MGSE9-12.N.Q: Quantities

MGSE9-12.N.Q.1b: Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without conversion factor provided and between English and Metric with conversion factor);

 Unit Conversions

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

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

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
 Multiplying Exponential Expressions
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Using Algebraic Expressions

MGSE9-12.A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form

MGSE9-12.A.SSE.3b: Complete the square in a quadratic expression to reveal the maximum and minimum value of the function defined by the expression.

 Quadratics in Vertex Form

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

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

MGSE9-12.A.CED: Creating Equations

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

 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

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. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

 Absolute Value Equations and Inequalities
 Circles
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Solving Equations by Graphing Each Side
 Standard Form of a Line

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

MGSE9-12.A.REI.1: Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.

 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Two-Step Equations

MGSE9-12.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 II
 Solving Equations on the Number Line
 Solving Formulas for any Variable
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

MGSE9-12.A.REI.4a: 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 ax² + bx + c = 0.

 Roots of a Quadratic

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 (limit to real number solutions).

 Modeling the Factorization of x2+bx+c
 Roots of a Quadratic

MGSE9-12.A.REI.5: Show and explain why the elimination method works to solve a system of two-variable equations.

 Solving Equations by Graphing Each Side
 Solving Linear Systems (Standard Form)

MGSE9-12.A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

 Cat and Mouse (Modeling with Linear Systems)
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)

MGSE9-12.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

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
 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 on the Number Line
 Standard Form of a Line

MGSE9-12.A.REI.12: Graph the solution set to a linear inequality in two variables.

 Linear Inequalities in Two Variables
 Systems of Linear Inequalities (Slope-intercept form)

MGSE9-12.F.IF: Interpreting Functions

MGSE9-12.F.IF.1: Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is 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

MGSE9-12.F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

 Absolute Value with Linear Functions
 Translating and Scaling Functions

MGSE9-12.F.IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence a₁=7, aₙ=a ₙ₋₁ +2; the sequence sₙ = 2(n-1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.

 Arithmetic Sequences
 Geometric Sequences

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

MGSE9-12.F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

 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

MGSE9-12.F.IF.8a: 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.

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

MGSE9-12.F.BF: Building Functions

MGSE9-12.F.BF.1a: Determine an explicit expression and the recursive process (steps for calculation) from context.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

MGSE9-12.F.BF.2: Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

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
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Translations
 Zap It! Game

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

MGSE9-12.F.LE.1b.: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

 Arithmetic Sequences
 Compound Interest
 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs
 Linear Functions

MGSE9-12.F.LE.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

 Drug Dosage
 Exponential Growth and Decay
 Half-life

MGSE9-12.F.LE.2: 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).

 Compound Interest
 Exponential Functions
 Exponential Growth and Decay
 Point-Slope Form of a Line
 Slope-Intercept Form of a Line

MGSE9-12.F.LE.5: Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a•dˣ) function in terms of context. (In the functions above, “m” and “b” are the parameters of the linear function, and “a” and “d” are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.

 Arithmetic Sequences
 Compound Interest
 Introduction to Exponential Functions

MGSE9-12.G.CO: Congruence

MGSE9-12.G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

 Circles
 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines

MGSE9-12.G.CO.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

MGSE9-12.G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

MGSE9-12.G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

MGSE9-12.G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

 Proving Triangles Congruent
 Reflections
 Rotations, Reflections, and Translations
 Translations

MGSE9-12.G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

MGSE9-12.G.SRT: Similarity, Right Triangles, and Trigonometry

MGSE9-12.G.SRT.1a: The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

 Dilations

MGSE9-12.G.SRT.1b: The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

 Dilations
 Similar Figures

MGSE9-12.G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

 Circles
 Dilations
 Similar Figures

MGSE9-12.G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

 Dilations
 Perimeters and Areas of Similar Figures
 Similarity in Right Triangles

MGSE9-12.G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

 Sine, Cosine, and Tangent Ratios

MGSE9-12.G.SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine, Cosine, and Tangent Ratios

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

MGSE9-12.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

MGSE9-12.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).

 Mean, Median, and Mode
 Reaction Time 2 (Graphs and Statistics)

MGSE9-12.S.ID.6a: Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize linear, quadratic and exponential models.

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

MGSE9-12.S.ID.6c: Using given or collected bivariate data, 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

MGSE9-12.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)

MGSE9-12.S.ID.8: Compute (using technology) and interpret the correlation coefficient “r” of a linear fit. (For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the “r” value.) After calculating the line of best fit using technology, students should be able to describe how strong the goodness of fit of the regression is, using “r”.

 Correlation

Correlation last revised: 4/4/2018

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