 Algebra and Modeling 912.A-APR.1.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Model polynomials Add and subtract polynomials Multiply polynomials 912.A-APR.1.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Model polynomials Add and subtract polynomials Multiply polynomials 912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.Also assesses:912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Write equations Solve linear equations Write inequalities Solve inequalities Rearrange formulas Word problems 912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.Also assesses:912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Write equations Solve linear equations Write inequalities Solve inequalities Rearrange formulas Word problems 912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Also assesses:912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Slope-intercept form Standard form Point-slope form Quadratic functions Linear, quadratic, and exponential functions Absolute value functions Solutions to a system of equations Elimination Graphing a system Substitution Any method Inequalities 912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Also assesses:912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Slope-intercept form Standard form Point-slope form Quadratic functions Linear, quadratic, and exponential functions Absolute value functions Solutions to a system of equations Elimination Graphing a system Substitution Any method Inequalities 912.A-CED.1.3 Represent 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. Systems of equations Linear inequalities 912.A-CED.1.3 Represent 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. Systems of equations Linear inequalities 912.A-REI.1.1 Explain 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. 912.A-REI.1.1 Explain 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. 912.A-REI.2.4 Solve quadratic equations in one variable. Square roots Factoring Completing the square Quadratic formula 912.A-REI.2.4 Solve quadratic equations in one variable. Square roots Factoring Completing the square Quadratic formula 912.A-REI.4.11 Explain why the x-coordinates of the points 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 to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.Also assesses: 912.A-REI.4.10 Understand 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). Function tables and graphs Systems of equations 912.A-REI.4.11 Explain why the x-coordinates of the points 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 to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.Also assesses: 912.A-REI.4.10 Understand 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). Function tables and graphs Systems of equations 912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Also assesses: 912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. Linear expressions and polynomials Factoring quadratics Completing the square Monomials and polynomials Exponential expressions Rational expressions Radical expressions 912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Also assesses: 912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. Linear expressions and polynomials Factoring quadratics Completing the square Monomials and polynomials Exponential expressions Rational expressions Radical expressions
 Functions and Modeling 912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Function transformations 912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Function transformations 912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Also assesses: 912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly 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).912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Interpret functions Identify functions Independent and dependent variables Exponential functions Absolute value functions Radical functions Mixed functions 912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Also assesses: 912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly 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).912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Interpret functions Identify functions Independent and dependent variables Exponential functions Absolute value functions Radical functions Mixed functions 912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.Also assesses:912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Linear functions Exponential functions Quadratic functions Linear, quadratic, and exponential functions Absolute value functions 912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.Also assesses:912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Linear functions Exponential functions Quadratic functions Linear, quadratic, and exponential functions Absolute value functions 912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.Also assesses:912.S-ID.3.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Rate of change Constant of variation Slope Regression lines 912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.Also assesses:912.S-ID.3.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Rate of change Constant of variation Slope Regression lines 912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Also assesses:912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Linear functions Quadratic functions Exponential functions Absolute value functions 912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Also assesses:912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Linear functions Quadratic functions Exponential functions Absolute value functions 912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.Also assesses:912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context. Linear and exponential growth and decay Identify linear and exponential functions Word problems 912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.Also assesses:912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context. Linear and exponential growth and decay Identify linear and exponential functions Word problems 912.F-LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).Also assesses:912.F-BF.1.1 Write a function that describes a relationship between two quantities.912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Linear functions Function operations Write functions Sequences Recursive formulas 912.F-LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).Also assesses:912.F-BF.1.1 Write a function that describes a relationship between two quantities.912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Linear functions Function operations Write functions Sequences Recursive formulas 912.F-LE.1.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 912.F-LE.1.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
 Statistics and the Number System 912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.Also assesses: 912.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Operations with rational exponents Simplify expressions with rational exponents Operations with radical expressions Simplify radical expressions Rational and irrational numbers 912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.Also assesses: 912.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Operations with rational exponents Simplify expressions with rational exponents Operations with radical expressions Simplify radical expressions Rational and irrational numbers 912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 912.S-ID.1.2 Use 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.Also assesses:912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Measures of central tendency Quartiles Variance and deviation Box-and-whisker plots Outliers 912.S-ID.1.2 Use 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.Also assesses:912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Measures of central tendency Quartiles Variance and deviation Box-and-whisker plots Outliers 912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Find probabilities 912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Find probabilities 912.S-ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Also assesses:912.S-ID.3.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.912.S-ID.3.9 Distinguish between correlation and causation. Scatter plots Correlation coefficients Regression lines 912.S-ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.Also assesses:912.S-ID.3.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.912.S-ID.3.9 Distinguish between correlation and causation. Scatter plots Correlation coefficients Regression lines
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