MGSE9-12.N.RN: The Real Number System

1.1: Extend the properties of exponents to rational exponents.

MGSE9-12.N.RN.1: Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents.

Exponents and Power Rules

MGSE9-12.N.CN: The Complex Number System

2.1: Perform arithmetic operations with complex numbers.

MGSE9-12.N.CN.1: Understand there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 are real numbers.

Points in the Complex Plane
Roots of a Quadratic

MGSE9-12.N.CN.2: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

MGSE9-12.N.CN.3: Find the conjugate of a complex number; use the conjugate to find the quotient of complex numbers.

Points in the Complex Plane
Roots of a Quadratic

2.2: Use complex numbers in polynomial identities and equations.

MGSE9-12.N.CN.7: Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square roots, completing the square, and the quadratic formula.

Points in the Complex Plane
Roots of a Quadratic

MGSE9-12.N.CN.9: Use the Fundamental Theorem of Algebra to find all roots of a polynomial equation.

Polynomials and Linear Factors

MGSE9-12.A.SSE: Seeing Structure in Expressions

3.1: Interpret the structure of expressions

MGSE9-12.A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

MGSE9-12.A.SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients, in context.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

MGSE9-12.A.SSE.1b: Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions

MGSE9-12.A.SSE.2: Use the structure of an expression to rewrite it in different equivalent forms.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

3.2: Write expressions in equivalent forms to solve problems

MGSE9-12.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MGSE9-12.A.SSE.3c: Use the properties of exponents to transform expressions for exponential functions.

Exponents and Power Rules

MGSE9-12.A.APR: Arithmetic with Polynomials and Rational Expressions

4.1: Perform arithmetic operations on polynomials

MGSE9-12.A.APR.1: Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

4.2: Understand the relationship between zeros and factors of polynomials

MGSE9-12.A.APR.2: 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
Polynomials and Linear Factors

MGSE9-12.A.APR.3: 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.

Polynomials and Linear Factors
Quadratics in Factored Form

4.3: Use polynomial identities to solve problems

MGSE9-12.A.APR.5: Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle.

Binomial Probabilities

MGSE9-12.A.CED: Creating Equations

5.1: Create equations that describe numbers or relationships

MGSE9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions.

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

MGSE9-12.A.CED.2: Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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

MGSE9-12.A.CED.3: Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.

Linear Inequalities in Two Variables
Linear Programming
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

MGSE9-12.A.CED.4: Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

MGSE9-12.A.REI: Reasoning with Equations and Inequalities

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

MGSE9-12.A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

6.2: Solve equations and inequalities in one variable

MGSE9-12.A.REI.4: Solve quadratic equations in one variable.

MGSE9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

6.3: Represent and solve equations and inequalities graphically

MGSE9-12.A.REI.11: Using graphs, tables, or successive approximations, show that the solution to the equation 𝘧(𝘹) = g(x) is the 𝘹-value where the 𝘺 -values of 𝘧(𝘹) and 𝑔(𝘹) are the same.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Circles
Exponential Functions
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

MGSE9-12.F.IF: Interpreting Functions

7.1: Interpret functions that arise in applications in terms of the context

MGSE9-12.F.IF.4: Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Slope-Intercept Form of a Line

MGSE9-12.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions

MGSE9-12.F.IF.6: 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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

7.2: Analyze functions using different representations

MGSE9-12.F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions

MGSE9-12.F.IF.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

MGSE9-12.F.IF.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function
Rational Functions

MGSE9-12.F.IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior.

Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

MGSE9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

MGSE9-12.F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Growth and Decay

MGSE9-12.F.BF: Building Functions

8.1: Build a function that models a relationship between two quantities

MGSE9-12.F.BF.1: Write a function that describes a relationship between two quantities.

MGSE9-12.F.BF.1b: Combine standard function types using arithmetic operations in contextual situations (Adding, subtracting, and multiplying functions of different types).

Addition and Subtraction of Functions

8.2: Build new functions from existing functions

MGSE9-12.F.BF.3: 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

MGSE9-12.F.BF.4: Find inverse functions.

MGSE9-12.F.BF.4b: Verify by composition that one function is the inverse of another.

Logarithmic Functions

MGSE9-12.F.BF.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

MGSE9-12.F.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

MGSE9-12.F.LE: Linear, Quadratic, and Exponential Models

9.1: Construct and compare linear, quadratic, and exponential models and solve problems

MGSE9-12.F.LE.4: 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.

Compound Interest

MGSE9-12.S.ID: Interpreting Categorical and Quantitative Data

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

MGSE9-12.S.ID.2: 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
Describing Data Using Statistics
Real-Time Histogram
Sight vs. Sound Reactions

MGSE9-12.S.IC: Making Inferences and Justifying Conclusions

11.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

MGSE9-12.S.IC.4: 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.

Estimating Population Size
Polling: City
Polling: Neighborhood

GSE9-12.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Real-Time Histogram
Sight vs. Sound Reactions