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.

Rational Numbers, Opposites, and Absolute Values
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.

Addition of Polynomials

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

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic 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.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x2+bx+c

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.

Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors

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.

Arithmetic Sequences
Geometric Sequences
Solving Two-Step Equations

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

Circles
Systems of Linear Inequalities (Slope-intercept form)

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.

Linear Inequalities in Two Variables
Linear Programming
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

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

Area of Triangles
Solving Formulas for any Variable

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.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

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.

Area of Triangles
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

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.

Roots of a Quadratic

AI-A.REI.4.b: Solve quadratic equations by:

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

Roots of a Quadratic

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

Modeling the Factorization of x2+bx+c

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

Roots of a Quadratic

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

Roots of a Quadratic

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

Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

2.4.3: Solve systems of equations.

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

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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.

Absolute Value Equations and Inequalities
Circles
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Standard Form of a Line

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);

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

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

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

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.

Linear Inequalities in Two Variables
Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

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).

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Logarithmic Functions
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Standard Form of a Line

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

Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

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.

Introduction to Functions
Logarithmic Functions
Radical Functions

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

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Introduction to Exponential Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Slope
Standard Form of a Line

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.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

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

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

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.

Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

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

General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

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.

Points, Lines, and Equations

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);

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

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

Exponential Functions

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

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

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.

Compound Interest
Direct and Inverse Variation
Exponential Functions
Introduction to Exponential Functions
Slope-Intercept Form of a Line

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.

Arithmetic Sequences
Compound Interest
Direct and Inverse Variation
Linear Functions
Slope-Intercept Form of a Line

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.

Compound Interest

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

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

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

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

Arithmetic Sequences
Linear Functions
Slope-Intercept Form of a Line

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

Arithmetic Sequences
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

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.

Compound Interest
Introduction to Exponential Functions

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.

Arithmetic Sequences
Compound Interest
Introduction to Exponential Functions

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).

Box-and-Whisker Plots
Histograms
Mean, Median, and Mode

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.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

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).

Box-and-Whisker Plots
Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

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.

Histograms

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.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

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.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

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

Correlation

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

Correlation

Correlation last revised: 4/4/2018

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