A.FGR: Functional & Graphical Reasoning – function notation, modeling linear functions, linear vs. nonlinear comparisons

A.FGR.2: Construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. Use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs.

A.FGR.2.1: Use mathematically applicable situations algebraically and graphically to build and interpret arithmetic sequences as functions whose domain is a subset of the integers.

Arithmetic Sequences
Arithmetic and Geometric Sequences

A.FGR.2.2: Construct and interpret the graph of a linear function that models real-life phenomena and represent key characteristics of the graph using formal notation.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time Graphs
Distance-Time Graphs - Metric
Slope-Intercept Form of a Line
Standard Form of a Line

A.FGR.2.3: Relate the domain and range of a linear function to its graph and, where applicable, to the quantitative relationship it describes. Use formal interval and set notation to describe the domain and range of linear functions.

Introduction to Functions

A.FGR.2.5: Analyze the difference between linear functions and nonlinear functions by informally analyzing the graphs of various parent functions (linear, quadratic, exponential, absolute value, square root, and cube root parent curves).

Linear Functions

A.GSR: Geometric & Spatial Reasoning – distance, midpoint, slope, area, and perimeter

A.GSR.3: Solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena.

A.GSR.3.1: Solve real-life problems involving slope, parallel lines, perpendicular lines, area, and perimeter.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Circumference and Area of Circles
Distance-Time Graphs
Distance-Time Graphs - Metric
Perimeter and Area of Rectangles

A.GSR.3.2: Apply the distance formula, midpoint formula, and slope of line segments to solve real-world problems.

Distance Formula
Distance-Time Graphs
Distance-Time Graphs - Metric

A.PAR: Patterning & Algebraic Reasoning – linear inequalities and systems of linear inequalities

A.PAR.4: Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena.

A.PAR.4.1: Create and solve linear inequalities in two variables to represent relationships between quantities including mathematically applicable situations; graph inequalities on coordinate axes with labels and scales.

Linear Inequalities in Two Variables

A.PAR.4.2: Represent constraints of linear inequalities and interpret data points as possible or not possible.

Linear Inequalities in Two Variables

A.PAR.4.3: Solve systems of linear inequalities by graphing, including systems representing a mathematically applicable situation.

Systems of Linear Inequalities (Slope-intercept form)

A.NR: Numerical Reasoning – rational and irrational numbers, square roots and cube roots

A.NR.5: Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots.

A.NR.5.1: Rewrite algebraic and numeric expressions involving radicals.

Operations with Radical Expressions
Simplifying Radical Expressions

A.PAR: Patterning & Algebraic Reasoning – quadratic expressions & equations

A.PAR.6: Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations.

A.PAR.6.1: Interpret quadratic expressions and parts of a quadratic expression that represent a quantity in terms of its context.

Quadratics in Polynomial Form

A.PAR.6.2: Fluently choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the expression.

Quadratics in Polynomial Form

A.PAR.6.3: Create and solve quadratic equations in one variable and explain the solution in the framework of applicable phenomena.

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

A.FGR: Functional & Graphical Reasoning – quadratic functions

A.FGR.7: Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model.

A.FGR.7.1: Use function notation to build and evaluate quadratic functions for inputs in their domains and interpret statements that use function notation in terms of a given framework.

Quadratics in Polynomial Form

A.FGR.7.2: Identify the effect on the graph generated by a quadratic function when replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.

Quadratics in Polynomial Form
Quadratics in Vertex Form
Translating and Scaling Functions

A.FGR.7.3: Graph and analyze the key characteristics of quadratic functions.

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

A.FGR.7.4: Relate the domain and range of a quadratic function to its graph and, where applicable, to the quantitative relationship it describes.

Graphs of Polynomial Functions

A.FGR.7.5: Rewrite a quadratic function representing a mathematically applicable situation to reveal the maximum or minimum value of the function it defines. Explain what the value describes in context.

Quadratics in Polynomial Form

A.FGR.7.6: Create quadratic functions in two variables to represent relationships between quantities; graph quadratic functions on the coordinate axes with labels and scales.

Quadratics in Polynomial Form
Quadratics in Vertex Form

A.FGR.7.8: Write a function defined by a quadratic expression in different but equivalent forms to reveal and explain different properties of the function.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form

A.PAR: Patterning & Algebraic Reasoning – exponential expressions and equations

A.PAR.8: Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations.

A.PAR.8.1: Interpret exponential expressions and parts of an exponential expression that represent a quantity in terms of its framework.

Compound Interest
Exponential Growth and Decay

A.PAR.8.3: Create exponential equations in two variables to represent relationships between quantities, including in mathematically applicable situations; graph equations on coordinate axes with labels and scales.

Compound Interest
Exponential Growth and Decay

A.FGR: Functional & Graphical Reasoning – exponential functions

A.FGR.9: Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions.

A.FGR.9.1: Use function notation to build and evaluate exponential functions for inputs in their domains and interpret statements that use function notation in terms of a context.

Exponential Functions
Introduction to Exponential Functions

A.FGR.9.2: Graph and analyze the key characteristics of simple exponential functions based on mathematically applicable situations.

Exponential Functions
Exponential Growth and Decay

A.FGR.9.3: Identify the effect on the graph generated by an exponential function when replacing f(x) with f(x) + k, and kf(x), for specific values of k (both positive and negative); find the value of k given the graphs.

Exponential Functions
Introduction to Exponential Functions

A.FGR.9.4: Use mathematically applicable situations algebraically and graphically to build and interpret geometric sequences as functions whose domain is a subset of the integers.

Arithmetic and Geometric Sequences
Geometric Sequences

A.DSR: Data & Statistical Reasoning – univariate data and single quantitative variables; bivariate data

A.DSR.10: Collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve real-life problems; Represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve real-life problems.

A.DSR.10.1: Use statistics appropriate to the shape of the data distribution to compare and represent center (median and mean) and variability (interquartile range, standard deviation) of two or more distributions by hand and using technology.

Box-and-Whisker Plots
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

A.DSR.10.2: Interpret differences in shape, center, and variability of the distributions based on the investigation, accounting for possible effects of extreme data points (outliers).

Populations and Samples
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

A.DSR.10.3: Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

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

A.DSR.10.4: Interpret the slope (predicted rate of change) and the intercept (constant term) of a linear model based on the investigation of the data.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

A.DSR.10.5: Calculate the line of best fit and interpret the correlation coefficient, r, of a linear fit using technology. Use r to describe the strength of the goodness of fit of the regression. Use the linear function to make predictions and assess how reasonable the prediction is in context.

Correlation

A.DSR.10.7: Distinguish between correlation and causation.

Correlation