Next Generation Learning Standards

1.1.1: Use properties of rational and irrational numbers.

AI-N.RN.3: Use properties and operations to understand the different forms of rational and irrational numbers.

AI-N.RN.3.a: Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.

Rational Numbers, Opposites, and Absolute Values

Square Roots

2.1.1: Interpret the structure of expressions.

AI-A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

AI-A.SSE.1.a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.

AI-A.SSE.1.b: Interpret expressions by viewing one or more of their parts as a single entity.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

AI-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

2.1.2: Write expressions in equivalent forms to reveal their characteristics.

AI-A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

AI-A.SSE.3.c: Use the properties of exponents to rewrite exponential expressions.

Dividing Exponential Expressions

2.2.1: Perform arithmetic operations on polynomials.

AI-A.APR.1: Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

2.2.2: Understand the relationship between zeros and factors of polynomials.

AI-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

2.3.1: Create equations that describe numbers or relationships.

AI-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.

Arithmetic Sequences

Geometric Sequences

Solving Two-Step Equations

AI-A.CED.2: Create equations and linear inequalities in two variables to represent a real-world context.

Circles

Linear Inequalities in Two Variables

Systems of Linear Inequalities (Slope-intercept form)

AI-A.CED.3: 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.

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

AI-A.CED.4: Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles

Solving Formulas for any Variable

2.4.1: Understand solving equations as a process of reasoning and explain the reasoning.

AI-A.REI.1a: Explain each step when solving a linear or quadratic equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Two-Step Equations

2.4.2: Solve equations and inequalities in one variable.

AI-A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

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 I

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

AI-A.REI.4: Solve quadratic equations in one variable.

AI-A.REI.4.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)Â˛ = q that has the same solutions. Understand that the quadratic formula is a derivative of this process.

AI-A.REI.4.b: Solve quadratic equations by:

AI-A.REI.4.b.ii: taking square roots, Recognize when the process yields no real solutions.

AI-A.REI.4.b.iii: factoring, Recognize when the process yields no real solutions.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

AI-A.REI.4.b.iv: completing the square, Recognize when the process yields no real solutions.

AI-A.REI.4.b.v: the quadratic formula, and Recognize when the process yields no real solutions.

AI-A.REI.4.b.vi: graphing. Recognize when the process yields no real solutions.

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

2.4.3: Solve systems of equations.

AI-A.REI.6a: Solve systems of linear equations in two variables both 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)

2.4.4: Represent and solve equations and inequalities graphically.

AI-A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

Absolute Value Equations and Inequalities

Circles

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Standard Form of a Line

AI-A.REI.11: Given the equations y = f(x) and y = g(x):

AI-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);

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

AI-A.REI.11.iii: interpret the solution in context.

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

AI-A.REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Inequalities in Two Variables

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

3.1.1: Understand the concept of a function and use function notation.

AI-F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Introduction to Functions

Linear Functions

Logarithmic Functions

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Standard Form of a Line

AI-F.IF.3: Recognize that a sequence is a function whose domain is a subset of the integers.

3.1.2: Interpret functions that arise in applications in terms of the context.

AI-F.IF.4: For a function that models a relationship between two quantities:

AI-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and

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

Quadratics in Vertex Form

Radical Functions

AI-F.IF.5: Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.

Introduction to Functions

Logarithmic Functions

Radical Functions

AI-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Introduction to Exponential Functions

Point-Slope Form of a Line

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Slope

Standard Form of a Line

3.1.3: Analyze functions using different representations.

AI-F.IF.7: Graph functions and show key features of the graph by hand and by using technology where appropriate.

AI-F.IF.7.a: Graph linear, quadratic, and exponential functions and show key features.

Absolute Value with Linear Functions

Addition and Subtraction of Functions

Exponential Functions

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

Translating and Scaling Functions

Zap It! Game

AI-F.IF.7.b: Graph square root and piecewise-defined functions, including step functions and absolute value functions, and show key features.

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

AI-F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.

AI-F.IF.8.a: For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Quadratics in Vertex Form

Roots of a Quadratic

AI-F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

3.2.1: Build a function that models a relationship between two quantities.

AI-F.BF.1: Write a function that describes a relationship between two quantities.

AI-F.BF.1.a: Determine a function from context. Define a sequence explicitly or steps for calculation from a context.

Arithmetic Sequences

Points, Lines, and Equations

3.2.2: Build new functions from existing functions.

AI-F.BF.3a: Using f(x) + k, k f(x), and f(x + k):

AI-F.BF.3a.i: identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative);

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

AI-F.BF.3a.ii: find the value of k given the graphs;

AI-F.BF.3a.iv: use technology to experiment with cases and explore the effects on the graph.

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

3.3.1: Construct and compare linear, quadratic, and exponential models and solve problems.

AI-F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

AI-F.LE.1.a: Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.

Compound Interest

Direct and Inverse Variation

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

Slope-Intercept Form of a Line

AI-F.LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.

Arithmetic Sequences

Compound Interest

Direct and Inverse Variation

Linear Functions

Slope-Intercept Form of a Line

AI-F.LE.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.

Compound Interest

Exponential Growth and Decay

AI-F.LE.2: Construct a linear or exponential function symbolically given:

AI-F.LE.2.i: a graph;

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Slope-Intercept Form of a Line

Standard Form of a Line

AI-F.LE.2.ii: a description of the relationship;

Arithmetic Sequences

Linear Functions

Slope-Intercept Form of a Line

AI-F.LE.2.iii: two input-output pairs (include reading these from a table).

Arithmetic Sequences

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Slope-Intercept Form of a Line

AI-F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Compound Interest

Introduction to Exponential Functions

3.3.2: Interpret expressions for functions in terms of the situation they model.

AI-F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

Arithmetic Sequences

Compound Interest

Exponential Growth and Decay

Introduction to Exponential Functions

4.1.1: Summarize, represent, and interpret data on a single count or measurement variable.

AI-S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).

Box-and-Whisker Plots

Histograms

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

AI-S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample standard deviation) of two or more different data sets.

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Sight vs. Sound Reactions

AI-S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Box-and-Whisker Plots

Describing Data Using Statistics

Least-Squares Best Fit Lines

Mean, Median, and Mode

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Stem-and-Leaf Plots

4.1.2: Summarize, represent, and interpret data on two categorical and quantitative variables.

AI-S.ID.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

AI-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variablesâ€™ values are related.

AI-S.ID.6.a: Fit a function to real-world 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

4.1.3: Interpret linear models.

AI-S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Cat and Mouse (Modeling with Linear Systems)

Correlation

Solving Using Trend Lines

Trends in Scatter Plots

AI-S.ID.8: Calculate (using technology) and interpret the correlation coefficient of a linear fit.

AI-S.ID.9: Distinguish between correlation and causation.

Correlation last revised: 1/22/2020

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