Algebra I
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Algebra I
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A.SSE.1Seeing Structure In ExpressionsInterpret The Structure Of ExpressionsInterpret expressions that represent a quantity in terms of its context.
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A.SSE.1.aSeeing Structure In ExpressionsInterpret The Structure Of ExpressionsInterpret parts of an expression, such as terms, factors, and coefficients.
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A.SSE.1.bSeeing Structure In ExpressionsInterpret The Structure Of ExpressionsInterpret complicated expressions by viewing one or more of their parts as a single entity.
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A.SSE.2Seeing Structure In ExpressionsInterpret The Structure Of ExpressionsUse the structure of an expression to identify ways to rewrite it.
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A.SSE.3Seeing Structure In ExpressionsWrite Expressions In Equivalent Forms To Solve ProblemsChoose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
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A.SSE.3.aSeeing Structure In ExpressionsWrite Expressions In Equivalent Forms To Solve ProblemsFactor a quadratic expression to reveal the zeros of the function it defines.
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A.APR.2Arithmetic With Polynomials And Rational ExpressionsUnderstand The Relationship Between Zeros And Factors Of PolynomialsKnow and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
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A.APR.6Arithmetic With Polynomials And Rational ExpressionsRewrite Rational ExpressionsRewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
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A.CED.1Creating EquationsCreate Equations That Describe Numbers Or RelationshipsCreate equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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A.CED.2Creating EquationsCreate Equations That Describe Numbers Or RelationshipsCreate equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
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A.CED.3Creating EquationsCreate Equations That Describe Numbers Or RelationshipsRepresent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context.
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A.CED.4Creating EquationsCreate Equations That Describe Numbers Or RelationshipsRearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
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A.REI.1Reasoning With Equations And InequalitiesUnderstand Solving Equations As A Process Of Reasoning And Explain The ReasoningExplain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
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A.REI.3Reasoning With Equations And InequalitiesSolve Equations And Inequalities In One VariableSolve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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A.REI.4Reasoning With Equations And InequalitiesSolve Equations And Inequalities In One VariableSolve quadratic equations in one variable.
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A.REI.4.bReasoning With Equations And InequalitiesSolve Equations And Inequalities In One VariableSolve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
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A.REI.10Reasoning With Equations And InequalitiesRepresent And Solve Equations And Inequalities GraphicallyUnderstand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
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F.IF.1Interpreting FunctionsUnderstand The Concept Of A Function And Use Function NotationUnderstand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
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F.IF.2Interpreting FunctionsUnderstand The Concept Of A Function And Use Function NotationUse function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
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F.IF.5Interpreting FunctionsInterpret Functions That Arise In Applications In Terms Of The ContextRelate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
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F.IF.7Interpreting FunctionsAnalyze Functions Using Different RepresentationsGraph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
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F.IF.7.aInterpreting FunctionsAnalyze Functions Using Different RepresentationsGraph linear and quadratic functions and show intercepts, maxima, and minima.
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S.ID.1Interpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On A Single Count Or Measurement VariableRepresent data with plots on the real number line (dot plots, histograms, and box plots).
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S.ID.2Interpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On A Single Count Or Measurement VariableUse statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
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S.ID.3Interpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On A Single Count Or Measurement VariableInterpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
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S.ID.4Interpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On A Single Count Or Measurement VariableUse the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
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S.ID.6Interpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On Two Categorical And Quantitative VariablesRepresent data on two quantitative variables on a scatter plot, and describe how the variables are related.
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S.ID.6.bInterpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On Two Categorical And Quantitative VariablesInformally assess the fit of a function by plotting and analyzing residuals.
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S.ID.6.cInterpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On Two Categorical And Quantitative VariablesFit a linear function for a scatter plot that suggests a linear association.
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S.ID.7Interpreting Categorical And Quantitative DataInterpret Linear ModelsInterpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
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S.ID.8Interpreting Categorical And Quantitative DataInterpret Linear ModelsCompute (using technology) and interpret the correlation coefficient of a linear fit.
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S.ID.9Interpreting Categorical And Quantitative DataInterpret Linear ModelsDistinguish between correlation and causation.
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S.IC.1Making Inferences And Justifying ConclusionsUnderstand And Evaluate Random Processes Underlying Statistical ExperimentsUnderstand statistics as a process for making inferences about population parameters based on a random sample from that population.
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S.MD.5.aUsing Probability To Make DecisionsUse Probability To Evaluate Outcomes Of DecisionsFind the expected payoff for a game of chance.
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N.Q .2QuantitiesReason Quantitatively And Use Units To Solve Problems.Define appropriate quantities for the purpose of descriptive modeling.
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N.Q .3QuantitiesReason Quantitatively And Use Units To Solve Problems.Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
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