FR: Functional Relationships

FR.1.BTAII: Interpret the structure of expressions, write expressions in equivalent forms to solve problems, perform arithmetic operations on functions, and understand the relationship between zeros and factors of polynomials.

FR.1.BTAII.1: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.

 Compound Interest
 Operations with Radical Expressions
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

FR.1.BTAII.2: Use the structure of an expression to identify ways to rewrite it.

 Equivalent Algebraic Expressions II
 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Solving Algebraic Equations II

FR.1.BTAII.3: Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.

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

FR.1.BTAII.4: Use various methods to factor quadratic polynomials; understand the relationship between the factored form of a quadratic polynomial and the zeros of a function.

 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form

FR.1.BTAII.5: Identify zeros of polynomials (linear, quadratic) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.

 Graphs of Polynomial Functions
 Modeling the Factorization of x2+bx+c
 Polynomials and Linear Factors
 Quadratics in Factored Form

FR.1.BTAII.6: Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.

 Absolute Value Equations and Inequalities
 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

FR.1.BTAII.7: Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.

 Solving Equations by Graphing Each Side
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

FR.1.BTAII.8: In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.

 Arithmetic Sequences
 Cat and Mouse (Modeling with Linear Systems)
 Compound Interest
 Introduction to Exponential Functions

RF: Representing Functions

RF.2.BTAII: Represent and solve equations and inequalities graphically and analyze functions using different representations.

RF.2.BTAII.1: 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 by using technology to graph the functions, making tables of values, finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are linear, polynomial, absolute value, exponential.

 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

RF.2.BTAII.2: Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Standard Form of a Line
 Translating and Scaling Functions
 Zap It! Game

RF.2.BTAII.5: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.

 Compound Interest
 Introduction to Exponential Functions

RF.2.BTAII.6: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Simplifying Algebraic Expressions II

RF.2.BTAII.7: Solve quadratic equations in one variable. 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. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring.

 Modeling the Factorization of x2+bx+c
 Roots of a Quadratic

RF.2.BTAII.8: Solve systems of equations consisting of linear equations and nonlinear equations in two variables 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)

FM: Function Modeling

FM.3.BTAII: Create equations that describe numbers or relationships, interpret functions that arise in applications in terms of a context, analyze functions using different representations, build a function that models a relationship between two quantities, and build new functions from existing functions.

FM.3.BTAII.1: Create equations and inequalities in one variable and use them to solve problems.

 Absolute Value Equations and Inequalities
 Arithmetic Sequences
 Compound Interest
 Exploring Linear Inequalities in One Variable
 Exponential Growth and Decay
 Geometric Sequences
 Modeling and Solving Two-Step Equations
 Quadratic Inequalities
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

FM.3.BTAII.2: Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.

 Absolute Value Equations and Inequalities
 Circles
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Solving Equations on the Number Line
 Standard Form of a Line
 Using Algebraic Equations

FM.3.BTAII.3: Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.

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

FM.3.BTAII.4: Rearrange literal equations using the properties of equality.

 Solving Formulas for any Variable

FM.3.BTAII.5: 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.

 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
 Radical Functions

FM.3.BTAII.6: Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes.

 Introduction to Functions
 Logarithmic Functions
 Radical Functions

FM.3.BTAII.7: Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.

 Cat and Mouse (Modeling with Linear Systems)
 Slope

FM.3.BTAII.8: Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.

 Absolute Value with Linear Functions
 Radical Functions
 Translating and Scaling Functions

FM.3.BTAII.9: Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context.

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

FM.3.BTAII.11: Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences
 Points, Lines, and Equations

FM.3.BTAII.12: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); Find the value of 𝑘 given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic representations for them.

 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

FM.3.BTAII.16: Solve linear inequalities and systems of linear inequalities in two variables by graphing.

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

FM.3.BTAII.17: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [e.g. The Fibonacci sequence is defined recursively by 𝘧(0) = 𝘧(1) = 1, 𝘧(𝘯+1) = 𝘧(𝘯) + 𝘧(𝘯-1) for 𝘯 ≥ 1.]

 Arithmetic Sequences
 Geometric Sequences

FM.3.BTAII.18: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

 Drug Dosage
 Exponential Growth and Decay
 Half-life

FM.3.BTAII.19: Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

 Absolute Value with Linear Functions
 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Compound Interest
 Exponential Functions
 Geometric Sequences
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

FM.3.BTAII.20: Use the properties of exponents to transform expressions for exponential functions.

 Exponents and Power Rules

SP: Statistics and Probability

SP.4.BTAII: Summarize, represent, and interpret data on a single count or a measurement variable and use probability to evaluate outcomes of decisions.

SP.4.BTAII.1: 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.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Real-Time Histogram
 Sight vs. Sound Reactions

SP.4.BTAII.2: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the 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
 Zap It! Game

SP.4.BTAII.3: Compute (using technology) and interpret the correlation coefficient of a linear fit.

 Correlation

Correlation last revised: 9/8/2017

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