ICD: Inferences and Conclusions from Data

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

ICD.M.3HS.4: Recognize the purposes of and differences among sample surveys, experiments and observational studies; explain how randomization relates to each.

Polling: City
Polling: Neighborhood

ICD.M.3HS.5: 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.3HS.6: 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.3HS.8: Use probabilities to make fair decisions (e.g., drawing by lots or using a random number generator).

Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

ICD.M.3HS.9: 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

PRR: Polynomials, Rational, and Radical Relationships

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

PRR.M.3HS.18: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x ²+ y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples.

Factoring Special Products

PRR.M.3HS.19: 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): Represent and solve equations and inequalities graphically.

PRR.M.3HS.23: 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.

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.3HS.24: 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
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Roots of a Quadratic
Zap It! Game

MM: Mathematical Modeling

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

MM.M.3HS.31: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Exponential Functions
General Form of a Rational Function
Geometric Sequences
Introduction to Exponential Functions
Linear Functions
Linear Inequalities in Two Variables
Logarithmic Functions
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Translating and Scaling Functions
Using Algebraic Equations

MM.M.3HS.32: 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

MM.M.3HS.33: 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.)

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

MM.M.3HS.34: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.)

Area of Triangles
Solving Formulas for any Variable

(Framing Text): Analyze functions using different representations.

MM.M.3HS.38: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

MM.M.3HS.38.a: Graph square root, cube root and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

MM.M.3HS.38.b: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline and amplitude.

Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

MM.M.3HS.40: 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
Quadratics in Vertex Form