### AI-N: Number and Quantity

#### AI-N.RN: The Real Number System

1.1.1: Use properties of rational and irrational numbers.

AI-N.RN.3: Use properties and operations to understand the different forms of rational and irrational numbers.

AI-N.RN.3.a: Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.

### AI-A: Algebra

#### AI-A.SSE: Seeing Structure in Expressions

2.1.1: Interpret the structure of expressions.

AI-A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

AI-A.SSE.1.a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.

AI-A.SSE.1.b: Interpret expressions by viewing one or more of their parts as a single entity.

AI-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it.

2.1.2: Write expressions in equivalent forms to reveal their characteristics.

AI-A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

AI-A.SSE.3.c: Use the properties of exponents to rewrite exponential expressions.

#### AI-A.APR: Arithmetic with Polynomials and Rational Expressions

2.2.1: Perform arithmetic operations on polynomials.

AI-A.APR.1: Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.

2.2.2: Understand the relationship between zeros and factors of polynomials.

AI-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.

#### AI-A.CED: Creating Equations

2.3.1: Create equations that describe numbers or relationships.

AI-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.

AI-A.CED.2: Create equations and linear inequalities in two variables to represent a real-world context.

AI-A.CED.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.

AI-A.CED.4: Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

#### AI-A.REI: Reasoning with Equations and Inequalities

2.4.1: Understand solving equations as a process of reasoning and explain the reasoning.

AI-A.REI.1a: Explain each step when solving a linear or quadratic 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.

2.4.2: Solve equations and inequalities in one variable.

AI-A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

AI-A.REI.4: Solve quadratic equations in one variable.

AI-A.REI.4.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Understand that the quadratic formula is a derivative of this process.

AI-A.REI.4.b.i: inspection, Recognize when the process yields no real solutions.

AI-A.REI.4.b.ii: taking square roots, Recognize when the process yields no real solutions.

AI-A.REI.4.b.iii: factoring, Recognize when the process yields no real solutions.

AI-A.REI.4.b.iv: completing the square, Recognize when the process yields no real solutions.

AI-A.REI.4.b.v: the quadratic formula, and Recognize when the process yields no real solutions.

AI-A.REI.4.b.vi: graphing. Recognize when the process yields no real solutions.

2.4.3: Solve systems of equations.

AI-A.REI.6a: Solve systems of linear equations in two variables both algebraically and graphically.

2.4.4: Represent and solve equations and inequalities graphically.

AI-A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

AI-A.REI.11: Given the equations y = f(x) and y = g(x):

AI-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);

AI-A.REI.11.ii: find the solutions approximately using technology to graph the functions or make tables of values; and

AI-A.REI.11.iii: interpret the solution in context.

AI-A.REI.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.

### AI-F: Functions

#### AI-F.IF: Interpreting Functions

3.1.1: Understand the concept of a function and use function notation.

AI-F.IF.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).

AI-F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

AI-F.IF.3: Recognize that a sequence is a function whose domain is a subset of the integers.

3.1.2: Interpret functions that arise in applications in terms of the context.

AI-F.IF.4: For a function that models a relationship between two quantities:

AI-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and

AI-F.IF.4.ii: sketch graphs showing key features given a verbal description of the relationship.

AI-F.IF.5: Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.

AI-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.

3.1.3: Analyze functions using different representations.

AI-F.IF.7: Graph functions and show key features of the graph by hand and by using technology where appropriate.

AI-F.IF.7.a: Graph linear, quadratic, and exponential functions and show key features.

AI-F.IF.7.b: Graph square root and piecewise-defined functions, including step functions and absolute value functions, and show key features.

AI-F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.

AI-F.IF.8.a: For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.

AI-F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### AI-F.BF: Building Functions

3.2.1: Build a function that models a relationship between two quantities.

AI-F.BF.1: Write a function that describes a relationship between two quantities.

AI-F.BF.1.a: Determine a function from context. Define a sequence explicitly or steps for calculation from a context.

3.2.2: Build new functions from existing functions.

AI-F.BF.3a: Using f(x) + k, k f(x), and f(x + k):

AI-F.BF.3a.i: identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative);

AI-F.BF.3a.ii: find the value of k given the graphs;

AI-F.BF.3a.iii: write a new function using the value of ??; and

AI-F.BF.3a.iv: use technology to experiment with cases and explore the effects on the graph.

#### AI-F.LE: Linear, Quadratic, and Exponential Models

3.3.1: Construct and compare linear, quadratic, and exponential models and solve problems.

AI-F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

AI-F.LE.1.a: Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.

AI-F.LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.

AI-F.LE.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.

AI-F.LE.2: Construct a linear or exponential function symbolically given:

AI-F.LE.2.i: a graph;

AI-F.LE.2.ii: a description of the relationship;

AI-F.LE.2.iii: two input-output pairs (include reading these from a table).

AI-F.LE.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.

3.3.2: Interpret expressions for functions in terms of the situation they model.

AI-F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

### AI-S: Statistics and Probability

#### AI-S.ID: Interpreting Categorical and Quantitative Data

4.1.1: Summarize, represent, and interpret data on a single count or measurement variable.

AI-S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).

AI-S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample standard deviation) of two or more different data sets.

AI-S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

4.1.2: Summarize, represent, and interpret data on two categorical and quantitative variables.

AI-S.ID.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.

AI-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variables’ values are related.

AI-S.ID.6.a: Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.

4.1.3: Interpret linear models.

AI-S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

AI-S.ID.8: Calculate (using technology) and interpret the correlation coefficient of a linear fit.

AI-S.ID.9: Distinguish between correlation and causation.

Correlation last revised: 9/15/2020

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