Alabama Common Core
N.CN.1: Know there is a complex number i such that i² = ?1, and every complex number has the form a + bi with a and b real.
Points in the Complex Plane - Activity A
N.CN.4: Extend polynomial identities to the complex numbers.
Modeling the Factorization of x2+bx+c
Points in the Complex Plane - Activity A
A.SSE.6: Interpret expressions that represent a quantity in terms of its context.
A.SSE.6.a: Interpret parts of an expression, such as terms, factors, and coefficients.
Finding Factors with Area Models
A.APR.9: 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.APR.10: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x ? a is p(a), so p(a) = 0 if and only if (x ? a) is a factor of p(x).
Dividing Polynomials Using Synthetic Division
A.APR.11: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
A.CED.16: Create equations and inequalities in one variable and use them to solve problems.
Using Algebraic Equations
Using Algebraic Expressions
A.CED.17: 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.18: 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.19: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Solving Formulas for any Variable
A.REI.21: 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
F.IF.22: 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.23: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Functions Involving Square Roots
F.IF.24: 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.25: 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.25.a: 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.25.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Polynomials and Linear Factors
F.IF.25.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.27: 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.28: Write a function that describes a relationship between two quantities.
F.BF.28.a: 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.29: 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.30: 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.TF.33: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
Cosine Function
Sine Function
Tangent Function
Unit Circle
F.TF.34: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
F.TF.35: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Cosine Function
Sine Function
Tangent Function
F.TF.36: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.
Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
S.ID.37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
S.IC.38: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Polling: City
Polling: Neighborhood
S.IC.40: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
S.IC.41: 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.
Polling: Neighborhood
Probability Simulations
S.IC.42: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Populations and Samples
Probability Simulations
S.IC.43: Evaluate reports based on data.
S.MD.44: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Probability Simulations
Theoretical and Experimental Probability
S.MD.45: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Correlation last revised: 3/17/2015