutations and combinations to compute probabilities of compound events and problems Define a random variable for quality of interestCalculate the expected value of a random valueDevelop a probability distribution for a random variable defined for a sample spaceHow can one differentiate between the three types of probability?What is conditional probability? How can one tell if two events will happen in sequence? How can one tell if two events are mutually exclusive? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generatedCC ALGEBRA IIQuarter: 4 Unit 13: StatisticsTimeframe: 14 DaysCCLS StandardsSkills and KnowledgeStudents will be able toOverarching ConceptsResources/MaterialsUnit AssessmentS-ID 2S-ID 4S-ID 5S-ID 6S-ID 7S-IC 1S-IC 3S-IC 4S-IC 5 Mathematical SkillsSummarize, represent, and interpret data on a single count or measurement variableSummarize, represent, and interpret data on a two categorical count of measurement variableInterpret Linear ModelsUnderstand and evaluate random processes underlying statistical experimentsMake inferences and justify conclusions from sample surveys, experiments and observational studiesKnowledgeUnderstanding statistics as a process for making inferences about population parameters based on a random sample Decide if a specified model is consistent with resultsUse data from a sample survey to interpret data Use data from a randomized experiment to compare two treatmentsUse statistics appropriate to the shape of the dataUse the mean and standard deviation of a set of data to fit it to the normal distribution curveSummarize categorical data for two categories in a two-way frequency tableRepresent data on two quantitative variables on a scatter plotInterpret the slope and intercept of a linear model in the context of the dataHow can measures of variation be determined and interpreted?How can one identify if a distribution is normal?What data display is appropriate for a given set of data?How is the likelihood of an event determined and communicated?How do you distinguish between a population and a sample? How do you design an experiment? How do you interpret normal probability distribution graphs? How do you find normal probability distributions?How do find and interpret Z scores?How do you make a meaningful point estimate and a margin of error? EngageNYMath BitsTenmarksEMathNote Packet Graphing CalculatorTeacher generated ................
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