Alabama Common Core

A.SSE.7: Interpret expressions that represent a quantity in terms of its context.

A.SSE.7.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Finding Factors with Area Models

A.SSE.9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.9.a: Factor a quadratic expression to reveal the zeros of the function it defines.

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

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

Quadratics in Factored Form

Roots of a Quadratic

A.SSE.9.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A.SSE.9.c: Determine a quadratic equation when given its graph or roots.

Polynomials and Linear Factors

A.SSE.9.d: Use the properties of exponents to transform expressions for exponential functions.

Exponential Functions - Activity A

Multiplying Exponential Expressions

A.APR.10: 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 - Activity A

A.CED.11: Create equations and inequalities in one variable and use them to solve problems.

Using Algebraic Equations

Using Algebraic Expressions

A.CED.12: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Linear Functions

Slope-Intercept Form of a Line - Activity A

A.CED.13: 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 Programming - Activity A

System of Two Quadratic Inequalities

Systems of Linear Inequalities (Slope-intercept form) - Activity A

A.CED.14: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

A.REI.15: Explain each step in solving a simple 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 - Activity A

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

A.REI.16: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

System of Two Quadratic Inequalities

A.REI.17: Solve quadratic equations in one variable.

A.REI.17.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x ? p)² = q that has the same solutions. Derive the quadratic formula from this form.

A.REI.17.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Factoring Special Products

Roots of a Quadratic

Square Roots

A.REI.19: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

A.REI.20: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Systems of Linear Equations - Activity A

A.REI.21: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

A.REI.22: 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.

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Function Machines 2 (Functions, Tables, and Graphs)

General Form of a Rational Function

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Quadratic and Absolute Value Functions

Rational Functions

Slope-Intercept Form of a Line - Activity B

A.REI.23: 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.

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

System of Two Quadratic Inequalities

Systems of Linear Inequalities (Slope-intercept form) - Activity A

F.IF.24: 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).

Cosine Function

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Functions Involving Square Roots

Introduction to Functions

Rational Functions

Sine Function

Tangent Function

F.IF.25: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Linear Functions

Points, Lines, and Equations

F.IF.26: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic and Geometric Sequences

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

F.IF.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.

Cosine Function

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Functions Involving Square Roots

Linear Functions

Logarithmic Functions: Translating and Scaling

Points, Lines, and Equations

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Rational Functions

Sine Function

Tangent Function

F.IF.28: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Functions Involving Square Roots

F.IF.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.

Direct Variation

Direct and Inverse Variation

Exponential Functions - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

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

F.IF.30.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Function Machines 2 (Functions, Tables, and Graphs)

Linear Functions

Point-Slope Form of a Line - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Slope-Intercept Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity B

F.IF.30.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Function Machines 2 (Functions, Tables, and Graphs)

Quadratic and Absolute Value Functions

Square Roots

F.IF.30.c: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Exponential Functions - Activity A

Function Machines 2 (Functions, Tables, and Graphs)

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Polynomials and Linear Factors

Sine Function

Tangent Function

F.IF.31: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.31.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Function Machines 2 (Functions, Tables, and Graphs)

Parabolas - Activity A

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

F.IF.31.b: Use the properties of exponents to interpret expressions for exponential functions.

Exponential Functions - Activity A

Multiplying Exponential Expressions

F.IF.32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Functions Involving Square Roots

Introduction to Functions

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Points, Lines, and Equations

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Rational Functions

Sine Function

Slope-Intercept Form of a Line - Activity A

Tangent Function

Using Algebraic Equations

Using Algebraic Expressions

F.BF.33: Write a function that describes a relationship between two quantities.

F.BF.33.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic and Geometric Sequences

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

F.BF.33.b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Polynomials

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

F.BF.34: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

F.BF.35: 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.

Translating and Scaling Functions

F.BF.36: Find inverse functions.

F.BF.36.a: 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.

Function Machines 3 (Functions and Problem Solving)

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

F.LE.37: Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.37.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Function Machines 2 (Functions, Tables, and Graphs)

Linear Functions

Point-Slope Form of a Line - Activity A

Points, Lines, and Equations

Slope-Intercept Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity B

F.LE.38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Exponential Functions - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Geometric Sequences

Linear Functions

Points, Lines, and Equations

Slope-Intercept Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity B

F.LE.39: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Function Machines 2 (Functions, Tables, and Graphs)

F.LE.40: Interpret the parameters in a linear or exponential function in terms of a context.

Exponential Functions - Activity A

Function Machines 2 (Functions, Tables, and Graphs)

Slope-Intercept Form of a Line - Activity B

S.ID.41: Represent data with plots on the real number line (dot plots, histograms, and box plots).

Box-and-Whisker Plots

Describing Data Using Statistics

Histograms

Line Plots

Populations and Samples

S.ID.42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Box-and-Whisker Plots

Line Plots

Mean, Median and Mode

Populations and Samples

Real-Time Histogram

S.ID.43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

S.ID.44: 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.

Correlation

Solving Using Trend Lines

S.ID.45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S.ID.45.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

S.ID.45.b: Informally assess the fit of a function by plotting and analyzing residuals.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

S.ID.45.c: Fit a linear function for a scatter plot that suggests a linear association.

Correlation

Lines of Best Fit Using Least Squares - Activity A

Scatter Plots - Activity A

Solving Using Trend Lines

S.ID.46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Points, Lines, and Equations

Slope-Intercept Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity B

S.ID.47: Compute (using technology) and interpret the correlation coefficient of a linear fit.

S.ID.48: Distinguish between correlation and causation.

S.CP.50: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Compound Independent Events

Compound Independent and Dependent Events

Correlation last revised: 3/17/2015

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.