PRR: Polynomial, Rational, and Radical Relationships

(Framing Text): Perform arithmetic operations with complex numbers.

PRR.M.A2HS.1: Know there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b real.

 Points in the Complex Plane
 Roots of a Quadratic

(Framing Text): Use complex numbers in polynomial identities and equations.

PRR.M.A2HS.3: Solve quadratic equations with real coefficients that have complex solutions. Instructional Note: Limit to polynomials with real coefficients.

 Points in the Complex Plane
 Roots of a Quadratic

(Framing Text): Interpret the structure of expressions.

PRR.M.A2HS.6: Interpret expressions that represent a quantity in terms of its context.

PRR.M.A2HS.6.a: Interpret parts of an expression, such as terms, factors, and coefficients.

 Compound Interest
 Exponential Growth and Decay
 Unit Conversions

PRR.M.A2HS.6.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

 Compound Interest
 Exponential Growth and Decay
 Translating and Scaling Functions
 Using Algebraic Expressions

PRR.M.A2HS.7: 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

(Framing Text): Perform arithmetic operations on polynomials.

PRR.M.A2HS.9: 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.

 Addition of Polynomials

(Framing Text): Understand the relationship between zeros and factors of polynomials.

PRR.M.A2HS.10: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

 Dividing Polynomials Using Synthetic Division

PRR.M.A2HS.11: 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.

 Polynomials and Linear Factors
 Quadratics in Factored Form

(Framing Text): Use polynomial identities to solve problems.

PRR.M.A2HS.13: Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

 Binomial Probabilities

(Framing Text): Understand solving equations as a process of reasoning and explain the reasoning.

PRR.M.A2HS.16: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Instructional Note: Extend to simple rational and radical equations.

 Radical Functions

(Framing Text): Represent and solve equations and inequalities graphically.

PRR.M.A2HS.17: 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.

 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

(Framing Text): Analyze functions using different representations.

PRR.M.A2HS.18: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

 Absolute Value with Linear Functions
 Exponential Functions
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions

TF: Trigonometric Functions

(Framing Text): Model periodic phenomena with trigonometric functions.

TF.M.A2HS.21: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

 Sound Beats and Sine Waves

(Framing Text): Prove and apply trigonometric identities.

TF.M.A2HS.22: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin (θ), cos (θ), or tan (θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle.

 Simplifying Trigonometric Expressions
 Sine, Cosine, and Tangent Ratios

MF: Modeling with Functions

(Framing Text): Create equations that describe numbers or relationships.

MF.M.A2HS.23: 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

MF.M.A2HS.24: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

 2D Collisions
 Air Track
 Compound Interest
 Determining a Spring Constant
 Golf Range
 Points, Lines, and Equations
 Slope-Intercept Form of a Line

(Framing Text): Interpret functions that arise in applications in terms of a context.

MF.M.A2HS.27: 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Function Machines 3 (Functions and Problem Solving)
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Logarithmic Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Translating and Scaling Sine and Cosine Functions

MF.M.A2HS.28: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (e.g., If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.)

 Introduction to Functions
 Logarithmic Functions
 Radical Functions

MF.M.A2HS.29: 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.

 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs

(Framing Text): Analyze functions using different representations.

MF.M.A2HS.30: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

MF.M.A2HS.30.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

 Absolute Value with Linear Functions
 Radical Functions

MF.M.A2HS.30.b: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

 Cosine Function
 Exponential Functions
 Exponential Growth and Decay
 Logarithmic Functions
 Logarithmic Functions: Translating and Scaling
 Sine Function
 Tangent Function

MF.M.A2HS.32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.)

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

(Framing Text): Build a function that models a relationship between two quantities.

MF.M.A2HS.33: Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.)

 Addition and Subtraction of Functions
 Function Machines 1 (Functions and Tables)
 Points, Lines, and Equations

(Framing Text): Build new functions from existing functions.

MF.M.A2HS.34: 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. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions 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

MF.M.A2HS.35: Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. (e.g., f(x) = 2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1.)

 Function Machines 3 (Functions and Problem Solving)
 Logarithmic Functions

(Framing Text): Construct and compare linear, quadratic, and exponential models and solve problems.

MF.M.A2HS.36: For exponential models, express as a logarithm the solution to a b to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

 Logarithmic Functions

ICD: Inferences and Conclusions from Data

(Framing Text): Understand and evaluate random processes underlying statistical experiments.

ICD.M.A2HS.39: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. (e.g., A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?)

 Polling: City
 Polling: Neighborhood
 Populations and Samples

(Framing Text): Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

ICD.M.A2HS.41: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

 Estimating Population Size
 Polling: City
 Polling: Neighborhood

ICD.M.A2HS.42: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

 Real-Time Histogram
 Sight vs. Sound Reactions

(Framing Text): Use probability to evaluate outcomes of decisions.

ICD.M.A2HS.44: Use probabilities to make fair decisions (e.g., drawing by lots or using a random number generator).

 Probability Simulations
 Theoretical and Experimental Probability

ICD.M.A2HS.45: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, and/or pulling a hockey goalie at the end of a game).

 Estimating Population Size
 Probability Simulations
 Theoretical and Experimental Probability

Correlation last revised: 4/7/2017

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