M3.A: Algebra

M3.A.SSE: Seeing Structure in Expressions

M3.A.SSE.A: Interpret the structure of expressions.

M3.A.SSE.A.1: 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

M3.A.APR: Arithmetic with Polynomials and Rational Expressions

M3.A.APR.A: Understand the relationship between zeros and factors of polynomials.

M3.A.APR.A.1: 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

M3.A.APR.A.2: 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.

Graphs of Polynomial Functions
Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

M3.A.APR.B: Use polynomial identities to solve problems.

M3.A.APR.B.3: Know and use polynomial identities to describe numerical relationships.

Factoring Special Products

M3.A.CED: Creating Equations

M3.A.CED.A: Create equations that describe numbers or relationships.

M3.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

M3.A.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.

Absolute Value Equations and Inequalities
Circles
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

M3.A.CED.A.3: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

M3.A.REI: Reasoning with Equations and Inequalities

M3.A.REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

M3.A.REI.A.1: Explain each step in solving an 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 Equations on the Number Line
Solving Two-Step Equations

M3.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.

Radical Functions

M3.A.REI.B: Represent and solve equations graphically.

M3.A.REI.B.3: 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 approximate solutions using technology.

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

M3.F: Functions

M3.F.IF: Interpreting Functions

M3.F.IF.A: Interpret functions that arise in applications in terms of the context.

M3.F.IF.A.1: 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.

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

M3.F.IF.A.2: 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.

Cat and Mouse (Modeling with Linear Systems)
Slope

M3.F.IF.B: Analyze functions using different representations.

M3.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.

M3.F.IF.B.3.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Zap It! Game

M3.F.IF.B.3.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

M3.F.IF.B.4: 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

M3.F.BF: Building Functions

M3.F.BF.A: Build new functions from existing functions.

M3.F.BF.A.1: 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.

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

M3.F.BF.A.2: Find inverse functions.

M3.F.BF.A.2.a: Find the inverse of a function when the given function is one-to-one.

Logarithmic Functions

M3.F.LE: Linear, Quadratic, and Exponential Models

M3.F.LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.

M3.F.LE.A.1: 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

M3.F.LE.A.2: For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Logarithmic Functions

M3.F.TF: Trigonometric Functions

M3.F.TF.A: Extend the domain of trigonometric functions using the unit circle.

M3.F.TF.A.1: Understand and use radian measure of an angle.

M3.F.TF.A.1.b: Use the unit circle to find sin theta, cos theta, and tan theta when theta is a commonly recognized angle between 0 and 2pi.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

M3.F.TF.A.2: 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

M3.F.TF.B: Prove and apply trigonometric identities.

M3.F.TF.B.3: Know and use trigonometric identities to find values of trig functions.

M3.F.TF.B.3.b: Given the quadrant of the angle, use the identity sin² theta + cos² theta = 1 to find sin theta given cos theta, or vice versa.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios

M3.G: Geometry

M3.G.CO: Congruence

M3.G.CO.A: Make geometric constructions.

M3.G.CO.A.1: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

M3.G.C: Circles

M3.G.C.A: Understand and apply theorems about circles.

M3.G.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.

Chords and Arcs
Circumference and Area of Circles
Inscribed Angles

M3.G.C.A.3: Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context.

Concurrent Lines, Medians, and Altitudes

M3.G.GPE: Expressing Geometric Properties with Equations

M3.G.GPE.A: Translate between the geometric description and the equation for a circle.

M3.G.GPE.A.1: Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

Circles

M3.S: Statistics and Probability

M3.S.ID: Interpreting Categorical and Quantitative Data

M3.S.ID.A: Summarize, represent, and interpret data on a single count or measurement variable.

M3.S.ID.A.1: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.

Polling: City
Populations and Samples
Real-Time Histogram

M3.S.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

M3.S.ID.B.2: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

M3.S.ID.B.2.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

M3.S.ID.B.2.b: Fit a linear function for a scatter plot that suggests a linear association.

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

M3.S.IC: Making Inferences and Justifying Conclusions

M3.S.IC.A: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

M3.S.IC.A.1: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City
Polling: Neighborhood

M3.S.IC.A.2: Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.

Polling: City

Correlation last revised: 9/24/2019

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