AA.DSP: Data Analysis, Statistics, and Probability

AA.DSP.1: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization and possible sources of bias relate to each.

Estimating Population Size
Polling: City
Polling: Neighborhood
Populations and Samples
Sight vs. Sound Reactions
Time Estimation

AA.DSP.2: Choose, create, and critique, with technology, mathematical models (linear, quadratic and exponential) for bivariate data sets. Use the models to interpolate and/or extrapolate, to answer questions, and to draw conclusions or make decisions, addressing limitations and long-term ramifications. Recognize when a change in model is needed. Interpret the correlation coefficient for linear models.

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

AA.DSP.3: Read, interpret, and make decisions about data summarized numerically using measures of center and spread, in tables, and in graphical displays (line graphs, bar graphs, scatterplots, and histograms), e.g., explain why the mean may not represent a typical salary; critique a graphical display by recognizing that the choice of scale can distort information.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Mean, Median, and Mode
Polling: City
Populations and Samples
Stem-and-Leaf Plots
Trends in Scatter Plots

AA.DSP.4: Analyze and compare univariate data of two or more different data sets using measures of center (mean, median, and mode), shape, and spread (range, interquartile range, standard deviation, percentiles, and variance) making use of technology. Understand the effects of outliers on the statistical summary of the data.

Box-and-Whisker Plots

AA.DSP.5: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models.

Lucky Duck (Expected Value)

AA.DSP.6: Evaluate the validity of claims based on empirical probabilities and theoretical probabilities, including those derived from dependent and independent events. Draw conclusions and make decisions in various probabilistic contexts. Make use of different representations of data including two-way tables and tree diagrams.

Independent and Dependent Events
Lucky Duck (Expected Value)
Spin the Big Wheel! (Probability)

AA.DSP.7: Determine the nature and number of elements in a finite sample space to model the outcomes of real-world events using the Fundamental Counting Principle, permutations, and combinations.

Permutations and Combinations

AA.LF: Linear Functions and Beyond

AA.LF.1: Model real-world situations involving arithmetic sequences and understand that they can be defined both recursively and with an explicit formula.

Arithmetic Sequences

AA.LF.3: Recognize functional relationships in real world contexts. Translate fluently among multiple representations (graphs, tables, equations, and verbal descriptions).

Absolute Value Equations and Inequalities
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Logarithmic Functions: Translating and Scaling
Quadratics in Polynomial Form
Roots of a Quadratic
Sine Function

AA.LF.5: Explore and describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, k f(x), f(kx), or f(x + k).

Absolute Value with Linear Functions
Exponential Functions
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Zap It! Game

AA.LF.7: Represent real-world problems using a system of linear equations and/or inequalities in two or three variables. Solve such systems graphically or with matrices, as appropriate to the system, with technology. Interpret the solution and determine whether it is reasonable.

Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

AA.QP: Quadratic and Other Polynomial Functions

AA.QP.1: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with technology. Interpret the solutions and determine whether they are reasonable.

Quadratics in Polynomial Form
Roots of a Quadratic

AA.QP.2: Understand that different forms of a quadratic equation can provide different information. Identify and interpret within a given context the vertex, intercepts, zeros, domain and range, and lines of symmetry.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

AA.QP.3: Represent real-world problems that can be modeled with polynomial functions using graphs and equations. Solve such problems with technology. Interpret the solutions and determine whether they are reasonable.

Graphs of Polynomial Functions
Polynomials and Linear Factors

AA.QP.4: Graph polynomial functions that model a real-world situation with technology. Identify, describe, and interpret key features in the context of the situation, such as intercepts, zeros, domain and range, end behavior, maxima and minima, and lines of symmetry.

Graphs of Polynomial Functions
Polynomials and Linear Factors

AA.EL: Exponential and Logarithmic Functions

AA.EL.1: Model real-world situations involving geometric sequences and understand that they can be defined both recursively and with an explicit formula.

Geometric Sequences

AA.EL.3: Represent real-world problems using exponential functions in one or two variables and solve such problems with technology. Interpret the solutions and determine whether they are reasonable.

Compound Interest
Exponential Functions
Exponential Growth and Decay

AA.EL.4: Graph exponential functions that model real-world situations with technology. Identify, describe, and interpret key features, such as intercepts, zeros, domain, range, asymptotic and end behavior.

Compound Interest
Exponential Functions
Exponential Growth and Decay

AA.EL.5: Given real-world contexts, identify the percent rate of change in exponential functions. Classify them as representing exponential growth or decay.

Compound Interest
Exponential Growth and Decay

AA.EL.6: Analyze growth and decay using absolute and relative change and make comparisons using absolute and relative difference.

Exponential Growth and Decay

AA.EL.7: Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions that model real-world situations using graphing technology and describe their inverse relationship. Use the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable.

Logarithmic Functions

AA.R: Rational, Radical, and Other Functions

AA.R.1: Represent and solve real-world problems that can be modeled with rational functions using tables, graphs, and equations. Graph rational functions with technology. Identify, describe, and interpret features, such as intercepts, zeros, asymptotes, domain and range, and end behavior.

General Form of a Rational Function
Rational Functions

AA.R.2: Represent and solve real-world problems that can be modeled with radical functions using tables, graphs, and equations. Graph radical functions with technology. Identify, describe, and interpret features, such as intercepts, zeros, asymptotes, domain and range, and end behavior.

Radical Functions

AA.R.3: Graph real-world functions including polynomial, rational, square root, step functions, absolute value functions, and piecewise-defined functions with technology. Identify and describe features, such as intercepts, domain and range, end behavior, asymptotic behavior, and/or lines of symmetry.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
General Form of a Rational Function
Radical Functions
Rational Functions
Translating and Scaling Functions