1 1st Nine Weeks Topic I - Quantities and Modeling 912.A-SSE.1: Interpret the structure of expressions 912.A-SSE.1: Interpret the structure of expressions 912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context. 912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context. 912.A-SSE.1.1.a: Interpret parts of an expression, such as terms, factors, and coefficients. 912.A-SSE.1.1.a: Interpret parts of an expression, such as terms, factors, and coefficients. 912.A-CED.1: Create equations that describe numbers or relationships 912.A-CED.1: Create equations that describe numbers or relationships 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. Linear equations Inequalities 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. Linear equations Inequalities Word problems 912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 912.A-REI.1: Understand solving equations as a process of reasoning and explain the reasoning 912.A-REI.1: Understand solving equations as a process of reasoning and explain the reasoning 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: Solve equations and inequalities in one variable 912.A-REI.2: Solve equations and inequalities in one variable 912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Linear equations Linear inequalities Compound inequalities 912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Linear equations Linear inequalities Compound inequalities 912.N-Q.1: Reason quantitatively and use units to solve problems. 912.N-Q.1: Reason quantitatively and use units to solve problems. 912.N-Q.1.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. 912.N-Q.1.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. 912.N-Q.1.2: Define appropriate quantities for the purpose of descriptive modeling. 912.N-Q.1.2: Define appropriate quantities for the purpose of descriptive modeling. 912.N-Q.1.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Precision Greatest possible error Percent error 912.N-Q.1.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Precision Greatest possible error Percent error Topic II - Understanding Functions 912.F-BF.1: Build a function that models a relationship between two quantities 912.F-BF.1: Build a function that models a relationship between two quantities 912.F-BF.1.1: Write a function that describes a relationship between two quantities. 912.F-BF.1.1: Write a function that describes a relationship between two quantities. 912.F-BF.1.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context. Sequences Linear functions 912.F-BF.1.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context. Sequences Linear functions 912.F-IF.1: Understand the concept of a function and use function notation 912.F-IF.1: Understand the concept of a function and use function notation 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). Independent and dependent variables Identify functions Domain and range 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). Independent and dependent variables Identify functions Domain and range 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. Evaluate a function Interpret function notation Tables and graphs 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. Evaluate a function Interpret function notation Tables and graphs 912.F-IF.1.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Mixed sequences Arithmetic sequences Geometric sequences Recursive formulas Explicit and recursive sequences 912.F-IF.1.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Mixed sequences Arithmetic sequences Geometric sequences Recursive formulas Explicit and recursive sequences 912.F-IF.2: Interpret functions that arise in applications in terms of the context 912.F-IF.2: Interpret functions that arise in applications in terms of the context 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. Proportional relationships Linear functions Word problems 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. Proportional relationships Linear functions Word problems 912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Topic III - Linear Functions, Equations, and Inequalities - Part A 912.F-BF.2: Build new functions from existing functions 912.F-BF.2: Build new functions from existing functions 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. Linear functions Absolute value functions 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. Linear functions Absolute value functions 912.F-LE.1: Construct and compare linear, quadratic, and exponential models and solve problems 912.F-LE.1: Construct and compare linear, quadratic, and exponential models and solve problems 912.F-LE.1.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. 912.F-LE.1.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. 912.F-LE.1.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 912.F-LE.1.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 912.F-LE.1.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 912.F-LE.1.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 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). Slope-intercept form Point-slope form 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). Slope-intercept form Point-slope form 912.F-LE.2: Interpret expressions for functions in terms of the situation they model 912.F-LE.2: Interpret expressions for functions in terms of the situation they model 912.F-LE.2.5: Interpret the parameters in a linear or exponential function in terms of a context. 912.F-LE.2.5: Interpret the parameters in a linear or exponential function in terms of a context. 912.F-IF.2: Interpret functions that arise in applications in terms of the context 912.F-IF.2: Interpret functions that arise in applications in terms of the context 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. Rate of change Constant of variation Slope 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. Rate of change Constant of variation Slope 912.F-IF.3: Analyze functions using different representations 912.F-IF.3: Analyze functions using different representations 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. 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. 912.F-IF.3.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima. 912.F-IF.3.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima. 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). 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). 912.A-CED.1: Create equations that describe numbers or relationships 912.A-CED.1: Create equations that describe numbers or relationships 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. 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. 912.A-REI.4: Represent and solve equations and inequalities graphically 912.A-REI.4: Represent and solve equations and inequalities graphically 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). 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).
 2 2nd Nine Weeks Topic IV - Linear Functions, Equations, and Inequalities - Part B 912.A-CED.1: Create equations that describe numbers or relationships 912.A-CED.1: Create equations that describe numbers or relationships 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. 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. 912.A-REI.4: Represent and solve equations and inequalities graphically 912.A-REI.4: Represent and solve equations and inequalities graphically 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. 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. 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. 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. 912.S-ID.3: Interpret linear models 912.S-ID.3: Interpret linear models 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. 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. Topic V - Statistical Models 912.S-ID.1: Summarize, represent, and interpret data on a single count or measurement variable 912.S-ID.1: Summarize, represent, and interpret data on a single count or measurement variable 912.S-ID.1.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). Line plots Histograms Box plots 912.S-ID.1.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). Line plots Histograms 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. 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. 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). 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). 912.S-ID.2: Summarize, represent, and interpret data on two categorical and quantitative variables 912.S-ID.2: Summarize, represent, and interpret data on two categorical and quantitative variables 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. 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. 912.S-ID.2.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 912.S-ID.2.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 912.S-ID.2.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. 912.S-ID.2.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. 912.S-ID.2.6.b: Informally assess the fit of a function by plotting and analyzing residuals. 912.S-ID.2.6.b: Informally assess the fit of a function by plotting and analyzing residuals. 912.S-ID.2.6.c: Fit a linear function for a scatter plot that suggests a linear association. 912.S-ID.2.6.c: Fit a linear function for a scatter plot that suggests a linear association. 912.S-ID.3: Interpret linear models 912.S-ID.3: Interpret linear models 912.S-ID.3.8: Compute (using technology) and interpret the correlation coefficient of a linear fit. 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. 912.S-ID.3.9: Distinguish between correlation and causation. Topic VI - Linear Systems 912.A-CED.1: Create equations that describe numbers or relationships 912.A-CED.1: Create equations that describe numbers or relationships 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. 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. 912.A-REI.3: Solve systems of equations 912.A-REI.3: Solve systems of equations 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.3.5: 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. Understand solutions Solve systems 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. Understand solutions Solve systems 912.A-REI.4: Represent and solve equations and inequalities graphically 912.A-REI.4: Represent and solve equations and inequalities graphically 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. 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. Topic VII - Exponential Relationships - Part A 912.N-RN.1: Extend the properties of exponents to rational exponents. 912.N-RN.1: Extend the properties of exponents to rational exponents. 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. 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. 912.N-RN.1.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Rational exponents Radical expressions 912.N-RN.1.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Rational exponents Radical expressions 912.N-RN.2: Use properties of rational and irrational numbers. 912.N-RN.2: Use properties of rational and irrational numbers. 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.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.